All Questions +0 230459 Questions

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$. When twelve more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes $2:1$. How read more ..

bader 2 hours ago

0

1

0

+1465

Algebra

bader 2 hours ago

0

1

+38

Please help! Thank you

Babette is thinking of a monic quadratic polynomial with real coefficients. She tells you that when she squares the roots of her quadratic, to form another monic quadratic with those squares as its roots, surprisingly, it is the same as the original. How read more ..

The vertices of a triangle are the points of intersection of the line y=-x-1, the line x=2, and the line y=2. Find the center of the circle passing through all three vertices. Enter the coordinates as an ordered pair.

greenplanet2050 3 hours ago

0

1

2

+38

Please Help! Geometry

Find the ordered triple $(p,q,r)$ that satisfies the following system:
p - 2q &= 3 - 4p + 7q, \\
q - 2r &= -2 - 5q, \\
p + r &= 9 + 10q.

greenplanet2050 3 hours ago

0

1

0

+1465

Algebra

bader 5 hours ago

0

1

+1465

Algebra

A bag contains yellow, green, blue, and white marbles. The ratio of yellow, green, blue, white marbles is $4:1:2:3$. If the bag contains $20$ marbles, then how many blue marbles are there?

Real numbers a and b satisfy
a + ab^2 = 250ab + ab^3
a - ab^2 = 240ab - 50b^2
Enter all possible values of a, separated by commas.

bader 5 hours ago

0

1

0

+1465

Algebra

bader 7 hours ago

0

1

0

+1465

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

bader Apr 19, 2024, 4:46:15 AM

0

1

0

+1465

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

bader Apr 19, 2024, 4:46:03 AM

0

1

0

+1465

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

bader Apr 19, 2024, 4:45:52 AM

0

1

0

+1465

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

bader Apr 19, 2024, 4:45:40 AM

0

1

0

+655

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

ABJeIIy Apr 19, 2024, 3:56:01 AM

0

1

0

+655

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

ABJeIIy Apr 19, 2024, 2:55:58 AM

0

1

+9

answer pls

y=ax^2+bx+c is graphed as a parabola
The parabola is graphed below. Find a+b+c. (The grid lines are one unit apart.)
a+b+c=

The graph of y=f(x) is shown in red below. Find f(-2).

gaberiellz Apr 19, 2024, 2:26:37 AM

0

1

0

+1465

Algebra

bader Apr 19, 2024, 1:45:15 AM

0

1

0

+1465

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

bader Apr 19, 2024, 1:44:34 AM

0

1

0

+1465

Probability

Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 3 orange balls and 2 purple read more ..

bader Apr 19, 2024, 1:44:20 AM

0

2

0

+8

Geometry Problems

difficult questions!
1.

2.
<#> 3.<#> read more ..

wendigo Apr 19, 2024, 12:15 AM

0

1

0

+593

Algebra

The function $f(x,y)$ gives an ordered pair as output. It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, read more ..

LiIIiam0216 Apr 18, 2024, 10:30 PM

0

1

0

+593

Algebra

Find all real numbers $x$ such that $f(x) = f(f(x))$, where $f(x) = x^2 - 3x + x^3 - 7x^2 + 5x.$

LiIIiam0216 Apr 18, 2024, 10:30 PM

0

1

+593

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

LiIIiam0216 Apr 18, 2024, 10:30 PM

0

1

0

+593

Algebra

LiIIiam0216 Apr 18, 2024, 10:29 PM

0

1

+593

Probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probablility that all three pieces are shorter than 2 units?

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

LiIIiam0216 Apr 18, 2024

0

2

1

+593

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

LiIIiam0216 Apr 18, 2024

0

1

0

+593

Geometry

LiIIiam0216 Apr 18, 2024

0

1

0

+854

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

Akhain1 Apr 18, 2024

0

1

+854

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

Akhain1 Apr 18, 2024

0

1

+854

Geometry

Find the number of ordered pairs of integers such that

Akhain1 Apr 18, 2024

0

1

+80

PLS HELP ASAP

Our badminton team has finished $60\%$ of its season. So far, we have won $40\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

Lilliam0216 Apr 18, 2024

0

1

+1465

Algebra

Three adults and three children are to be seated at a circular table. In how many different ways can they be seated if each child must be next to at least one adult? (Two seatings are considered the same if one can be rotated to form the read more ..

bader Apr 18, 2024

0

1

+1465

Counting

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

bader Apr 18, 2024

0

1

+1465

Counting

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a scientist? (Two seatings are considered equivalent if one read more ..

bader Apr 18, 2024

0

1

0

+655

Counting

ABJeIIy Apr 18, 2024

0

1

+1465

Algebra

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$. When $6$ more juniors join the class, and $1$ senior drops the class, the ratio of the number of juniors to the number of seniors becomes $18:7$. How read more ..

A line and a circle intersect at and as shown below. Find the distance between and .
The circle is x^2 + y^2 = 20.
The line is y = -4.

bader Apr 18, 2024

0

1

0

+655

Geometry

ABJeIIy Apr 18, 2024

0

1

0

+655

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

ABJeIIy Apr 18, 2024

0

1

0

+655

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

ABJeIIy Apr 18, 2024

0

1

+655

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

ABJeIIy Apr 18, 2024

0

1

+655

Geometry

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

ABJeIIy Apr 18, 2024

0

1

+343

Inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

ChiIIBill Apr 18, 2024

0

1

+343

Inequality

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

ChiIIBill Apr 18, 2024

0

1

+343

Inequality

Points A,B and C are given in the coordinate plane. There exists a point Q and a constant k such that for any point P ,
If ,and , then find the constant K.
This is hard but please give me an answer read more ..

ChiIIBill Apr 18, 2024

0

1

+6

Hard Math geometry problem

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $7$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $2$ times as much money as read more ..

TX4181941 Apr 18, 2024

+1

1

0

+1465

Algebra

bader Apr 18, 2024

0

1

+1465

Algebra

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 = 24$. What is the value of $b$ in this ordered pair?

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $\frac{28}{9}$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

bader Apr 18, 2024

0

1

0

+1465

Algebra

bader Apr 18, 2024

0

1

+1465

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

Let $a$ and $b$ be the roots of the quadratic equation $2x^2 - 7x + 2 = -x^2 + 4x + 9.$ Find $\frac{1}{a-1}+\frac{1}{b-1}.$

bader Apr 18, 2024

0

1

0

+343

Algebra

ChiIIBill Apr 18, 2024

0

1

0

+343

Algebra

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c+x^2-8x$.

ChiIIBill Apr 18, 2024

0

1

0

+343

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

ChiIIBill Apr 18, 2024

0

1

0

+1465

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

bader Apr 18, 2024

0

1

0

+1465

Geometry

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction. read more ..

bader Apr 18, 2024

0

1

0

+1465

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

bader Apr 18, 2024

0

1

0

+16

Algebra

For every integer n≥1, let P(n) denote the product of the first n odd numbers:
P(n)=1×3×5×⋯×(2n−1)
Prove that for all integers n≥1, P(n)=(2n)!/2^n×n!.

Sxchen1110 Apr 18, 2024

0

1

0

+343

Algebra

All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?

ChiIIBill Apr 17, 2024

0

1

0

+343

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

ChiIIBill Apr 17, 2024

0

1

0

+343

Algebra

For a certain value of k, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

ChiIIBill Apr 17, 2024

0

1

0

+343

Algebra

Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water. She thinks the solution is a little strong, so she drains $150$ mL from the beaker, adds $150$ mL of water, and stirs the solution. Ruth thinks the solution is read more ..

ChiIIBill Apr 17, 2024

0

1

0

+170

Algebra

In a store window, there was a box of berries having a total weight of $200$ kg. The berries were $99\%$ water, by weight. After two days in the sun, the water content of the berries was only $80\%$, by weight. What was the total weight read more ..

Boseo Apr 17, 2024

0

1

0

+1465

Geometry

In the diagram below, $O$ is the center of the circle, and $\overline{UV}$ is a diameter. Find $\angle XYZ$, in degrees.

bader Apr 17, 2024

0

1

0

+1465

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

bader Apr 17, 2024

0

1

0

+1465

Geometry

In cyclic quadrilateral $PQRS,$
angle P = angle Q = angle R
Find the largest angle in quadrilateral $PQRS,$ in degrees.

bader Apr 17, 2024

0

1

+1465

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

bader Apr 17, 2024

0

1

0

+1465

Counting

bader Apr 17, 2024

0

1

0

+1465

Geometry

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

bader Apr 17, 2024

0

1

0

+1002

Geometry

Find the total surface area and the volume of the conical frustum below.

kittykat Apr 17, 2024

0

1

0

+1002

Geometry

Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

kittykat Apr 17, 2024

0

1

0

+1002

Algebra

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

kittykat Apr 17, 2024

0

1

0

+1002

Algebra

Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

kittykat Apr 17, 2024

0

1

0

+1002

Algebra

Find the number of real numbers that are not in the domain of the function $$f(x) = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}.$$

kittykat Apr 17, 2024

0

1

0

+1002

Algebra

Find the smallest real number $x$ in the domain of the function $$f(x) = \sqrt{(x-3)^2-(x+3)^2}.$$

kittykat Apr 17, 2024

0

1

0

+1002

Probability

The grid below is made up of line segments, like the line segment in red. There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number of squares read more ..

kittykat Apr 17, 2024

0

1

0

+1002

Probability

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

kittykat Apr 17, 2024

0

1

0

+1002

Probability

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain read more ..

kittykat Apr 17, 2024

0

1

0

+4

How do I do this?

You spin each spinner, roll a die, and find the sum. How many different sums are possible? Spinner 1: 1,2,3,4,5,6 Die: 1,2,3,4,5,6 Spinner 2: 2,3,4

CatsVsDogs Apr 17, 2024

+1

1

+209

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

fjeihqoO Apr 17, 2024

0

1

0

+209

Probability

fjeihqoO Apr 17, 2024

0

1

0

+209

Geometry

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

fjeihqoO Apr 17, 2024

0

1

0

+209

help inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

fjeihqoO Apr 17, 2024

0

1

+51

dice. many dice. roll. painted.

The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size.
a. How many of the smaller cubes have exactly one black face?
b. How many of the smaller cubes do not have any black faces?
c. read more ..

Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2*1/2*4*1/6
B = 12*128
C = 1*8*1/5^2 read more ..

fjeihqo0 Apr 17, 2024

0

1

0

+158

Algebra

siIviajendeukie Apr 17, 2024

0

1

+158

Algebra

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

Find the number of ways that Magnus can give out 12 identical stickers to 8 of his friends. (Not everyone has to get a sticker.)
Find the number of ways that Magnus can give out 12 identical stickers to 8 of his friends, if every friend read more ..

siIviajendeukie Apr 17, 2024

0

1

+158

Counting

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 95% water, by weight. After two days in the sun, the water content of the berries was only 90%, by weight. What was the total weight of the read more ..

siIviajendeukie Apr 17, 2024

0

1

0

+158

Algebra

siIviajendeukie Apr 17, 2024

0

1

+4

PLEASE HELP

In a 5 by 5 grid, each of the 25 small squares measures 2 cm by 2 cm and is shaded. Five unshaded circles are then placed on top of the grid as shown. The area of the visible shaded region can be written in the form A-Bpi square cm. What is the value read more ..

The numbers , , , ... , , ... is a geometric sequence. If is three more than , and is seven more than , what is the value of ? Express your answer as a common fraction.

deper Apr 17, 2024

0

1

+208

Please Help, Thank YOU if you try or help :)

A right circular cone is sliced into four pieces by planes parallel to its base, as shown in the figure. All of these pieces have the same height. What read more ..

aboslutelydestroying Apr 17, 2024

0

1

+208

Please Help, Thank YOU if you try or help :)

Let O be the origin. Points P and Q lie in the first quadrant. The slope of line segment OP is 7 and the slope of line segment is 10. If then compute the slope of line segment
Note: The point read more ..

aboslutelydestroying Apr 17, 2024

0

1

0

+158

Geometry

siIviajendeukie Apr 17, 2024

0

1

0

+158

Geometry

A rectangle in the coordinate plane is shown below. A line with slope 1/3 splits this rectangle into two regions with equal area. What is the y-intercept of this line?
The rectangle is at (2,1), (2,-1), (-2,1), (-2,-1). read more ..

siIviajendeukie Apr 17, 2024

0

1

0

+158

Geometry

A line and a circle intersect at A and B as shown below. Find the distance between A and B.
The circle is x^2 + y^2 = 1, and the line is y = x.

siIviajendeukie Apr 17, 2024

0

1

+158

Algebra

Let x and y be real numbers. If x and y satisfy:
x^2 + y^2 = 4x - 18y + 25
then find the largest value of x and simpify giving your answer in exact form and radicals!

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If PQ = 36, PM = 22, read more ..

siIviajendeukie Apr 17, 2024

0

1

0

+158

Geometry

siIviajendeukie Apr 16, 2024

0

2

0

+158

Geometry

Find the circumradius of triangle ABC.

siIviajendeukie Apr 16, 2024

0

2

0

+158

Geometry

Find the inradius of triangle ABC.

siIviajendeukie Apr 16, 2024

0

1

0

+158

Algebra

Points A, B, and c are given in the coordinate plane. There exists a point Q and a constant k such that for any point P,
PA^2 + PB^2+PC^2=3PQ^2 + k
If A = (4, -1), B = (8, 2), and C = (-7, 4), then find the constant k.
<read more ..

siIviajendeukie Apr 16, 2024

0

1

0

+655

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

ABJeIIy Apr 16, 2024

0

1

+8

Confusing question on a math test

The logo for a new company is a circle divided into 21 same-sized sectors. Three of the sectors are white, and the others are different colors.
The area of one of the white sectors is 13π/54 inches squared.
What is the radius of read more ..

Let

Find the largest three-digit value of such that is an integer.
Letting y=f(x), we get that y(y+1)=x, and y(y+1) is a three-digit number.
Solve for y read more ..

FireflySky Apr 16, 2024

0

1

+64

Solve for y

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

SilviaJendeukie Apr 16, 2024

-1

1

+655

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

ABJeIIy Apr 16, 2024

-1

1

+655

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

ABJeIIy Apr 16, 2024

0

1

+655

Counting

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

ABJeIIy Apr 16, 2024

0

1

+655

Geometry

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

ABJeIIy Apr 16, 2024

0

1

+655

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

ABJeIIy Apr 16, 2024

0

1

+655

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

ABJeIIy Apr 16, 2024

0

1

0

+655

Algebra

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.) read more ..

ABJeIIy Apr 16, 2024

0

1

0

+655

Algebra

A line passes through the points A, B, and C. Find y.
A = (-7,2), B = (8,-14), C = (10,y)

ABJeIIy Apr 16, 2024

0

1

0

+655

Algebra

Find all values of $a$ that satisfy the equation
\[\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.\]

ABJeIIy Apr 16, 2024

0

1

+655

Algebra

Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

ABJeIIy Apr 16, 2024

-1

1

0

+655

Algebra

ABJeIIy Apr 16, 2024

+1

1

3

+178

Science

Make a cone out of a piece of paper, make some measurements and estimates. Remember that
Measure the mass of your cone.
Measure the cross-sectional area of your cone.
Measure the terminal velocity read more ..

If we wanted to measure terminal velocity, we could see how far something falls, measure how long that takes, and divide to get the terminal velocity.
On the other hand, that method would fail if the object were still accelerating up to its terminal read more ..

ABJelly Apr 16, 2024

+1

1

2

+178

Science

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $214$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

ABJelly Apr 16, 2024

0

1

2

+655

Algebra

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

Point D is the midpoint of median \overline{AM} of triangle ABC. Point E is the midpoint of \overline{AB}, and point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle AMC if [ABC] =180.

ABJeIIy Apr 16, 2024

0

1

0

+655

Inequality

Solve the inequality x^3 + 4x > 5x^2 + 28x + x^3. Write your answer in interval notation.

ABJeIIy Apr 16, 2024

+1

1

+178

Science

Stars, like the sun cannot run on chemical energy. If they did, we estimated that they would burn through all their fuel within a few thousand years.
Stars run on nuclear energy. In the sun, this is almost entirely the energy given off when hydrogen read more ..

German physicist Max Planck built a theory of black body radiation and used it to help start the field of quantum mechanics.
Planck's theory predicted:
In this formula, is the peak frequency of radiation coming read more ..

ABJelly Apr 16, 2024

+1

2

1

+178

Science

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

ABJelly Apr 16, 2024

+1

1

0

+178

Compute

ABJelly Apr 16, 2024

+1

1

0

+178

Series

Compute

ABJelly Apr 16, 2024

0

2

0

+655

Counting

ABJeIIy Apr 16, 2024

-1

1

+655

Counting

In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

There is a group of five children, where two of the children are twins. In how many ways can I distribute $3$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

ABJeIIy Apr 16, 2024

-1

1

0

+655

Counting

ABJeIIy Apr 16, 2024

-1

1

0

+655

help geometry

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

In triangle PQR, M is the midpoint of \overline{QR}. Find PM.

ABJeIIy Apr 16, 2024

0

1

0

+655

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, and BC read more ..

ABJeIIy Apr 16, 2024

+1

1

0

+178

Fill in the blanks to make a true equation:

ABJelly Apr 16, 2024

0

2

0

+854

help geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

Akhain1 Apr 15, 2024

0

1

0

+854

help geometry

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

Akhain1 Apr 15, 2024

+1

1

0

+178

Geometric Series

Letbe an infinite geometric series. The sum of the series is 3 The sum of the squares of all the terms is 4 Find the common ratio.

ABJelly Apr 15, 2024

+1

1

0

+178

Geometric Series

Compute the sum

ABJelly Apr 15, 2024

+1

1

0

+178

Geometric Series

Fill in the blanks to make the statement true:
The infinite geometric series with first term and common ratio has a sum of .
4
10 read more ..

ABJelly Apr 15, 2024

0

1

0

+8

I would really appreciate help on this I have to turn it in tomorrow

I would really appreciate help on this I have to turn it in tomorrow but teach requires work not just answers Thank you!
1) What is the solution to the equation given the interval [0, pi ). Show all work for credit.
csc^2 + csc read more ..

FireflySky Apr 15, 2024

0

1

0

+854

help geometry

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

Akhain1 Apr 15, 2024

0

1

+50

Matrices system

If A and B are matrices and x and y are vectors such that they aren't multiple of each other and:
Ax = y, Ay = x + 2y and
Bx = x + y, By = 2y.
There are scalars a, b, c, and d that satisfy: read more ..

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

helloworldhello Apr 15, 2024

0

1

+854

help geometry

If A is a matrix and x, y are vectors such that neither is a multiple of the other and Ax = y and Ay = x + 2y, how do we find a and b when we have that (A^5) x = ax + by?

Akhain1 Apr 15, 2024

0

1

+50

Matrices with repeated exponents

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

helloworldhello Apr 15, 2024

0

1

+854

help geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

Akhain1 Apr 15, 2024

0

1

+854

help geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

Akhain1 Apr 15, 2024

+1

1

3

+367

Geometry

y =6x^2 - 9x + c, y = 5x^2 - 3x
Let c be a real number, and consider the system of quadratic equations
For which values of does this system have:
(a) Exactly one real solution
(b) More than one real solution? read more ..

magenta Apr 15, 2024

+1

1

+9

pls answer asap

1. Let Find the values of find the value of X for which f(x) is not defined. Enter all such values, separated by commas
2.Let Then this equation can be expressed in the form (x+a)(y+b)=c for some constants a b and c Enter your answer read more ..

gaberiellz Apr 15, 2024

+1

3

2

+5

PLZ HLP ASAP

In parallelogram $EFGH,$ let $M$ be the point on $\overline{EF}$ such that $FM:ME = 1:1,$ and let $N$ be the point on $\overline{EH}$ such that $HN:NE = 1:1.$ Line segments $\overline{FH}$ and $\overline{GM}$ intersect at $P,$ and line segments $\overline{FH}$ read more ..

bigmathdudeperson Apr 15, 2024

0

1

+367

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

magenta Apr 15, 2024

0

1

+367

Geometry

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

magenta Apr 15, 2024

0

1

0

+367

Geometry

magenta Apr 15, 2024

0

1

+4

HELP-DUE TODAY!!!!!

A line and a circle intersect at and as shown below. Find the coordinates of the midpoint of AB.

[asy]
usepackage("amsmath");
usepackage("amssymb");
unitsize(2 cm);<#> pair A, B;<#> A = dir(240);<#> read more ..

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Hermionegranger Apr 15, 2024

0

1

0

+1002

Geometry

kittykat Apr 15, 2024

0

1

0

+1002

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

kittykat Apr 15, 2024

0

1

+1002

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

kittykat Apr 15, 2024

0

1

0

+593

Counting

LiIIiam0216 Apr 15, 2024

0

1

0

+593

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

LiIIiam0216 Apr 15, 2024

0

1

0

+593

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

LiIIiam0216 Apr 15, 2024

0

1

0

+593

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

LiIIiam0216 Apr 15, 2024

0

1

0

+367

Algebra

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

magenta Apr 15, 2024

0

1

0

+367

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

magenta Apr 15, 2024

0

1

0

+367

Algebra

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

magenta Apr 15, 2024

0

1

0

+367

Algebra

Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.

magenta Apr 15, 2024

0

1

0

+1037

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, so that at least one square is yellow, and at least one square read more ..

parmen Apr 15, 2024

0

1

0

+1037

Counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters read more ..

parmen Apr 15, 2024

0

1

0

+1037

Probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 2 units?

parmen Apr 15, 2024

0

1

0

+1037

Counting

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

parmen Apr 15, 2024

0

1

0

+1037

Counting

In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?

parmen Apr 15, 2024

0

1

0

+1037

Counting

a) A baking club wants to form an executive committee. There are 12 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 2 people?
b) A baking club wants to form read more ..

parmen Apr 15, 2024

+1

1

+178

Geometric Series

Evaluate the infinite geometric series
Express your answer as a fraction with integer numerator and denominator.

What is the tenth term in the geometric sequence 9, 3, 1, 1/3,...?

ABJelly Apr 15, 2024

+1

1

+178

Geometric Series

ABJelly Apr 15, 2024

0

1

2

+24

Find the area of triangle ABC if AB = 6, BC=8, and angle ABC = 135 degrees.

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.
The two lines are y = x and y = 2x.

Starry Apr 15, 2024

0

1

0

+593

Algebra

LiIIiam0216 Apr 15, 2024

0

1

0

+593

Algebra

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x + 2y
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

LiIIiam0216 Apr 15, 2024

0

1

0

+593

Coordinates

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 20.
The line is y = -4.

LiIIiam0216 Apr 15, 2024

0

1

+158

Algebra

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

siIviajendeukie Apr 15, 2024

0

1

+158

Algebra

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

siIviajendeukie Apr 15, 2024

0

1

+158

Algebra

In triangle ABC, point D is on side AC such that line segment BD bisects angle ABC. If angle A = 30 degrees, angle C = 90 degrees, and AC = 12, then find the area of triangle ABD.
I've been trying and still can't read more ..

siIviajendeukie Apr 15, 2024

0

1

2

+24

Geometry

Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

Starry Apr 15, 2024

0

1

0

+158

Algebra

siIviajendeukie Apr 15, 2024

0

1

0

+158

Algebra

Find the number of real numbers that are not in the domain of the function $$f(x) = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}.$$

siIviajendeukie Apr 15, 2024

0

1

0

+158

Algebra

Find the smallest real number $x$ in the domain of the function $$f(x) = \sqrt{(x-3)^2-(x+3)^2}.$$

siIviajendeukie Apr 15, 2024

0

2

0

+8

Geometry

Please try to solve these
1.

2.
<#> 3.<#> read more ..

wendigo Apr 15, 2024

0

1

0

+158

Algebra

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

siIviajendeukie Apr 15, 2024

0

1

0

+158

Algebra

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

siIviajendeukie Apr 15, 2024

0

1

0

+158

Algebra

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

siIviajendeukie Apr 15, 2024

0

1

0

+158

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $15$ days earlier. If the job needs to be completed $40$ days earlier, how many additional workers should be hired?

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

For a certain value of $k$, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

siIviajendeukie Apr 14, 2024

+1

1

+24

help pls

Determine the smallest positive integer n such that 5^n equivalent n^5 mod 3.

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

MEMEGOD Apr 14, 2024

+1

1

+158

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

Let f(x) = \left \lfloor \frac{2 - 3x}{x + 3} + x^2 \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

siIviajendeukie Apr 14, 2024

0

1

+158

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

Let
f(x) = \sqrt{x - \sqrt{x}}
Find the largest three-digit value of x such that f(x) is an integer.

siIviajendeukie Apr 14, 2024

0

1

0

+158

Algebra

siIviajendeukie Apr 14, 2024

0

1

0

+593

Algebra

Evaluate the infinite geometric series
0.4 + 0.016 +...
Express your answer as a fraction with integer numerator and denominator.

LiIIiam0216 Apr 14, 2024

0

1

0

+1037

Geometry

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (2,4),$ $B = (-3,1),$ and $C = (1,7)$, then find the constant read more ..

parmen Apr 14, 2024

0

1

0

+1037

Geometry

A rectangle in the coordinate plane is shown below. A line with slope $\frac{1}{3}$ splits this rectangle into two regions with equal area. What is the $y$-intercept of this line?
The rectangle has coordinates (-1,-1), (-1,1), read more ..

parmen Apr 14, 2024

0

1

0

+1037

Geometry

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $11,$ and the slope of line segment $\overline{OQ}$ is $13.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

parmen Apr 14, 2024

0

1

0

+1037

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

parmen Apr 14, 2024

0

1

0

+1465

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $4$ hours and 20 minutes, but when there is a wind blowing from Penthaven to Jackson at $50$ miles per hour, the trip takes $4$ hours and read more ..

bader Apr 14, 2024

0

1

+64

Find the ordered quintuplet that satisfies the system of equations

For a certain value of k, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

SilviaJendeukie Apr 14, 2024

0

1

0

+1465

Algebra

bader Apr 14, 2024

0

2

0

+1465

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $25$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}15$ p.m. read more ..

bader Apr 14, 2024

0

1

0

+593

help counting

The grid below is made up of line segments, like the line segment in red. There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number of squares read more ..

LiIIiam0216 Apr 14, 2024

0

1

0

+593

help me

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

LiIIiam0216 Apr 14, 2024

0

1

0

+593

need help

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain read more ..

LiIIiam0216 Apr 14, 2024

0

1

0

+1002

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

kittykat Apr 14, 2024

0

1

0

+1002

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

kittykat Apr 14, 2024

0

1

0

+1465

Algebra

A geometric sequence has 400 terms. The first term is 500 and the common ratio is \frac{11}{12}. How many terms of this sequence are greater than $1?$

bader Apr 14, 2024

0

1

0

+1465

Algebra

In a geometric sequence, the 23rd term is 26 and the 26th term is 10. What is the 28th term?

bader Apr 14, 2024

0

1

0

+1465

Algebra

In an arithmetic sequence, the 23rd term is 2, and the 35th term is 3. What is the 38th term?

bader Apr 14, 2024

0

1

0

+1465

Algebra

Find constants $A$ and $B$ such that
\frac{2x + 11}{x^2 - 1} = \frac{A}{x + 1} + \frac{B}{x - 1}\]
for all $x$ such that $x \neq -1$ and $x \neq 1$.

bader Apr 14, 2024

0

1

0

+593

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 Apr 14, 2024

0

1

0

+593

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Apr 14, 2024

0

1

0

+593

plz help

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

LiIIiam0216 Apr 14, 2024

0

1

+80

pls help anyone

I run a book club with n people, not including myself. Every day, for 400 days, I invite 5 members in the club to review a book. What is the smallest positive integer n so that I can avoid ever having the exact same group of 5 members over all 400 days read more ..

The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.
(a) How many of the smaller cubes have exactly one black face?
(b) How many of the smaller cubes do not have any read more ..

Lilliam0216 Apr 14, 2024

0

1

0

+655

Counting

ABJeIIy Apr 14, 2024

0

1

0

+655

Counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

ABJeIIy Apr 14, 2024

0

1

0

+655

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

ABJeIIy Apr 14, 2024

0

1

0

+655

help counting

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

ABJeIIy Apr 14, 2024

0

1

0

+655

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if everything mathematician must be between two scientists? (Two seatings are considered read more ..

ABJeIIy Apr 14, 2024

0

1

+655

Counting

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

ABJeIIy Apr 14, 2024

0

1

0

+854

Algebra

Akhain1 Apr 14, 2024

0

1

0

+854

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

Akhain1 Apr 14, 2024

0

1

0

+854

Algebra

All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?

Akhain1 Apr 14, 2024

0

1

0

+854

Algebra

All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $480$ square foot wall, in minutes?

Akhain1 Apr 14, 2024

0

1

0

+854

Algebra

All members of our painting team paint at the same rate. If $45$ members can paint a specific wall in $60$ minutes, then how long would it take $12$ members to paint the same wall, in minutes?

Akhain1 Apr 14, 2024

+1

1

+854

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

Akhain1 Apr 14, 2024

0

1

0

+655

Algebra

ABJeIIy Apr 13, 2024

0

1

0

+655

Algebra

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

ABJeIIy Apr 13, 2024

0

1

0

+655

Algebra

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

ABJeIIy Apr 13, 2024

0

1

+18

Re-Asking Another Problem

Let M, N, and P be the midpoints of sides TU, US, and ST of triangle STU respectively. Let UZ be the altitude of the triangle. If angle TSU = 62 degrees and angle STU = 29 degrees, then what is angle NZM + angle NPM in read more ..

Points M, N, and O are the midpoints of sides KL, LJ, and JK, respectively, of triangle JKL. Points P, Q, and R are the midpoints of NO, OM, and MN, respectively. If the area of triangle PQR is 12, then what is the area of triangle JQR?<read more ..

Ranger897 Apr 13, 2024

0

1

+18

Re-Asking Question

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

Ranger897 Apr 13, 2024

0

2

0

+655

Algebra

ABJeIIy Apr 13, 2024

0

1

0

+655

Algebra

The system of equations
\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5\]
has exactly one solution. What is $z$ in this solution?

ABJeIIy Apr 13, 2024

0

1

0

+655

Algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

ABJeIIy Apr 13, 2024

0

1

+655

Need help

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

ABJeIIy Apr 13, 2024

0

1

+655

Help plz

Points M, N, and O are the midpoints of sides KL, LJ, and JK, respectively, of triangle JKL. Points P, Q, and R are the midpoints of NO, OM, and MN, respectively. If the area of triangle PQR is 12, then what is the area of triangle JQR?<read more ..

ABJeIIy Apr 13, 2024

0

2

+18

Geometry Help Please :P

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly three ch read more ..

Ranger897 Apr 13, 2024

0

1

2

+80

pls help ASAP

Let M, N, and P be the midpoints of sides TU, US, and ST of triangle STU respectively. Let UZ be the altitude of the triangle. If angle TSU = 62 degrees and angle STU = 29 degrees, then what is angle NZM + angle NPM in read more ..

Lilliam0216 Apr 13, 2024

0

1

2

+18

Let M, N, and P be the midpoints of sides TU, US, and ST of triangle STU respectively. Let UZ be the altitude of the triangle. If

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

Ranger897 Apr 13, 2024

0

1

0

+655

Counting

ABJeIIy Apr 13, 2024

+1

1

2

+5

Find the speed and CW/CCW of the particle with parametric equations.

If you can't read the $LaTeX$, it is:
The position of a particle is given by the parametric equations
$x=3+2\sin(2t)$
$y=4+2\cos(2t)$
as $t$ ranges over all real numbers.
What is the speed of this particle, read more ..

Expand (x^2 + 1/x)*(x + x^4)^3.

myphofstahs Apr 13, 2024

0

1

0

+655

Algebra

ABJeIIy Apr 13, 2024

0

1

+16

A translation maps A ti A' and B to B'. We know AA'=6, AB=5, and AB'=5 find BA'

Equilateral triangle ABC is inscribed in a circle. Let P be a point on arc BC. Given that PB=18 and PC=7 find PA.

RedDragon1 Apr 13, 2024

0

1

+16

Question

A,B,C, and D are distinct points on the plane. A rotation about point O maps A to B, B to C, and C to D. We know angle AOD is 24 Enter all three possible degree measures (between 0 and 180) of angle AOB separated read more ..

RedDragon1 Apr 13, 2024

0

1

+16

Question

In the diagram below, Point A is sqrt(3) units above O. Whenever Tasha moves a point, she translates the point sqrt(2) units to the right. Whenever Richard moves a point, he rotates the point clockwise about point O by 90˚
In read more ..

RedDragon1 Apr 13, 2024

0

2

1

+16

Question

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

RedDragon1 Apr 13, 2024

0

1

0

+854

Geometry

Akhain1 Apr 13, 2024

0

1

0

+854

Geometry

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

Akhain1 Apr 13, 2024

0

2

0

+854

Geometry

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

Akhain1 Apr 13, 2024

0

1

0

+854

Geometry

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region. read more ..

Akhain1 Apr 13, 2024

0

1

0

+854

Geometry

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

Akhain1 Apr 13, 2024

+1

1

+19

Try to solve this difficult probability question: [DUPLICATE]

Try to solve this difficult probability question:
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than $10$ times? read more ..

Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EAD$ is $9.$ If $AE:EB = 3:4$ and the height of parallelogram $ABCD$ is $10$, read more ..

blueorange Apr 13, 2024

0

1

0

+854

Geometry

Akhain1 Apr 13, 2024

0

1

0

+30

3D Geometry

Problem 1.
A tetrahedron is considered trirectangular if one of the vertices forms 3 90-angles. What is the volume of a trirectangular tetrahedron ABCD if one its faces is a 8,10,12 triangle?
Problem 2.
Let ABCD read more ..

Mather459 Apr 13, 2024

+1

1

+854

Geometry

In triangle ABC, point X is on side BC such that AX=13,BX=10,CX=10, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

What is the sum of the series ? (Note: The number is in Fibonacci Sequence)

Akhain1 Apr 13, 2024

0

2

1

+208

Please Help, Thank you if you help or try :)

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

aboslutelydestroying Apr 13, 2024

0

1

0

+854

Geometry

Akhain1 Apr 12, 2024

0

1

0

+854

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

Akhain1 Apr 12, 2024

0

2

0

+854

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

Akhain1 Apr 12, 2024

0

1

0

+854

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

Akhain1 Apr 12, 2024

0

1

0

+854

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

Akhain1 Apr 12, 2024

0

2

0

+85

Hard Geometry

Very few people have solved these problems
1.

2.
<#> read more ..

Akhaim1 Apr 12, 2024

0

1

0

+854

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

Akhain1 Apr 12, 2024

0

1

+854

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{1 + \cfrac{1}{4}}}}.

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 b + b^2 a = 6,$ then what is $a^3 + b^3?$

Akhain1 Apr 12, 2024

0

1

0

+854

Algebra

Akhain1 Apr 12, 2024

0

1

0

+854

System

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a & + & 2b & + & 3c & + & 4d & + & 5e & = & 47, \\
2a & + & 3b & + & 4c & + & 5d & + & e read more ..

Akhain1 Apr 12, 2024

0

1

+367

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

magenta Apr 12, 2024

0

1

+367

Geometry

Find t if the expansion of the product of 2x^3 + x^2 - 3x + 5 and x^4 - 7x^3 + tx^2 - 11x + 15 has no x^2 term.

magenta Apr 12, 2024

0

1

+1030

Algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} read more ..

blackpanther Apr 12, 2024

0

1

0

+1030

Algebra

blackpanther Apr 12, 2024

0

1

+1030

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}

Problem 1.
Find the number of positive integer pairs (x,y) that satisfy xy ≤ 35.
Problem 2.
Find the number of positive integer pairs (x,y) that satisfy 20x ≥ 24y and x < 360. read more ..

blackpanther Apr 11, 2024

+1

2

3

+30

Tricky problems

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

Mather459 Apr 11, 2024

0

1

+1030

Algebra

A circle is inscribed into a right triangle. From the center of the circle a perpendicular is dropped on the hypotenuse, dividing the hypotenuse into two segments of length 12 and 5. What is the sum of the legs of the triangle?
I did read more ..

blackpanther Apr 11, 2024

0

1

2

+75

Geometry problem, need help fast!

Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 + 15x + 23. Compute a^4 + b^4.

moneydude242 Apr 11, 2024

0

1

+1037

Algebra

Let a and b be the roots of the quadratic x^2 - 5x + 3 = 2x^2 + 15x - 10. Find the quadratic whose roots are a^2 + a + 1 and b^2 + b + 1.

parmen Apr 11, 2024

0

1

+1037

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 11x - 2. Compute (a - 4) + (b - 4).

parmen Apr 11, 2024

0

2

1

+819

Algebra

Problem 1. I am placing pieces on a 3 × 3 square board such that pieces are placed on non-adjacent squares (squares that are not directly above, below, left, or right of another square). How many ways are there for me to place 4 pieces on his 3 × 3 board?
Problem read more ..

maximum Apr 11, 2024

+1

1

+5

Help please

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 9x - 17. Find
\frac{u^2}{v} + \frac{v^2}{u}.

isasejahr Apr 11, 2024

0

1

0

+1037

Algebra

parmen Apr 11, 2024

0

1

0

+1037

Algebra

Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 + 12x - 13. Find 1/a^2 + 1/b^2.

parmen Apr 11, 2024

0

1

0

+1037

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of x such that f(x) is an integer.

parmen Apr 11, 2024

0

1

+52

Trigonometric Laws and Identities

A 30-foot ramp is used to move product to a loading dock. The ramp makes a 24° angle with the horizontal. The ramp is to be replaced with a ramp that is 50 feet long. What angle does this replacement ramp make with the horizontal? Round your answer to the read more ..

What is the exact value of sin(-pi/12)?
Please explain!

xXValeXx Apr 11, 2024

0

2

1

+52

What is the exact value of sin(-pi/12)?

Evaluate a^3 - \dfrac{1}{a^3} if a^2 - a - 1 = 0.

xXValeXx Apr 11, 2024

0

1

0

+1037

Algebra

parmen Apr 11, 2024

0

1

2

+20

Select the correct answer. Which equation is equivalent to the given equation?

x^2+16x=22
(x+4)^2=22
(x+8)^2=86
(x+8)^2=38 read more ..

x^2+16x=22
(x+4)^2=22
(x+8)^2=86
(x+8)^2=38 read more ..

MasterUtopia Apr 11, 2024

0

1

0

+20

Which equation is equivalent to the given equation?

MasterUtopia Apr 11, 2024

0

1

2

+20

Select the correct answer. A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket a

Select the correct answer. A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket
an average of 200 tickets for each show. The company estimates that for each $0.25 increase in the read more ..

x^2-x-56=0
answer choices
x = 7
x = 8 read more ..

MasterUtopia Apr 11, 2024

0

1

+20

Select all the correct answers. What are the solutions of this equation?

Find the length $BC$, to two decimal places.

MasterUtopia Apr 11, 2024

0

1

2

+1037

trig

Find the length AC, rounded to two decimal places.

parmen Apr 11, 2024

0

1

+1037

trig

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

parmen Apr 11, 2024

0

1

0

+367

Algebra

magenta Apr 11, 2024

0

1

0

+367

help Algebra

For certain values of k and m, the system
3a + 2b = 12 - 5a + 7b
8a + 6b = k - a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

magenta Apr 11, 2024

0

1

0

+367

Inequality

Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

magenta Apr 11, 2024

0

1

+367

Inequality

Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

magenta Apr 11, 2024

+1

1

+343

Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

ChiIIBill Apr 11, 2024

+1

1

+343

Geometry

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

ChiIIBill Apr 11, 2024

0

1

+343

Geometry

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

ChiIIBill Apr 11, 2024

0

1

0

+209

Counting

fjeihqoO Apr 11, 2024

0

1

0

+209

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

fjeihqoO Apr 11, 2024

0

1

0

+209

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

fjeihqoO Apr 11, 2024

0

1

0

+209

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

fjeihqoO Apr 11, 2024

+1

1

2

+19

Try to solve this difficult probability question: [DUPLICATE]

Try to solve this difficult probability question:
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than $10$ times? read more ..

Hello,
Given an isosceles triangle ABC where AB=AC and the base BC is of length 8 cm. The height from A to the base BC divides it into two segments, BD and DC. If the length of BD is 3 cm, what is the length of segment DC and the height read more ..

blueorange Apr 11, 2024

0

1

2

+4

Exploring the properties of Isosceles triangles

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

yvonne910rhodes Apr 11, 2024

0

2

1

+20

Geometry

Question 1) How many positive five-digit integers contain the digit grouping "24" at least once? For instance, 24380 and 24440 are two such integers to include, but 23480 and 42034 do not meet the restrictions.
Question 2) For how many read more ..

MasterUtopia Apr 11, 2024

0

1

3

+6

Math question help

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

timmynotjimmy Apr 11, 2024

0

1

+854

help geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

Akhain1 Apr 11, 2024

0

1

0

+854

help geometry

Akhain1 Apr 11, 2024

0

1

0

+854

help geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Akhain1 Apr 11, 2024

0

2

0

+593

Trapzoid

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

LiIIiam0216 Apr 11, 2024

0

2

0

+593

Trapezoid

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

LiIIiam0216 Apr 11, 2024

+1

1

2

+30

Counting problems

Problem 1.
Andy is placing pieces on a 3 × 3 square board such that pieces are placed on non-adjacent squares (squares that are not directly above, below, left, or right of another square). How many ways are there for Andy to place 4 pieces on his read more ..

Find the sum of all solutions to

Mather459 Apr 10, 2024

0

2

1

+4

Pls help!!!

In parallelogram $EFGH,$ let $M$ be the point on $\overline{EF}$ such that $FM:ME = 1:1,$ and let $N$ be the point on $\overline{EH}$ such that $HN:NE = 1:1.$ Line segments $\overline{FH}$ and $\overline{GM}$ intersect at $P,$ and line segments $\overline{FH}$ read more ..

types0uls Apr 10, 2024

0

2

0

+593

Geometry

LiIIiam0216 Apr 10, 2024

0

2

0

+593

Geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

LiIIiam0216 Apr 10, 2024

0

1

0

+367

Triangle

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

magenta Apr 10, 2024

0

1

0

+60

help with geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

nathanl6656 Apr 10, 2024

0

1

0

+60

help plz

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

nathanl6656 Apr 10, 2024

0

1

0

+60

need help

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

nathanl6656 Apr 10, 2024

0

1

0

+60

Triangle

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

nathanl6656 Apr 10, 2024

0

1

0

+1002

help geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

kittykat Apr 10, 2024

0

1

0

+1002

help angles

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

kittykat Apr 10, 2024

0

1

0

+1002

Help coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

kittykat Apr 10, 2024

0

1

0

+1002

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

kittykat Apr 10, 2024

0

1

+1037

Geometry

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

parmen Apr 10, 2024

0

1

0

+1037

Area

parmen Apr 10, 2024

0

1

0

+1037

Triangle

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, and BC read more ..

parmen Apr 10, 2024

0

1

0

+1763

Help geometry

In triangle PQR, M is the midpoint of \overline{QR}. Find PM.

tomtom Apr 10, 2024

0

1

0

+1763

Need help

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

tomtom Apr 10, 2024

0

1

0

+1763

Help trapezoid

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

tomtom Apr 10, 2024

0

1

0

+1763

Help plz

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

tomtom Apr 10, 2024

0

3

0

+854

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

Akhain1 Apr 10, 2024

0

1

0

+854

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

Akhain1 Apr 10, 2024

0

1

0

+854

Geometry

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

Akhain1 Apr 10, 2024

0

1

0

+854

Geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

Akhain1 Apr 10, 2024

+1

1

+9

kinda urgent

Write the following expression as a single combination (n choose k) so that k doesn't equal 1 and n-k doesn't equal 1.
(38 choose 5)+(38 choose 32)=(n choose k)

A baking club wants to form an executive committee. There are $20$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $7$ people, including Mark?

coolerthanu Apr 10, 2024

0

1

0

+209

Counting

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

A baking club wants to form an executive committee. There are $20$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $7$ people?

fjeihqoO Apr 10, 2024

0

1

0

+209

Probability

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

fjeihqoO Apr 10, 2024

+1

1

+7

Help

Represent the sum of the complex numbers −4+3i and −2−i on the complex plane.
Use the Point and Segment tools to plot all required points and segments.
I need it graphed read more ..

In how many ways can the numbers through be entered once each into the five boxes below so that all the given inequalities are true?
___ > ___ > ___ > ___ < ___

justtryinpass Apr 10, 2024

0

1

0

+209

Counting

fjeihqoO Apr 10, 2024

0

1

+209

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

fjeihqoO Apr 10, 2024

+1

2

1

+5

Find tan 7pi/4

I know how to get the answer, but are we expected to know and memorize the different values of cosine and sin with radians. Like are we supposed to know what sin 7pi/4 without a calculator. Because the last step is (sin 7pi/4)/(cos 7pi/4). I have absolutely read more ..

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

sticknotes.com Apr 10, 2024

0

1

0

+51

seating

fjeihqo0 Apr 10, 2024

0

1

+209

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

fjeihqoO Apr 10, 2024

0

2

0

+209

Counting

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

fjeihqoO Apr 10, 2024

0

1

+209

Probability

Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 3 orange balls and 2 purple read more ..

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

fjeihqoO Apr 10, 2024

0

1

0

+209

Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

fjeihqoO Apr 10, 2024

+1

1

2

+51

xt to each other.

Find the number of ways of choosing three people in a circular table with 12 people, so that no two people are next to each other. Use this image: read more ..

Bobby the fly starts at the point (0,0) in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After 12 steps, how many different points could Franklin end up at?

fjeihqo0 Apr 10, 2024

0

1

2

+51

franklin on the coordinate plane

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

fjeihqo0 Apr 10, 2024

0

1

+655

Algebra

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

ABJeIIy Apr 9, 2024

0

1

+655

Algebra

Please do not leave out steps while solving this problem

ABJeIIy Apr 9, 2024

0

1

+85

Geometry Problem

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

Akhaim1 Apr 9, 2024

0

1

+655

Algebra

I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons read more ..

ABJeIIy Apr 9, 2024

0

2

1

+655

Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

ABJeIIy Apr 9, 2024

0

1

+655

Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 99% water, by weight. After two days in the sun, the water content of the berries was only 90%, by weight. What was the total weight of read more ..

ABJeIIy Apr 9, 2024

0

2

1

+655

Algebra

Let be an arithmetic sequence. Let denote the sum of the first terms. If and then find

ABJeIIy Apr 9, 2024

+1

2

1

+178

Arithmetic Sequences

Let be an arithmetic sequence. If and , then find .

ABJelly Apr 9, 2024

+1

1

+178

Arithmetic Sequences

In a geometric sequence, the 23rd term is 16 and the 26th term is 12. What is the 32nd term?

ABJelly Apr 9, 2024

+1

1

+178

Arithmetic Sequences

Let a_1, a_2, a_3, \dots be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_1 = \frac{1}{2}$ and $S_{2} = \frac{1}{2},$ then find $S_{15}.$

ABJelly Apr 9, 2024

0

1

+655

Algebra

aboslutelydestroying ●

ABJeIIy Apr 9, 2024

0

1

2

+655

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 + a_5 = 7 and a_2 + a_4 = 6, then find a_1.

ABJeIIy Apr 9, 2024

0

1

+655

Series

If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?

ABJeIIy Apr 9, 2024

0

1

+655

Algebra

If $s$ is a real number, then what is the smallest possible value of $2s^2 - 8s + 19 - 7s^2 - 8s + 20$?

ABJeIIy Apr 9, 2024

0

2

1

+655

Algebra

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?

ABJeIIy Apr 9, 2024

0

1

+655

Algebra

When the same constant is added to the numbers 60, 100 and 165 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

ABJeIIy Apr 9, 2024

+1

1

+178

Arithmetic sequences

A geometric sequence has 400 terms. The first term is 1000 and the common ratio is How many terms of this sequence are greater than 1?

ABJelly Apr 9, 2024

+1

3

2

+178

help me please!!

In a geometric sequence, the 23rd term is 26 and the 26th term is 12. What is the 32nd term?

ABJelly Apr 9, 2024

+1

1

+178

please help

In an arithmetic sequence, the 23rd term is and the 35th term is . What is the 48th term?

ABJelly Apr 9, 2024

+1

1

+178

Arithmetic sequences

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

ABJelly Apr 9, 2024

0

1

+209

Counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members read more ..

fjeihqoO Apr 9, 2024

0

1

+209

Counting

In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?
In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
In read more ..

fjeihqoO Apr 9, 2024

0

1

0

+209

Counting

fjeihqoO Apr 9, 2024

0

2

1

+209

Domain

Let
f(x) = \frac{2x + 3}{x^2 + 7}.
Find the domain of $f$. Give your answer using interval notation.

Let S = {1, 2, . . . , 2021}, and let F denote the set of functions f : S → S. For a function f ∈ F, let Tf = f 2021(s) : s ∈ S , where f 2021(s) denotes f(f(· · ·(f(s))· · ·)) with 2021 copies of f. Compute the remainder when sigma notation f∈F read more ..

fjeihqoO Apr 9, 2024

0

3

1

+16

Combinatorics

Let ABTCD be a convex pentagon with area 22 such that AB = CD and the circumcircles of triangles TAB and TCD are internally tangent. Given that ∠ATD = 90◦ , ∠BTC = 120◦ , BT = 4, and CT = 5, compute the area of triangle TAD.

Sxchen1110 Apr 8, 2024

0

3

2

+16

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

Sxchen1110 Apr 8, 2024

+1

2

+209

Geometry

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 30^\circ$.

fjeihqoO Apr 8, 2024

0

3

+209

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

fjeihqoO Apr 8, 2024

+1

1

2

+209

Geometry

asinus ●●

fjeihqoO Apr 8, 2024

+2

1

3

+30

Help Please

Problem 1
Arpit has 184756 penguins that waddle a unique lattice path from (0,0) to (10,10) on the coordinate plane (penguins only take unit length steps up or to the right). Arpit also has many penguin counters that read more ..

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

Mather459 Apr 8, 2024

0

1

+209

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

fjeihqoO Apr 8, 2024

0

1

2

+209

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

fjeihqoO Apr 8, 2024

0

3

1

+209

Algebra

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

fjeihqoO Apr 8, 2024

0

3

0

+854

Geometry

Akhain1 Apr 8, 2024

0

2

+51

conditions

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 3
The sum of the digits is 12
I got 3, its not correct. help is appreciated read more ..

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?
I got 36, its not right i cant figure out why

fjeihqo0 Apr 8, 2024

0

3

0

+51

help plz

fjeihqo0 Apr 8, 2024

0

2

+16

Cartesian plane question

Question:
Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is A (x) + B (y) =C, where A is positive, and A, B, and C are integers with the greatest common divisor 1.)
It read more ..

Write the equation of the line below in the form A(x) + B(x) = C, where A, B, and C are integers with greatest common divisor 1, and A is positive.
The line consists of two known points: (-4, 2) and (1, -1)

Seraphspace Apr 8, 2024

0

2

1

+16

Cartesian plane question

A line passes through the points A, B, and C. Find y.
A = (-3, 5)
B = (1, -2)
C = (6, y) read more ..

Seraphspace Apr 8, 2024

0

1

2

+16

Cartesian plane question

Question:
Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is A (x) + B (y) =C, where A is positive, and A, B, and C are integers with the greatest common divisor 1.) read more ..

Seraphspace Apr 8, 2024

0

2

1

+16

Cartesian plane question

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

Seraphspace Apr 8, 2024

0

1

+854

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

Akhain1 Apr 8, 2024

0

2

1

+854

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

Akhain1 Apr 8, 2024

0

2

1

+854

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

Akhain1 Apr 8, 2024

0

1

2

+854

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

Akhain1 Apr 8, 2024

0

2

1

+854

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

Akhain1 Apr 8, 2024

0

1

+854

Geometry

So, n = k/y. Given k is 1 kg m^1 and y is 1 kg m^−1 what is n?
Thanks in advance

Akhain1 Apr 8, 2024

0

2

1

+4

So, n = k/y. Given k is 1 kg m^1 and y is 1 kg m^−1 what is n?

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probablility that all three pieces are shorter than 5 units?
Thanks for the help!

jessjdpope Apr 8, 2024

0

2

+95

Using Geometry with Probability

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

ZBRS7311 Apr 8, 2024

0

2

1

+343

Functions

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

ChiIIBill Apr 8, 2024

0

3

0

+343

Function

ChiIIBill Apr 8, 2024

+1

1

2

+19

Probability Question

Try to solve this difficult probability question:
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than $10$ times? read more ..

Are you able to solve these problems?
1.

2.
<#> read more ..

blueorange Apr 8, 2024

0

1

3

+85

Geometry!

Find all real numbers $x$ such that $f(x) = f(f(x))$, where $f(x) = x^2 - 3x + x^3 - 7x^2 + 5x.$

Akhaim1 Apr 8, 2024

0

1

+343

help Algebra

The function $f(x,y)$ gives an ordered pair as output. It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, read more ..

ChiIIBill Apr 8, 2024

0

1

2

+343

Function

MaxWong ●●

ChiIIBill Apr 7, 2024

0

1

+343

Function

Let $f(x) = px + q$, where $p$ and $q$ are real numbers. Find $p+q$ if $f(f(f(x))) = 64x - 105 - 30x + 70 + 32x - 12$.

The function
f(x) = \frac{cx}{(4x - 5)(3x + 2)}
satisfies $f(f(x))=x$ for all real numbers $x\neq \frac{5}{4}$ and $x \neq -\frac{2}{3}$. Find $c$.

ChiIIBill Apr 7, 2024

0

1

0

+343

Function

ChiIIBill Apr 7, 2024

0

2

5

+208

Please Help, Thank YOU if you try or help :)

Question 1) How many positive five-digit integers contain the digit grouping "24" at least once? For instance, 24380 and 24440 are two such integers to include, but 23480 and 42034 do not meet the restrictions.
Question 2) For how many read more ..

The points (1, 7), (13, 16) and (7,k), where k is an integer, are vertices of a triangle. What is the sum of the values of kfor which the area of the triangle is a minimum?

aboslutelydestroying Apr 7, 2024

0

2

+208

Geometry Problem, Please help, Thank YOU if you try or help :)

A standard deck of playing cards has 52 cards divided into four suits (clubs, diamonds, hearts, spades). Each suit consists of nine "number cards", each containing a different number from 2 to 10, and four "face cards" that include a jack, a queen, a king read more ..

aboslutelydestroying Apr 7, 2024

0

2

5

+208

Please Help. Thank YOU if you try or help :)

aboslutelydestroying Apr 7, 2024

0

2

1

+64

Compute

Fill in the blanks to make a true equation:
1/n(n+3)=blank/n+blank/n+3.

SilviaJendeukie Apr 7, 2024

0

1

4

+64

Fill in the blanks to make a true equation:

Function f has an inverse. The graph of f^-1 passes through (3,-6). Define g(x) = 2f(3x) - 5. Function g also has an inverse. What point must the graph of g^-1 pass through?

SilviaJendeukie Apr 7, 2024

+1

1

+5

HELP

If {} is an arithmetic sequence, = 1, and = 625, evaluate:
+++...+

Tigergaming2464 Apr 7, 2024

+1

2

+208

Hard Algebra 2 problem, anyone can lend me a hand, Thank YOU if you try or help :)

A four-digit natural number "abcd" is "balanced" if a + d = b + c. What is the probability that it is a "balanced" if a four-digit natural number is randomly selected?

aboslutelydestroying Apr 7, 2024

0

2

+208

Please help, Thank YOU if you try :)

MaxWong ●●

aboslutelydestroying Apr 7, 2024

0

2

+208

Please Help, Thank YOU if you try :)

For how many positive values of n are both and 3n four-digit base 9 integers?

MaxWong ●●

aboslutelydestroying Apr 7, 2024

0

1

2

+64

Sum

Compute the sum

aboslutelydestroying ●●

SilviaJendeukie Apr 7, 2024

0

2

3

+208

Please Help, Thank YOU if you try :)

ABCDEF is a regular hexagon. M and N are the midpoints of DE and AF. P is the intersection of two lines BM and DN. What is the ratio of DP to PN? Express your answer read more ..

If n is a positive integer, what is the sum of all possible values of n for which +72 is a perfect square?

aboslutelydestroying Apr 7, 2024

+1

2

5

+208

Please Help, Thank YOU if you help :)

MaxWong ●●●●●

aboslutelydestroying Apr 7, 2024

0

2

+208

Please Help, Thank YOU if you try :)

A square and isosceles triangle of equal height are side-by-side, as shown, with both bases on the x-axis. The lower right vertex of the square and the lower left read more ..

Evaluate the infinite geometric series 0.4+0.12+0.036+0.0108...

aboslutelydestroying Apr 7, 2024

0

3

1

+64

Geometric series

Points A, B, and c are given in the coordinate plane. There exists a point Q and a constant k such that for any point P,
PA^2 + PB^2+PC^2=3PQ^2 + k
If A = (4, -4), B = (3, 5), and C = (-1, 2), then find the constant k.
<read more ..

SilviaJendeukie Apr 7, 2024

0

1

5

+39

Help! and include explanation

What is the limit of the function?
Select True or False for each limit statement.
limx→−∞(−2x3−2x)=∞
limx→∞(2x4+6x3−2x)=∞ read more ..

rerebas Apr 7, 2024

0

1

2

+15

Limit of function

Find the inradius of triangle ABC.

wilmaaaa Apr 7, 2024

0

1

+854

Geometry

Find the circumradius of triangle ABC.

Akhain1 Apr 7, 2024

0

2

1

+854

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If PQ = 36, PM = 22, read more ..

Akhain1 Apr 7, 2024

0

1

+819

Geometry

Find the sum 1/2!+2/3!+3/4!+...+(n−1)/n!. Express your answer in terms of n.

maximum Apr 7, 2024

0

2

4

+208

Algebra 2 interesting question, Thank YOU if you try :)

Let x and y be real numbers. If x and y satisfy:
x^2 + y^2 = 4x - 8y + 25
then find the largest value of x and simpify giving your answer in exact form and radicals!

aboslutelydestroying Apr 7, 2024

0

1

2

+39

Let x and y be real numbers. If x and y satisfy:

A line and a circle intersect at A and B as shown below. Find the distance between A and B.
Asymptote code below!

[asy]
usepackage("amsmath");
usepackage("amssymb");read more ..

rerebas Apr 7, 2024

0

1

2

+39

Help and please explain

A rectangle in the coordinate plane is shown below. A line with slope 1/3 splits this rectangle into two regions with equal area. What is the y-intercept of this line?
(-2,3) _____ (4,3)
read more ..

rerebas Apr 7, 2024

0

2

+39

Help, and include explanation

Let O be the origin. Points P and Q lie in the first quadrant. The slope of line segment OP is 1 and the slope of line segment is 3. If then compute the slope of line segment
Note: The point read more ..

rerebas Apr 7, 2024

0

2

1

+39

Please help and include explanation

Question 1: Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $20$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at read more ..

rerebas Apr 7, 2024

0

2

6

+10

URGENT! Plz help!

●●●●●●

ThreeLetters Apr 6, 2024

0

1

4

+13

Factorization Problem

I was just wondering if there was a way to solve the systems of equations a+b+c=x, ab+ac+bc=y, and abc=z, given that a,b,c,x,y,z are integers. I know that this is basically asking for the cubic formula, but I was wondering if there was a nier way to do read more ..

Alan ●●●●

sussusus Apr 6, 2024

+1

4

2

+208

Please Help, Thank YOU if you try

In the figure above, DF is the diameter of the semicircle. Rectangle ABCD and BEFG are congruent, and EF is on the diameter DF. Find the measure of&read more ..

The sum of the first 10 terms of a geometric sequence is 10, and the sum of the first 30 terms of the same sequence is 70. Find the sum of the first 40 terms.

aboslutelydestroying Apr 6, 2024

0

2

+208

Please help, Thank YOU if you try :)

{ } is a geometric sequence with common ratio r > 0. If = 1, = , then find the sum of the first 4 terms of { } .

aboslutelydestroying Apr 6, 2024

+1

3

2

+208

Please help, Thank YOU if you try :)

{} is an arithmetic sequence, find the sum of the first 20 terms.

aboslutelydestroying Apr 6, 2024

0

1

2

+208

Please help, Thank YOU if you try :)

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BC$.

aboslutelydestroying Apr 6, 2024

0

2

1

+854

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BZ$.

Akhain1 Apr 6, 2024

0

1

+854

Geometry

In the figure, angles $\angle ABC$ and $\angle AST$ are right angles. If $AC = 35,$ then what is $AS$?

Akhain1 Apr 6, 2024

+1

2

4

+854

Geometry

aboslutelydestroying ●●●●

Akhain1 Apr 6, 2024

0

2

1

+854

Geometry

Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square. If $PQ = 1$ and $PR = 1$, then what is the side length of the square?

Find the sum of first 17 terms in the following of the sequence
1, 4, 5, 9, 14, 23, 37 . . .
If the 17th term is 4,558 and the 18th term is 7,375 .

Akhain1 Apr 6, 2024

0

3

+208

Please help, Thank YOU if you try

Find all values of x that satisfy

aboslutelydestroying Apr 6, 2024

0

2

3

+208

Please help, Thank YOU if you try :)

ABCDEF is a regular hexagon. M and N are the midpoints of DE and AF. P is the intersection of two lines BM and DN. What is the ratio of DP to PN? Express your answer as read more ..

aboslutelydestroying Apr 6, 2024

0

3

2

+208

Please help, Thank YOU if you try :)

In triangle $ABC,$ $D$ is on side $\overline {AB}.$ We know $\triangle ABC \sim \triangle ACD$. If $BC = BD,$ what is $\angle B$ in degrees?

aboslutelydestroying Apr 6, 2024

0

4

0

+854

Geometry

Akhain1 Apr 6, 2024

0

3

1

+854

Geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

In triangle $ABC$, point $X$ is on side $\overline{BC}$ such that $AX = 5,$ $BX = 5,$ and the circumcircles of triangles $ABX$ and $ACX$ have the same radius. Find the area of triangle $ABC$.

Akhain1 Apr 6, 2024

0

4

0

+854

Geometry

Akhain1 Apr 6, 2024

0

3

0

+854

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

Akhain1 Apr 6, 2024

0

2

0

+854

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

Akhain1 Apr 6, 2024

0

5

0

+854

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

Akhain1 Apr 6, 2024

+1

2

1

+854

Coordinates

A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,-4),$ $B = (-3,12),$ and $C = (4,y),$ then find $y.$

asinus ●

Akhain1 Apr 5, 2024

0

4

1

+854

Lines

Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 8x - 3y$.

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

Akhain1 Apr 5, 2024

+1

2

1

+854

Coordinates

asinus ●

Akhain1 Apr 5, 2024

0

3

4

+85

Geometry Questions!!

Can you solve these?
1.

2.
<#> 3.<#> read more ..

Akhaim1 Apr 5, 2024

0

3

1

+18

Linear Algebraic Equations

Solve for n if

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?

Umeko1.0 Apr 5, 2024

0

3

1

+593

Circle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle BAC = 42^\circ$. Find $\angle PBC$ in degrees.

LiIIiam0216 Apr 5, 2024

0

4

0

+593

Triangle

LiIIiam0216 Apr 5, 2024

0

4

0

+593

Geometry

In the diagram, chords $\overline{XY}$ and $\overline{VW}$ are extended to meet at $U.$ If $\angle U = 30^\circ$, minor arc $XY$ is $180^\circ$, and minor arc $VW$ is $90^\circ$. Find arc $WY$, in degrees.

LiIIiam0216 Apr 5, 2024

0

4

1

+593

Line

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.) read more ..

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

LiIIiam0216 Apr 5, 2024

0

4

0

+593

Geometry

LiIIiam0216 Apr 5, 2024

0

3

2

+11

this one confuses me

Planets X, Y and Z take 360, 450 and 540 days, respectively, to rotate around the same sun. If the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are on the same line again?
a read more ..

Cindy wishes to arrange her coins into X piles, each consisting of the same number of coins, Y. Each pile will have more than one coin and no pile will have all the coins. If there are 22 possible values for Y given all of the restrictions, what is the read more ..

cheeeeeeese Apr 5, 2024

0

2

+11

help

So I don't know what I'm doing when turning a repeating decimal into a fraction, I've done this so much before but my brain is so cooked right now so I need help. The equation for what to do would be helpful.

cheeeeeeese Apr 5, 2024

+1

3

1

+5

Im studying for honors and idk what I'm doing

Let a and b and 2x2 - 8x + 7 = x^2 - 4x + 13. be the roots of the quadratic. Compute a^3*b + a*b^3

tragicallycanadian Apr 5, 2024

+1

2

1

+655

help algebra

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 41
2a + 3b + 4c + 5d + e = 15
3a + 4b + 5c + 1d + 2e = 34 read more ..

ABJeIIy Apr 5, 2024

0

2

0

+655

help with system

ABJeIIy Apr 5, 2024

0

2

1

+655

need help with system

For certain values of k and m, the system
3a + 2b = 2
6a + 2b = k + 3a + mb
has infinitely many solutions (a,b). What are k and m? read more ..

The degree of polynomial p is 11, and the degree of polynomial q is 7. Find all possible degrees of the polynomial p+q. Keep in mind that the degree can cancel out each other

ABJeIIy Apr 5, 2024

+1

4

2

+5

Urgent Need help

The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?

hibobhi Apr 5, 2024

0

2

1

+655

i need help

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

ABJeIIy Apr 4, 2024

0

3

1

+655

help me plz

Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.

ABJeIIy Apr 4, 2024

0

3

1

+655

help hard algebra

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x - 8y + 17x - 5y + 25,
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

ABJeIIy Apr 4, 2024

0

2

1

+655

help me with algebra

ABJeIIy Apr 4, 2024

+2

4

2

+208

Please help, Thank YOU if you try

Please evaluate

If { an} is an arithmetic sequence, a1 = 1, and a100 = 625, evaluate

aboslutelydestroying Apr 4, 2024

+2

4

1

+208

Please help, Thank YOU if you try.

Using 3 of the points in the set { (x, y) | x, y are integers, 1 ≤ x ≤3, and 3 ≤ y ≤ 10}, how many triangles can be formed?

aboslutelydestroying Apr 4, 2024

0

4

1

+208

Please Help, Thank YOU

Cindy wishes to arrange her coins into X piles, each consisting of the same number of coins, Y. Each pile will have more than one coin and no pile will have all the coins. If there are 22 possible values for Y given all of the restrictions, what is the read more ..

aboslutelydestroying Apr 4, 2024

0

2

+208

Please Help. Thank YOU

Planets X, Y and Z take 360, 450 and 540 days, respectively, to rotate around the same sun. If the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are on the same line again? (Note: read more ..

aboslutelydestroying Apr 4, 2024

+2

3

5

+208

Please Help.

Lamant has a box containing only red marbles, blue marbles and green marbles. He needs to select at least 24 marbles without replacement to be sure at least one of them is green. He needs to select at least 20 marbles without replacement to be sure at least read more ..

aboslutelydestroying Apr 4, 2024

0

2

1

+208

Someone please help me on this question.

Point B is the image of point A under a dilation with center O. If OB = 60, and the scale factor of the dilation is 4, then what is OA?
O---A-----B

aboslutelydestroying Apr 4, 2024

0

2

0

+593

Geometry

LiIIiam0216 Apr 4, 2024

0

5

0

+593

Transformations

A dilation with scale factor k takes figure A to figure B. Find the sum of all possible values of k.

Figure read more ..

LiIIiam0216 Apr 4, 2024

0

2

0

+593

Rotation

Let A1, A2, A3., ..., A15, A16 be a regular polygon. A rotation centered at A4 with an angle of X takes A3 to A5. Given that X < 180, find X in degrees.

LiIIiam0216 Apr 4, 2024

+1

3

4

+655

help me plz

Find all values of $a$ that satisfy the equation
\[\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.\]

Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

ABJeIIy Apr 4, 2024

0

2

1

+655

need help help

If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

ABJeIIy Apr 4, 2024

0

3

+655

help I have no idea

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $7$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

ABJeIIy Apr 3, 2024

0

2

+655

need help

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x^2 + \frac{3}{5}y^2 - 2x + 8y.

ABJeIIy Apr 3, 2024

0

2

0

+655

help help

ABJeIIy Apr 3, 2024

0

3

1

+655

help with algebra now

Let
f(x) = \frac{(2x + 3)(x - 7)}{\sqrt{x}}
Find the domain of f(x). Give your answer using interval notation.

Find the domain of the function f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.

ABJeIIy Apr 3, 2024

0

3

1

+593

Domain

Find all real numbers x such that (3x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3.

LiIIiam0216 Apr 3, 2024

0

3

0

+593

Equation

LiIIiam0216 Apr 3, 2024

0

2

1

+593

Quadratic

Find the minimum value of the expression $x^2+y^2+2x-4y+8+10x-12y$ for real $x$ and $y$.

Find all values of $x$ which do not satisfy $$1 \le 4-3x+5x < 10-8x.$$ Express your answer in interval notation.

LiIIiam0216 Apr 3, 2024

0

1

0

+593

Algebra

LiIIiam0216 Apr 3, 2024

0

3

+80

whats the height?

A box has a certain length, width, and height. The length of the box is equal to twice its width, as well as equal to 5 less than its height. If the total surface area of the box is 234, then what is the height of the box?

Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

Lilliam0216 Apr 3, 2024

+1

2

1

+655

help plz help

Find the vertex of the graph of the equation y = -2x^2 + 8x + 15 - 3x^2 + 7x - 25

ABJeIIy Apr 3, 2024

0

1

+655

I need help with this

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

ABJeIIy Apr 3, 2024

0

3

0

+655

help me help

ABJeIIy Apr 3, 2024

0

2

0

+655

help with algebra

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = -1.$ If $a = 2,$ then find $b.$

ABJeIIy Apr 3, 2024

0

3

0

+655

help help

Fill in the blanks with numbers to make a true equation
3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 = __ (x + __)^3 + __(x + __)^2 + __x + ___

ABJeIIy Apr 3, 2024

0

3

1

+18

Urgent-Help!

What is (sqrt of 10)/(4th sqrt of 10) equals 10 raised to what power?

Solve the inequality $(x - 2)(x + 6) \le x^2 + 14.$ Write your answer in interval notation.

Umeko1.0 Apr 3, 2024

0

2

1

+655

help with algebra

Find the number of integers $n$ that satisfy $n^2 < 64 - 20n - n^2.$

ABJeIIy Apr 3, 2024

0

2

1

+655

need help

Write the values of $x$ that satisfy $-8 \le x + 17 < -3 - 5x$ as an interval.

ABJeIIy Apr 3, 2024

0

3

1

+655

help plz help

Let
\[f(x) = \frac{2x + 3}{x^2 + 7}.\]
Find the range of $f$. Give your answer using interval notation.

ABJeIIy Apr 3, 2024

0

2

1

+655

need help

In a geometric sequence, the $23$rd term is $16$ and the $26$th term is $18$. What is the $24$th term?

ABJeIIy Apr 2, 2024

0

2

1

+655

help me help

In a geometric sequence, the $23$rd term is $16$ and the $24$th term is $24$. What is the $28$th term?

ABJeIIy Apr 2, 2024

0

3

1

+655

help algebra

Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

ABJeIIy Apr 2, 2024

0

5

2

+655

i need help

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{11}{12}.$ How many terms of this sequence are greater than $1?$

ABJeIIy Apr 2, 2024

0

3

1

+655

help help

A geometric sequence has $400$ terms. The first term is $1000$ and the common ratio is $-\frac{8}{9}.$ How many terms of this sequence are greater than $1?$

ABJeIIy Apr 2, 2024

0

3

1

+655

help need help

When the same constant is added to the numbers $60,$ $120,$ and $140,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

ABJeIIy Apr 2, 2024

0

3

1

+655

help me with algebra

The system of equations
{xy}/{x + y} = 1,{xz}/{x + z} = 1, {yz}/{y + z} = 3
has exactly one solution. What is z in this solution?

ABJeIIy Apr 2, 2024

0

3

1

+655

help algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{1 + \cfrac{1}{4}}}}.

ABJeIIy Apr 2, 2024

0

3

0

+655

help me help help

ABJeIIy Apr 2, 2024

0

4

1

+655

help algebra

Let x and y be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

ABJeIIy Apr 2, 2024

0

2

+655

help me

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

ABJeIIy Apr 2, 2024

0

3

+655

help plz algebra

CPhill ●●●

ABJeIIy Apr 2, 2024

0

1

2

+655

help help

Let a and b be the roots of 5x^2 - 11x + 4 = -3x^2 - 17x + 5. Find a^3 + b3.

Let u and v be the solutions to 3x^2 + 5x + 7 = -4x^2 + 3x - 14. Find 1/u^2 + 1/v^2.

ABJeIIy Apr 2, 2024

0

3

1

+655

help algebra

How many ways can I put down two indistinguishable pieces on an ordinary 8x8 chessboard, if the pieces must either be in the same row or be in the same column?

ABJeIIy Apr 2, 2024

0

3

1

+18

Chess dubs

For how many three-digit positive integers is the sum of the digits equal to 5?

Umeko1.0 Apr 2, 2024

0

2

1

+18

Halp: Urgent!

Let a1, a2, a3, ..., a9, a10 be an arithmetic series. If a1 + a3 = 12 and a2 + a4 + a6 = 8, then find a1.

Umeko1.0 Apr 2, 2024

0

4

1

+655

plz help help

Laverne starts counting out loud by ${}5$'s. She starts with $2$. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds $20,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

ABJeIIy Apr 2, 2024

0

3

1

+655

need help now

Bosco ●

ABJeIIy Apr 2, 2024

0

3

1

+655

help help

Let a1, a2, a3, ... be an arithmetic series. Let Sn denote the sum of the first n terms. If S1 = 5 and S2 = 15, then find S15.

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

ABJeIIy Apr 2, 2024

0

3

0

+655

help plz

ABJeIIy Apr 2, 2024

0

2

0

+655

help me help

Find the minimum distance from any lattice point to the line $y = \frac{5}{3} x + \frac{12}{7}.$

ABJeIIy Apr 2, 2024

0

3

1

+655

help me plz

What is the area of the region bounded by the graphs of $y = |x + 2| - |x - 2|$ and $y = |x + 1| - |x - 5|$?

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

ABJeIIy Apr 2, 2024

0

4

0

+655

help plz

ABJeIIy Apr 2, 2024

0

3

5

+655

need help

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

ABJeIIy Apr 2, 2024

0

2

+655

Quadratic

https://imgur.com/a/4vuTIpm
14. A game show uses a large spinner of radius 15 feet that rotates at a constant rate to determine which prizes contestants win. The figure above provides a representation of the wheel in the xy-plane read more ..

ABJeIIy Apr 2, 2024

0

3

0

+9

Can someone Help me with my precalc question?

ddddddddddd Apr 2, 2024

+1

4

0

+9

Can someone help me with this precalc question? very stuck.

https://imgur.com/a/4vuTIpm
PLEASE I HAVE AN EXAM TM MORNING AND THIS IS THE ONE QUESTION IM STUCK ON IN THE REVIEW

ddddddddddd Apr 2, 2024

+1

2

1

+178

help me please!

Find constants A and B such that for all x such that and .

Find all solutions of the equation

ABJelly Apr 2, 2024

+1

2

1

+178

please help!!

Let and be real numbers such that
What is the largest possible value of

ABJelly Apr 2, 2024

+1

3

1

+178

Let and be real numbers such that What is the largest possible value of

An expression is well-defined if you can compute its value without any illegal operations. Examples of expressions that are not well-defined include and . For what values of is the expression
well-defined? read more ..

ABJelly Apr 2, 2024

+2

4

1

+178

please help me!!

Can you solve this?
Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square. If $PQ = 6$ and $PR = 6$, then what is the side read more ..

ABJelly Apr 2, 2024

0

2

1

+854

Geometry

Can you solve this?
In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 1$ and $DF = 2$, then read more ..

Akhain1 Apr 2, 2024

0

3

1

+854

Triangle

Can you solve this?
In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 18$, $BC = 18$, $CE = 6$, $AC = 14$ and $AB = 10$, then what is $DE$ read more ..

Akhain1 Apr 2, 2024

0

3

1

+854

Triangles

Can you do these difficult geometry questions?
1.

2.
<#> read more ..

Akhain1 Apr 2, 2024

0

2

+85

Circles

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

Akhaim1 Apr 2, 2024

0

3

0

+1002

Counting

kittykat Apr 2, 2024

0

3

0

+1002

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

kittykat Apr 2, 2024

0

2

1

+1002

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

kittykat Apr 2, 2024

0

5

1

+1002

Counting

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

kittykat Apr 2, 2024

+1

2

1

+655

help algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

ABJeIIy Apr 2, 2024

0

3

1

+655

plz help me

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

ABJeIIy Apr 1, 2024

0

3

1

+655

need help

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 4x + 5. Compute (a - 4b)(b - 4a).

ABJeIIy Apr 1, 2024

0

3

1

+655

help with algebra

Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 14x + 2. Compute a^3/b^3 + b^3/a^3.

ABJeIIy Apr 1, 2024

0

3

1

+655

Roots

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 = 24$. What is the value of $b$ in this ordered pair?

ABJeIIy Apr 1, 2024

0

3

1

+655

help I need help

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

ABJeIIy Apr 1, 2024

0

3

1

+655

help me help me

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

ABJeIIy Apr 1, 2024

0

4

0

+854

Polygon

Akhain1 Apr 1, 2024

0

2

1

+854

Polygon

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

Akhain1 Apr 1, 2024

0

5

0

+655

help with algebra help

ABJeIIy Apr 1, 2024

0

4

1

+655

i need help now

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

(1) Let a1, a2, a3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a1, a2, a3, \dots, a{10} be real numbers such that read more ..

ABJeIIy Apr 1, 2024

0

3

0

+655

help me plz

ABJeIIy Apr 1, 2024

0

4

1

+655

help with algebra now

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

Find constants A and B such that
\frac{2x + 11 - 5x + 17}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}
for all $x$ such that $x\neq -1$ and $x\neq 2$.

ABJeIIy Apr 1, 2024

0

3

0

+655

help me help

ABJeIIy Apr 1, 2024

0

4

1

+655

help me fast

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
x^2 - 2x + 1
x^2 - 4x - 4
x^2 + 6x - 9 read more ..

Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$

ABJeIIy Apr 1, 2024

0

3

0

+655

really need help

ABJeIIy Apr 1, 2024

0

3

0

+655

I need help plz

Simplify the expression
\frac{3}{\sqrt{2}} + \frac{1}{\sqrt{18}} - \frac{6}{\sqrt{3}} + \frac{9}{\sqrt{2}}

ABJeIIy Apr 1, 2024

0

3

0

+655

help me plz

Let $r$ and $s$ be the roots of $2x^2 + 5x - 13 = x^2 - 4x + 7.$ Find $r^2 + s^2.$

ABJeIIy Apr 1, 2024

0

5

0

+655

help need help

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} + \frac{1}{\sqrt{18}}.

ABJeIIy Apr 1, 2024

0

6

0

+854

Algebra

What is the smallest positive integer value of n such that (√3/2-sqrt(2)/2*i)^n is real?

Akhain1 Apr 1, 2024

0

2

0

+854

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

Akhain1 Apr 1, 2024

0

3

1

+854

Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to 3.15. Gary orders a bagel and four muffins, which comes out to 7.85. Larry orders a piece of toast, two bagels, and three muffins, which comes out to 9.75. read more ..

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 21m + 6n + 15m - 5n + ___

Akhain1 Apr 1, 2024

0

3

0

+655

help me now

ABJeIIy Apr 1, 2024

0

2

0

+655

Need help now

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 5} = \frac{3b}{5}.

ABJeIIy Apr 1, 2024

0

3

0

+655

Really need help

Find the area of the region that is enclosed by the graph of the equation
4x^2 - 12x + 4y^2 + 56y - 491 = 8x - 16y + 301

ABJeIIy Apr 1, 2024

0

5

0

+655

help help help

Let $B$ be the reflection of $A$ over the line $y = \frac{1}{2} x + 2$. Find the coordinates of $B$ if $A = (5,-1)$.

ABJeIIy Apr 1, 2024

0

5

0

+655

help help

A line and a circle intersect at A and B. Find the coordinates of the midpoint of \overline{AB}.
The ilne is y = 3x - 2, and the circle is (x - 4)^4 + (y - 5)^2 = 68.

ABJeIIy Apr 1, 2024

0

4

0

+655

plz help fast

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

ABJeIIy Apr 1, 2024

0

3

0

+655

help meeeee!

Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$

ABJeIIy Apr 1, 2024

0

3

1

+655

help i really need help!

Solve the inequality x^3 + 4x > 5x^2 + 28x + x^3. Write your answer in interval notation.

For an integer n, the inequality
x^2 + nx + 15 < -21 - 7x + x^2
has no real solutions in x. Find the number of different possible values of n.

ABJeIIy Apr 1, 2024

0

4

0

+655

help plz! I need help!

ABJeIIy Apr 1, 2024

+1

3

1

+178

please help!!

Let , , and be real numbers such that What is the largest possible value of ?

Let . Evaluate . (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)

ABJelly Apr 1, 2024

+1

4

1

+178

please help!!

Find all values of t such that . If you find more than one value, then list the values you find in increasing order, separated by commas.

ABJelly Apr 1, 2024

+1

4

1

+178

please help!!

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

ABJelly Apr 1, 2024

0

4

0

+618

Polygon

bingboy Apr 1, 2024

0

4

0

+209

Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

fjeihqoO Apr 1, 2024

0

4

0

+209

counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

fjeihqoO Apr 1, 2024

0

2

1

+209

Probability

Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 3 orange balls and 2 purple read more ..

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

fjeihqoO Mar 31, 2024

0

1

+209

Counting

Let S be the set of all real numbers of the form
(a_1)/(3) + (a_2)/(3^2) + (a_3)/(3^3) + ...
where (a_i) is equal to either 0 or 1 or 2 for each i.
(a) Is the number 1/4 in the set S? read more ..

fjeihqoO Mar 31, 2024

0

4

0

+158

Algebra

siIviajendeukie Mar 31, 2024

+1

2

+158

Algebra

Compute
1 + \frac{3}{6} + \frac{15}{6^2} + \frac{27}{6^3}

Compute
\frac{1}{1 \times 4} + \frac{1}{7 \times 10} + \frac{1}{37 + 40}

siIviajendeukie Mar 31, 2024

+1

3

2

+158

Algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} read more ..

siIviajendeukie Mar 31, 2024

0

3

0

+158

Algebra

siIviajendeukie Mar 31, 2024

0

3

1

+16

Geometry

Let the incircle of △ABC be tangent to AB, BC, AC at points M, N, P, respectively. If ∡BAC = 30◦ , find [BP C] [ABC] · [BMC] [ABC] , where [ABC] denotes the area of △ABC.

Let
f(x)=(x-1)(x-3)(x+5)+72
Find the sum of all values of x such that f(x)=72 .

Sxchen1110 Mar 31, 2024

0

3

2

+8

Help Quick

Let
p(x)=1-(1/x)
what is p^6(-1/2)

hearth222 Mar 31, 2024

0

5

0

+8

I need help

hearth222 Mar 31, 2024

0

3

0

+84

Counting

Find the number of positive integers that satisfy both the following conditions:
* Each digit is a 1 or a 2 or 3
* The sum of the digits is 5

cooIcooIcooI17 Mar 31, 2024

0

3

0

+84

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

cooIcooIcooI17 Mar 31, 2024

0

2

0

+84

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

cooIcooIcooI17 Mar 31, 2024

0

4

0

+84

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

cooIcooIcooI17 Mar 31, 2024

0

4

0

+209

help counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

fjeihqoO Mar 31, 2024

0

3

0

+209

counting

Franklin the fly starts at the point (0,0) in the coordinate plane. At each step, Franklin takes a step to the right, left, up, or down. After 2 steps, how many different points could Franklin end up at?

fjeihqoO Mar 31, 2024

0

5

0

+209

counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

fjeihqoO Mar 31, 2024

0

5

0

+209

Counting

In how many ways can the numbers through be entered once each into the five boxes below so that all the given inequalities are true?
___ > ___ > ___ > ___ < ___

fjeihqoO Mar 31, 2024

0

3

0

+1465

Series

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 = 5 and a_2 + a_4 + a_6 + a_8 + a_{10} = 7, then find a_1.

bader Mar 31, 2024

0

3

0

+1465

Counting

Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6 in a row so that the sum of any two adjacent numbers is even.

bader Mar 31, 2024

-1

2

1

+357

Square

In the diagram, $ABCD$ is a square. Find $\sin \angle PAQ.$

Find the area of triangle $ABC,$ given that $AH=11$ and $HD=5.$

falafronk Mar 31, 2024

-1

2

0

+357

Triangle

falafronk Mar 31, 2024

+1

3

1

+357

Semicircles

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 31, 2024

0

3

0

+357

geometry

falafronk Mar 31, 2024

0

4

0

+655

Polynomial

There exists a polynomial f(x) and a constant k such that
(x^2 - 2x - 5) f(x) = 2x^4 - 4x^3 + kx^2.
What is k?

ABJeIIy Mar 31, 2024

0

4

0

+655

Coefficient

What is the coefficient of x in (x^3 + x^2 + x + 1)(7x^6 + 8x^5 - 4x^4 - 10x^3 + 12x^2 - 2x - 8)?

ABJeIIy Mar 31, 2024

0

3

0

+655

Polynomial

Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

ABJeIIy Mar 31, 2024

+1

2

1

+158

Fractions

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $2.$ The sum of the cubes of all the terms is $4.$ Find the common ratio.

siIviajendeukie Mar 31, 2024

0

2

1

+158

Series

Compute the sum
1 + \frac{1}{5} + \frac{4}{25} + \frac{8}{25} + \frac{16}{625}

siIviajendeukie Mar 31, 2024

0

2

1

+158

Sum

The system of equation
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5
has exactly one solution. What is $z$ in this solution?

siIviajendeukie Mar 31, 2024

0

2

0

+1002

System

kittykat Mar 31, 2024

0

3

1

+1002

help me

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

kittykat Mar 31, 2024

0

4

1

+1763

Constant term

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

tomtom Mar 31, 2024

0

2

0

+1763

System

tomtom Mar 31, 2024

0

3

1

+1763

Coefficient

Expand (x^2 + 1/x)*(x + x^4)^3.

Expand (x^2 + 1/x)*(x + x^4)^3.

tomtom Mar 31, 2024

0

2

1

+1763

Expand

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

tomtom Mar 31, 2024

0

2

1

+1037

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

parmen Mar 31, 2024

0

3

1

+1037

geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

parmen Mar 30, 2024

0

2

0

+1037

help geometry

parmen Mar 30, 2024

0

3

1

+1037

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

parmen Mar 30, 2024

0

4

1

+343

Probability

Compute
I got 0 but it was incorrect. I think I might be doing something wrong. Thanks!

ChiIIBill Mar 30, 2024

0

3

2

+29

Complex Number Arithmetic

jilin73 Mar 30, 2024

0

2

1

+64

Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the first n terms. If S_5=1/5 and S_10=1/10 then find S_15

Let f(x)= |x| and g(x)=x^2
Find all values of x for which f(x)>g(x)

SilviaJendeukie Mar 30, 2024

0

4

1

+4

pls help!!!!! due soon

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

bananapants25 Mar 30, 2024

0

3

1

+1002

Algebra

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

kittykat Mar 30, 2024

0

4

0

+1002

Domain

kittykat Mar 30, 2024

0

2

1

+64

Arithmetic Sequence

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 1000, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming read more ..

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

SilviaJendeukie Mar 30, 2024

0

4

0

+209

Probability

fjeihqoO Mar 30, 2024

0

4

2

+64

Arithmetic Sequence

Let a_1, a_2, a_3, ..., a_11, a_12 be an arithmetic sequence. If and , then find a_1.

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

SilviaJendeukie Mar 30, 2024

0

2

1

+1763

counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

tomtom Mar 30, 2024

0

2

1

+1763

counting

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

tomtom Mar 30, 2024

0

3

0

+209

Algebra

fjeihqoO Mar 30, 2024

0

3

0

+209

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

fjeihqoO Mar 30, 2024

0

4

0

+209

Algebra

All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $480$ square foot wall, in minutes?

fjeihqoO Mar 30, 2024

0

2

0

+209

Painting

All members of our painting team paint at the same rate. If $45$ members can paint a specific wall in $60$ minutes, then how long would it take $12$ members to paint the same wall, in minutes?

fjeihqoO Mar 30, 2024

0

3

0

+209

Rate problem

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

fjeihqoO Mar 30, 2024

0

3

0

+209

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

fjeihqoO Mar 30, 2024

0

4

0

+209

Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to 3.15. Gary orders a bagel and four muffins, which comes out to 7.85. Larry orders a piece of toast, two bagels, and three muffins, which comes out to 9.75. read more ..

fjeihqoO Mar 30, 2024

0

2

1

+1763

help geometry

An isosceles triangle has side lengths $8$ cm, $10$ cm and $10$ cm. The longest side of a similar triangle is $20$ cm. What is the perimeter of the larger triangle, in centimeters?

Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base. The areas of the cross sections are $216\sqrt{3}$ square feet and $200$ square feet. The two planes are $4$ feet apart. How far read more ..

tomtom Mar 30, 2024

0

3

1

+1465

need help

A circle is inscribed in a rhombus with sides of length 4 cm. If the two acute angles in the rhombus each measure $90^{\circ}$, what is the length of the circle's radius? Express your answer in simplest radical form.

bader Mar 30, 2024

0

2

1

+1465

Geometry

Triangle $ABC$ is similar to triangle $XYZ$ with side $AB$ measuring $14$ units, side $BC$ measuring $8$ units and side $XY$ measuring $16$ units. What is the measure of side $YZ?$

bader Mar 30, 2024

0

2

0

+1465

Triangle

bader Mar 30, 2024

0

2

0

+1465

Geometry

In rectangle $ABCD$, points $E$ and $F$ lie on segments $AB$ and $CD$, respectively, such that $AE = \frac{AB}{8}$ and $CF = \frac{CD}{5}$. Segment $BD$ intersects segment $EF$ at $P$. What fraction of the area of rectangle $ABCD$ lies in triangle $EBP$? read more ..

bader Mar 30, 2024

0

3

1

+854

need help

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3 - 4p + 7q,
q - 2r = -2 - 5q,
p + r = 9 + 10q.

A bag contains yellow, green, blue, and white marbles. The ratio of yellow, green, blue, white marbles is $4:1:2:3$. If the bag contains $20$ marbles, then how many blue marbles are there?

Akhain1 Mar 30, 2024

0

2

1

+854

Ratios

Real numbers $a$ and $b$ satisfy
a + ab^2 = 250ab + ab^3
a - ab^2 = 240ab - 50b^2
Enter all possible values of a, separated by commas.

Akhain1 Mar 30, 2024

0

4

0

+854

Help algebra

Akhain1 Mar 30, 2024

0

4

1

+209

Counting

Find the number of times the digit $9$ appears in the list of all integers from $1$ to $750$. (The number $ 99 $, for example, is counted twice, because $9$ appears two times in it.)

At a meeting, five scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the scientists must all sit together (in five consecutive seats) and the mathematicians must sit read more ..

fjeihqoO Mar 30, 2024

0

3

0

+209

Help with counting

fjeihqoO Mar 30, 2024

0

4

0

+209

Help probability

A point is randomly chosen inside a square of side length 2. What is the probability that the distance between the chosen point and the nearest corner of the square is between 1/2 and 1?

fjeihqoO Mar 30, 2024

0

4

0

+854

Roots

Let $a$ and $b$ be the roots of the quadratic equation $2x^2+6x-14=x^2-8x+2$. What is the value of $(2a-3)(4b-6)$?

Akhain1 Mar 30, 2024

0

5

0

+854

help quadratic

One root of the quadratic equation $x^2 + bx -28 = 4x + 14$ is $-7$. What is the value of $b$?

Akhain1 Mar 30, 2024

0

3

0

+854

Quadratic

The quadratic equation $3x^2+4x-9 = 2x^2-6x+1$ has two real roots. What is the sum of the squares of these roots?

Akhain1 Mar 30, 2024

+1

3

1

+178

Please help!!!

What values of x satisfy ? Express your answer in interval notation.

Find all c such that |c+5| - 3c = 10. Enter all the solutions, separated by commas.

ABJelly Mar 30, 2024

+1

4

1

+178

Please help!!

Suppose a does not equal 0. Compute log_{8^a} 4^b in terms of a and b.

ABJelly Mar 30, 2024

+1

4

1

+178

Please help

Fill in the blanks with numbers to make a true equation
3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 = __ (x + __)^3 + __(x + __)^2 + __x + ___

ABJelly Mar 30, 2024

0

3

0

+854

Need help

Akhain1 Mar 30, 2024

0

4

0

+854

Parabola

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a + b + c$. (The grid lines are one unit apart.)
The parabola passes through (-3,7), (-1,5), and (2,8).

Akhain1 Mar 30, 2024

0

5

0

+854

Triangle

In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $\frac{AP}{2} = \frac{PQ}{5} = \frac{QB}{11}$ and $\frac{AR}{8} = \frac{RC}{13},$ then find $\frac{[QBC]}{[CRQ]}.$

Akhain1 Mar 30, 2024

0

5

0

+854

triangle

In triangle $ABE,$ $C$ and $D$ are points on sides $\overline{BE}.$ If $BD = 18$, $CE = 7$, $[ABC] = 13$, and $[ADE] = 22$, then find $[ACD]$.

Akhain1 Mar 30, 2024

0

2

+51

triple trouble

a. A baking club wants to form an executive committee. There are 12 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 5 people?
b. A baking club wants to form an executive committee. read more ..

I run a book club with z people, not including myself. Every day, for 400 days, I invite 5 members in the club to review a book. What is the smallest positive integer z so that I can avoid ever having the exact same group of 5 members over all 400 days read more ..

fjeihqo0 Mar 30, 2024

0

2

+51

hey guys

How are linear velocity and angular velocity related?
Drag a word, phrase, or equation into each box to correctly complete the statements.
Angular velocity is the change in distance over time, where distance is _____.
Angular read more ..

fjeihqo0 Mar 30, 2024

0

5

0

+52

How are linear velocity and angular velocity related?

xXValeXx Mar 30, 2024

0

3

0

+854

help with triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ = 36$, $PM read more ..

Akhain1 Mar 30, 2024

0

3

0

+1002

Sequence

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$

kittykat Mar 30, 2024

0

3

0

+1002

Algebra

All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

kittykat Mar 30, 2024

0

2

1

+1002

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

kittykat Mar 30, 2024

0

4

0

+1002

Counting

kittykat Mar 30, 2024

0

3

0

+854

Polynomials

Let $f(x) = x^3 + 3x^2 + 4x - 7$ and $g(x) = 2x^8 - 8x^7 + 4x^6 - x^5$. What is the coefficient of $x^2$ in the sum $f(x) + g(x)$?

Akhain1 Mar 29, 2024

0

6

0

+854

Polynomials

Let $b$ be a constant. What is the smallest possible degree of the polynomial $f(x) + b \cdot g(x)$, where $f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5$ and $g(x) = x^15 - 3x^14 - 2x^13 - 6x^12 + 14x - 10$?

Akhain1 Mar 29, 2024

0

5

0

+854

Algebra

Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

Akhain1 Mar 29, 2024

0

4

0

+854

Polynomials

Determine all of the following for $f(x) \cdot g(x)$, where $f(x) = -x^2+ 8x - 5$ and $g(x) = x^3 - 11x^2 + 2x$.
Leading term
Leading coefficient
Degree read more ..

Akhain1 Mar 29, 2024

0

4

1

+854

Triangle

Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

Akhain1 Mar 29, 2024

0

5

0

+854

Geometry

Akhain1 Mar 29, 2024

0

3

2

+64

Geometric Sequence

A geometric sequence has 400 terms. The first term is 1000 and the common ratio is -1/3 How many terms of this sequence are greater than 1?

The equation has exactly two different complex solutions. Find all possible complex values for .
Basically I expanded it and stuff and then made a quadratic and used the discriminant to get . So . But the problem wants all complex read more ..

SilviaJendeukie Mar 29, 2024

0

3

2

+4

Help Please

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

somebodyrandom Mar 29, 2024

0

5

0

+854

help angles

Akhain1 Mar 29, 2024

0

2

0

+854

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

Akhain1 Mar 29, 2024

0

4

1

+854

Angles

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$,
<read more ..

Akhain1 Mar 29, 2024

0

4

0

+854

Geometry

Akhain1 Mar 29, 2024

0

2

0

+854

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, read more ..

Akhain1 Mar 29, 2024

0

4

3

+854

help coordinates

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = 3,$ then find the side length of the hexagon.

Akhain1 Mar 29, 2024

0

3

1

+854

Hexagon

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, and a regular -gon, all with the same side length, also completely read more ..

Akhain1 Mar 29, 2024

0

3

0

+854

Polygons

Akhain1 Mar 29, 2024

0

4

1

+854

Diagonals

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

A sphere of radius $4$ inches is inscribed in a cone with a base of radius $8$ inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth.

Akhain1 Mar 29, 2024

0

4

1

+854

geometry

Rose has a spherical plum of radius $2$ and a spherical watermelon of radius $8$. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, she places a golf ball inside read more ..

Akhain1 Mar 29, 2024

0

3

1

+854

geometry

A sphere is inscribed in a cone with height $3$ and base radius $3$. What is the ratio of the volume of the sphere to the volume of the cone?

Akhain1 Mar 29, 2024

0

3

1

+854

help geometry

Consider the quadratic equation ax^2 + bx + c = 0 with a, b, c integers from -4 to 4 and a is not 0. The solutions to this equation are in the form where D is square free . Determine the largest possible value of D.

Akhain1 Mar 29, 2024

0

2

1

+80

HELP

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

Lilliam0216 Mar 29, 2024

0

3

0

+593

Constants

LiIIiam0216 Mar 29, 2024

0

3

0

+593

Help with floor

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

LiIIiam0216 Mar 29, 2024

0

3

7

+85

Hard geometry probs

Don't be dicouraged if you can't solve these
1.

2.
<#> read more ..

●●●●●●●

Akhaim1 Mar 29, 2024

0

4

0

+593

Inequalities

(1) Let a_1, a_2, a_3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a_1, a_2, a_3, \dots, a_{10} be real numbers such that read more ..

LiIIiam0216 Mar 29, 2024

0

3

1

+593

Absolute value

Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30

The largest term in the binomial expansion of is of the form , where and are relatively prime positive integers. What is the value of ?
Please help! Thank you so much! All I know is to use the binomial read more ..

LiIIiam0216 Mar 29, 2024

+1

4

2

+38

Please Help! Thank you

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

greenplanet2050 Mar 29, 2024

0

3

1

+854

Polygon

jilin73 ●

Akhain1 Mar 28, 2024

0

3

1

+854

Quadrilateral

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region. read more ..

hairyberry ●

Akhain1 Mar 28, 2024

0

3

0

+854

Polygons

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

Akhain1 Mar 28, 2024

0

6

0

+854

Quadrilateral

Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EAD$ is $9.$ If $AE:EB = 3:4$ and the height of parallelogram $ABCD$ is $10$, read more ..

Akhain1 Mar 28, 2024

0

5

0

+854

help geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

Akhain1 Mar 28, 2024

0

2

1

+51

halp!

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if the mathematicians must all sit together (in 4 consecutive seats) and the 3 scientists must read more ..

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

fjeihqo0 Mar 28, 2024

0

2

1

+51

help plz

Four adults and four students are to be seated at a circular table. In how many different ways can they be seated if each adult must be next to two students? (Two seatings are considered the same if one can be rotated to form the other.) read more ..

fjeihqo0 Mar 28, 2024

0

2

+51

help

How are linear velocity and angular velocity related?
Drag a word, phrase, or equation into each box to correctly complete the statements.
Angular velocity is the change in distance over time, where distance is _____.
Angular read more ..

fjeihqo0 Mar 28, 2024

0

2

1

+52

How are linear velocity and angular velocity related?

Two wheel gears are connected by a chain. The larger gear has a radius of 8 centimeters and the smaller gear has a radius of 3 centimeters. The smaller gear completes 24 revolutions in 20 seconds.
What is the linear velocity of each read more ..

xXValeXx Mar 28, 2024

0

3

1

+52

Angular and Linear Velocities

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

xXValeXx Mar 28, 2024

+1

3

1

+854

Geometry

WillBill ●

Akhain1 Mar 28, 2024

0

2

0

+854

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

Akhain1 Mar 28, 2024

0

4

0

+854

help geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

Akhain1 Mar 28, 2024

0

5

0

+854

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

Akhain1 Mar 28, 2024

0

4

0

+854

help geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

Akhain1 Mar 28, 2024

0

3

10

+85

Geometry

Not so hard problems
1.

2.
<#> 3.<#> read more ..

●●●●●●●●●●

Akhaim1 Mar 28, 2024

0

5

0

+593

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

LiIIiam0216 Mar 28, 2024

0

2

+593

Rate question

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

LiIIiam0216 Mar 28, 2024

0

3

0

+854

Polynomial

Akhain1 Mar 28, 2024

0

4

0

+854

Polynomial

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

Akhain1 Mar 28, 2024

0

3

0

+854

Coefficient

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

Akhain1 Mar 28, 2024

0

3

1

+593

Quadratic

If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?

Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

LiIIiam0216 Mar 28, 2024

0

6

1

+854

Sum

If $s$ is a real number, then what is the smallest possible value of $2s^2 - 8s + 19 - 7s^2 - 8s + 20$?

Akhain1 Mar 28, 2024

0

3

1

+593

I need help

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?

LiIIiam0216 Mar 28, 2024

0

4

1

+593

help me

When the same constant is added to the numbers $60,$ $120,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

LiIIiam0216 Mar 28, 2024

0

4

0

+854

Series

Akhain1 Mar 28, 2024

0

5

0

+854

Series

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.

Akhain1 Mar 28, 2024

0

2

+80

I checked the other posts and they all didn't work.

Jeri finds a pile of money with at least 200. If she puts 50of the pile in her left pocket, gives away 2/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away 200 of the original read more ..

Laverne starts counting out loud by ${}5$'s. She starts with $2$. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds $20,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

Lilliam0216 Mar 28, 2024

0

4

1

+854

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

Akhain1 Mar 28, 2024

0

4

1

+854

Series

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

Akhain1 Mar 28, 2024

0

5

0

+854

Function

Akhain1 Mar 28, 2024

0

5

1

+854

Coordinates

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

Akhain1 Mar 28, 2024

0

2

1

+854

Logarithm

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

Akhain1 Mar 28, 2024

0

4

0

+84

Probability

cooIcooIcooI17 Mar 28, 2024

0

4

0

+84

help with counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

cooIcooIcooI17 Mar 28, 2024

0

3

0

+84

need help

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

cooIcooIcooI17 Mar 28, 2024

0

4

0

+84

Counting question

Find the number of positive integers that satisfy both the following conditions:
Each digit is a $1$ or a $2$ or a $3$
The sum of the digits is $5$

cooIcooIcooI17 Mar 28, 2024

0

3

1

+84

help counting

Joanna has six beads that she wants to assemble into a bracelet. Four of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

cooIcooIcooI17 Mar 28, 2024

0

5

1

+41

Help

Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $2$ steps, how many different points could Franklin end up at?

Solarblade Mar 28, 2024

0

4

1

+84

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

cooIcooIcooI17 Mar 28, 2024

0

3

0

+84

help plz

cooIcooIcooI17 Mar 28, 2024

0

3

1

+84

help counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $300,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between read more ..

cooIcooIcooI17 Mar 28, 2024

0

3

1

+84

counting

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if the mathematicians must all sit together (in 4 consecutive seats) and the 3 scientists must read more ..

cooIcooIcooI17 Mar 28, 2024

0

2

1

+28

seating wars

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

coolcoolcool17 Mar 28, 2024

0

4

1

+28

Ms. Q's deck of cards...

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if each child must be next to two adults? (Two seatings are considered the same if one can be rotated to form the other.)

coolcoolcool17 Mar 28, 2024

0

3

2

+28

a child has to sit next to two adults

Let $x$, $y$, and $z$ be nonzero real numbers. Find all possible values of
\frac{x}{|x|} + \frac{y}{|y|} + \frac{z}{|z|} + \frac{x + y + z}{|x + y + z|}

coolcoolcool17 Mar 28, 2024

0

3

1

+1002

help algebra

hairyberry ●

kittykat Mar 27, 2024

0

2

1

+1002

Absolute value

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

Find $x$ if $\log_2 (\log_3 x) = \log_3 (\log_2 x).$

kittykat Mar 27, 2024

0

4

2

+1002

Logarithm

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

kittykat Mar 27, 2024

0

2

1

+1002

Logarithms

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained inside both triangles read more ..

kittykat Mar 27, 2024

0

6

0

+854

help geometry

Akhain1 Mar 27, 2024

0

3

1

+854

Laser

Let $ABCD$ be a square with side length $1.$ A laser is located at vertex $A,$ which fires a laser beam at point $X$ on side $\overline{BC},$ such that $BX = \frac{1}{2}.$ The beam reflects off the sides of the square, until it ends up at another read more ..

Let A1 A2 A3 ... A15 be a regular polygon. A rotation centered at $A_4$ with an angle of $\alpha$ takes $A_3$ to $A_5$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees.

Akhain1 Mar 27, 2024

0

4

0

+854

Rotation

Akhain1 Mar 27, 2024

0

4

0

+854

Dilation

Point $B$ is the image of point $A$ under a dilation with center $O$. If $OB = 30$, and the scale factor of the dilation is $5$, then what is $OA$?

Akhain1 Mar 27, 2024

0

3

1

+357

Rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

Find the area of parallelogram ABCD.

falafronk Mar 27, 2024

0

6

0

+357

Parallelogram

falafronk Mar 27, 2024

0

2

1

+357

Rhombus

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

falafronk Mar 27, 2024

0

3

0

+357

help trapezoid

falafronk Mar 27, 2024

0

2

0

+1465

Counting question

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

bader Mar 27, 2024

0

3

0

+1465

help counting

Determine the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

bader Mar 27, 2024

0

2

0

+1465

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

bader Mar 27, 2024

0

2

0

+1465

Counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three history textbooks are next to each other?

bader Mar 27, 2024

0

4

1

+4

help me!

Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 5, AC = 5, CB = 8
i dont really get how this works help plz!!

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

helpmeeee Mar 27, 2024

0

5

0

+854

Quadrilateral

Akhain1 Mar 27, 2024

0

4

0

+854

Triangle question

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

Akhain1 Mar 27, 2024

0

3

0

+854

help geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

Akhain1 Mar 27, 2024

0

2

3

+85

Hard Geometry Problems

These are difficult
1.

2.
<#> 3.<#> read more ..

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

Akhaim1 Mar 27, 2024

0

5

0

+854

Medians of a Triangle

Akhain1 Mar 27, 2024

0

2

1

+357

Trapezoid

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.

falafronk Mar 27, 2024

0

3

0

+357

Angles

falafronk Mar 27, 2024

0

3

1

+357

Triangle

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

You decide to take advantage of the store’s payment plan. The Chromebook costs $499.99. The payment plan’s terms are as follows: 18 equal monthly payments, 6% interest p.a., compounded monthly. What is the total cost that you will end up paying for the read more ..

falafronk Mar 27, 2024

0

4

2

+64

PLEASE HELP ASAP

All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co read more ..

SilviaJendeukie Mar 27, 2024

0

3

1

+357

Triangle

Bosco ●

falafronk Mar 27, 2024

0

3

2

+357

Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$

falafronk Mar 27, 2024

0

3

1

+357

Altitudes

The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

falafronk Mar 27, 2024

0

4

0

+593

Circles

LiIIiam0216 Mar 27, 2024

0

2

0

+593

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
\[f(p) = f(q) = f(r) = f(s) = 1\]
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

LiIIiam0216 Mar 27, 2024

-1

5

1

+593

Quadratic

Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.

Let $f(x) = x^2 + bx + 2 - 3x + 8$ for all real numbers $x$. For what real values of $b$ is $-2$ not in the range of the function $f(x)$? Express your answer in interval notation.

LiIIiam0216 Mar 27, 2024

0

3

0

+593

Quadratic

LiIIiam0216 Mar 27, 2024

+1

3

1

+5

help

A cylinder has a height of 6 centimeters and a diameter of 20 centimeters. What is its volume? Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

cubic centimeters

Arrange the following numbers in increasing order (smallest first, biggest last)
A = 2^(1/2)*4^(1/6)
B = (128)^(1/12)/64^(1/3)
C = (8^(1/5))^(2^2) read more ..

Notheydude23 Mar 27, 2024

0

3

0

+593

Numbers

LiIIiam0216 Mar 27, 2024

0

4

0

+593

Inequality

Solve the inequality
\[\frac{3-z}{z+1} \ge 2 + 7z.\]
Write your answer in interval notation.

LiIIiam0216 Mar 27, 2024

0

7

0

+593

Help inequality

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

LiIIiam0216 Mar 27, 2024

0

7

0

+593

Inequality

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

LiIIiam0216 Mar 27, 2024

+1

6

2

+10

URGENT question

All members of our painting team paint at the same rate. If $8$ members can paint a specific wall in $45$ minutes, then how long would it take $18$ members to paint the same wall, in minutes?

For a certain value of k, the system
x + y + 3z = 10 - x + 5y,
4x + 2y + 5z = 7 + 11y + 19z,
kx + z = 3 + 5y
has no solutions. What is this value of k?

ThreeLetters Mar 27, 2024

0

5

1

+593

System

Let a and b be the roots of the quadratic x^2 - 5x + 3 = -2x^2 + 11x - 14. Find the quadratic whose roots are a^2 and b^2.
x^2 + ___x + ___

LiIIiam0216 Mar 27, 2024

0

5

1

+593

Quadratic

Let a and b be the solutions to 7x^2 + x - 5 = -3x^2 - 9x - 4. Compute (a - 4)/(b - 4) + (b - 4)/(a - 4).

LiIIiam0216 Mar 27, 2024

0

3

0

+593

Algebra

LiIIiam0216 Mar 26, 2024

0

4

1

+593

Quadratic

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.

Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 - 17x + 6. Find 1/a^3 + 1/b^3.

LiIIiam0216 Mar 26, 2024

0

4

0

+593

Quadratic

LiIIiam0216 Mar 26, 2024

0

6

1

+357

Quadratic

Fill in the blanks to make a quadratic whose roots are 5 and -5.
x^2 + ___ x + ___

Bosco ●

falafronk Mar 26, 2024

0

3

1

+80

Solutions

Consider the quadratic equation ax^2 + bx + c = 0 with a, b, c integers from -4 to 4 and a is not 0. The solutions to this equation are in the form where D is square free . Determine the largest possible value of D.

The area of a square, in square units, is 38 more than 10 times the length of a side of the square, in units.
Find all possible values for the side length of the square.

Lilliam0216 Mar 26, 2024

0

2

1

+80

Area of a square

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

Lilliam0216 Mar 26, 2024

0

4

1

+357

Solid Geometry

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

falafronk Mar 26, 2024

0

3

0

+357

Pyramids

falafronk Mar 26, 2024

0

4

0

+357

help with geometry

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

falafronk Mar 26, 2024

0

4

1

+357

Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side AO and arc AB. Find the radius of the circle.

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

falafronk Mar 26, 2024

0

4

1

+854

Minimum

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

Akhain1 Mar 26, 2024

0

3

1

+854

help with floor

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

Akhain1 Mar 26, 2024

0

3

0

+854

Help algebra

Akhain1 Mar 26, 2024

0

5

0

+1002

Counting problem

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

kittykat Mar 26, 2024

0

5

0

+1002

Counting question

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

kittykat Mar 26, 2024

0

6

1

+357

help hard geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

falafronk Mar 26, 2024

0

4

0

+357

Semicircles

falafronk Mar 26, 2024

0

3

1

+618

Rectangle

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

bingboy Mar 26, 2024

0

2

1

+618

Geometry

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

bingboy Mar 26, 2024

0

3

1

+1465

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

bader Mar 26, 2024

0

3

1

+1465

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

bader Mar 26, 2024

0

3

1

+1465

Rates

Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

bader Mar 26, 2024

0

4

0

+593

Probability

LiIIiam0216 Mar 26, 2024

0

5

1

+593

need help

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 Mar 26, 2024

0

3

1

+593

counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Mar 26, 2024

+1

4

1

+593

need help

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

LiIIiam0216 Mar 26, 2024

0

5

4

+593

counting question

Help I need Venn Diagram
Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school.
$62$ read more ..

LiIIiam0216 Mar 26, 2024

0

5

1

+593

help counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters if exactly read more ..

LiIIiam0216 Mar 26, 2024

-1

7

0

+593

Counting

LiIIiam0216 Mar 26, 2024

0

3

1

+854

Chords

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX. read more ..

A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ, and is tangent to the other two sides. If XY = 10, XZ = 10, and YZ = 10*sqrt(2), then find the area of the semicircle.

Akhain1 Mar 26, 2024

0

5

1

+854

Semicircle

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

Akhain1 Mar 26, 2024

0

3

1

+854

Tangent circles

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

Akhain1 Mar 26, 2024

+1

6

1

+854

need help

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

Akhain1 Mar 26, 2024

0

4

1

+854

help coordinates

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
\[PA^2 + PB^2 + PC^2 = 3PQ^2 + k.\]
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

Akhain1 Mar 26, 2024

0

2

1

+854

Coordinates

3D Geometry problems
1.

2.
<#> 3.<#> read more ..

Akhain1 Mar 26, 2024

0

4

2

+85

More Geometry

Can you solve these?
1.

2.
<#> 3.<#> read more ..

Akhaim1 Mar 26, 2024

0

3

+85

Geometry

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
\[x^2 + y^2 = 4x - 8y + 17x - 5y + 25,\]
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

Akhaim1 Mar 25, 2024

0

5

1

+1465

Circle

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid.

bader Mar 25, 2024

0

4

0

+357

Pyramid

falafronk Mar 25, 2024

0

4

1

+357

Prism

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

falafronk Mar 25, 2024

0

7

0

+357

Prism

falafronk Mar 25, 2024

0

5

3

+1465

help with trig

Let \theta be an acute angle. If $\cos \theta = \frac{1}{4},$ then what is $\sin \theta?$

Let x be an acute angle such that \tan x + \sec x = 0. Find $\cos x$.

bader Mar 25, 2024

0

4

1

+1465

Trig

The cone below has a lateral surface area of $16 \sqrt{5} \cdot \pi$. Find the volume of the cone.

bader Mar 25, 2024

-1

3

0

+343

Cone

ChiIIBill Mar 25, 2024

0

6

0

+4

Circles

What is the length of PC?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.
https://static.k12.com/nextgen_media/assets/8093696-NG_GMT_SemB_10_UT_04.png

Sugarplum Mar 25, 2024

-1

3

0

+343

Solid geo

Triangle $ABC$ below is rotated completely around side $\overline{BC}$, sweeping out a solid in space. Find the volume of the solid. read more ..

ChiIIBill Mar 25, 2024

-1

5

0

+343

3d geo

A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

ChiIIBill Mar 25, 2024

+1

3

1

+343

3d geo

Find the total surface area and the volume of the conical frustum below.

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

ChiIIBill Mar 25, 2024

0

5

0

+854

Polygon

Akhain1 Mar 25, 2024

0

4

0

+854

Square

In the diagram, ABCD is a square. Find PR.

L, M, N, O, are midpoints of sides.
Side AB = 12

Akhain1 Mar 25, 2024

0

3

1

+854

Perimeter

The perimeter of the triangle below is an integer. What is the smallest possible value of the perimeter? (Assume that the triangle is non-degenerate.) read more ..

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

Akhain1 Mar 25, 2024

0

3

0

+357

Square

falafronk Mar 25, 2024

0

4

2

+357

Square

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

falafronk Mar 25, 2024

0

4

0

+357

Geometry

falafronk Mar 25, 2024

0

2

0

+357

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

falafronk Mar 25, 2024

+1

3

2

+854

counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

Akhain1 Mar 25, 2024

+1

4

1

+357

Geometry

In triangle ABC, point X is on side BC such that AX = 10, BC = 10, CX = 5, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 25, 2024

+1

5

0

+357

Triangle

falafronk Mar 25, 2024

+1

2

1

+458

Triangle

Find the circumradius of triangle $ABC.$

Write as a product of two monic quadratics with integer coefficients.

booboo44 Mar 25, 2024

+1

5

+14

help me out!!

Find the inradius of triangle ABC.

svphxxo Mar 25, 2024

-1

3

1

+458

Triangle

svphxxo ●

booboo44 Mar 25, 2024

-1

5

0

+357

Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side $\overline{AO}$ and arc $AB.$ Find the radius of the circle.

falafronk Mar 25, 2024

-1

5

0

+357

triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

falafronk Mar 25, 2024

0

4

0

+854

help counting

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five chi read more ..

Akhain1 Mar 25, 2024

-1

5

0

+357

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $BC = \sqrt{3}$, then find $AB$. read more ..

falafronk Mar 25, 2024

-1

3

0

+357

Circles

The two circles below are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$

falafronk Mar 25, 2024

-1

6

0

+357

Circle

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

falafronk Mar 25, 2024

-1

5

0

+357

help maximum

Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.

falafronk Mar 25, 2024

0

5

1

+70

Find the area of triangle ABC, given that AH=11 and HD=5.

Find the area of triangle ABC, given that AH=11 and HD=5. read more ..

Triangle DEF is equilateral. Find AE read more ..

faiafronk Mar 25, 2024

0

5

1

+70

equilateral trianlge (last time was wrong)

In triangle ABC, point X is on side BC such that AX = 13, BC = 10, CX = 4, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.
(no diagram)

faiafronk Mar 25, 2024

0

6

1

+70

geometry

Semicircles are constructed on AB, AC,and BC. A circle is tangent to all three semicircles. Find the radius of the circle. read more ..

faiafronk Mar 25, 2024

0

4

1

+70

help!

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

faiafronk Mar 25, 2024

-1

5

0

+357

Minimum

falafronk Mar 25, 2024

-1

4

0

+357

Temperature

The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?

falafronk Mar 25, 2024

-1

5

1

+357

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BZ$.

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BC$.

falafronk Mar 25, 2024

-1

3

1

+357

Geometry

In the diagram below, P is a point inside square ABCD. Find x.

falafronk Mar 25, 2024

-1

3

1

+357

Square

Two lines $p$ and $q$ intersect at $X$. The angle between lines $p$ and $q$ is $45^\circ$. Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$. Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection read more ..

falafronk Mar 25, 2024

-1

3

1

+357

Geometry

Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.

falafronk Mar 25, 2024

0

2

1

+1763

Algebra

Find all values of t such that \lfloor t\rfloor = 3t + 4 - \lfloor 2t \rfloor. If you find more than one value, then list the values you find in increasing order, separated by commas.

tomtom Mar 25, 2024

0

4

0

+618

Floor function

bingboy Mar 25, 2024

0

3

0

+618

Function

The function f(x) is defined for 1 \le x \le 5 as follows:
-2x + 4 & \text{if }1 \le x \le 2, \\
5 - x & \text{if }2 < x \le 3, \\
9 - 2x & \text{if }3 < x \le 4, \\
6 - x & \text{if }4 < x \le read more ..

bingboy Mar 25, 2024

0

3

1

+618

help counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

bingboy Mar 25, 2024

0

4

1

+84

counting

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 4 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 40 miles per hour, the trip takes 5 hours. How many read more ..

cooIcooIcooI17 Mar 25, 2024

0

4

1

+1763

Algebra

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

tomtom Mar 25, 2024

-1

6

0

+357

help how do you do this

falafronk Mar 25, 2024

0

5

0

+357

help geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

falafronk Mar 25, 2024

0

6

0

+357

need help

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

falafronk Mar 25, 2024

0

4

1

+357

help geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle ABC = 60^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

hairyberry ●

falafronk Mar 25, 2024

0

7

0

+357

Geometry

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 1 and QC = 4. Find sin angle PAQ.

falafronk Mar 24, 2024

0

5

0

+357

help with triangle

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

falafronk Mar 24, 2024

0

5

0

+357

help plz

In triangle ABC, point X is on AC such that angle BXA=90 degrees, AX=12 and CX=5 What is BX?

falafronk Mar 24, 2024

0

3

1

+1002

Area

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

Point P is on the side of line AC of triangle ABC such that angle ACB =angle ABC, and angle ABC - angle ACB = 42 degrees. Find angle PBC in degrees.

kittykat Mar 24, 2024

0

4

1

+4

Help

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

Kyle111 Mar 24, 2024

0

4

0

+1002

Triangle

kittykat Mar 24, 2024

0

2

1

+1002

Triangle

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

kittykat Mar 24, 2024

0

3

1

+1002

Triangle

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

kittykat Mar 24, 2024

0

5

0

+1002

need help

kittykat Mar 24, 2024

-1

4

1

+1002

help geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

In parallelogram EFGH, let M be the point on EF such that FM:ME = 3:5 and let N be the point on EH such that HN:NE = 2:5. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ/FH.

kittykat Mar 24, 2024

0

4

1

+1002

geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

kittykat Mar 24, 2024

0

5

1

+357

Triangle

How many real solutions are there to the equation √x+5= |2x|? (Note: Both x and 5 are under the same square root symbol)

falafronk Mar 24, 2024

0

3

1

+16

Please Help

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

Arhantio Mar 24, 2024

0

2

1

+357

help counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

falafronk Mar 24, 2024

0

5

0

+357

counting

falafronk Mar 24, 2024

0

3

0

+1030

help geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

blackpanther Mar 24, 2024

0

3

1

+1030

Trapezoid

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Mar 24, 2024

0

4

1

+1030

Polygons

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

blackpanther Mar 24, 2024

0

7

0

+854

need help

Akhain1 Mar 24, 2024

0

3

1

+854

Circle sector

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

Let $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19.$ Point $P$ is on segment $AB$ with $AP = 7$, and $Q$ is on segment $CD$ with $CQ = 8$. The line through $P$ and $Q$ intersects the circle at $X$ and $Y$. If $PQ = 25$, find read more ..

Akhain1 Mar 24, 2024

0

3

1

+357

help geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

falafronk Mar 24, 2024

0

5

1

+357

help!! need help

Find the area of triangle ABC, given that AH=11 and HD=5 read more ..

falafronk Mar 24, 2024

0

4

+70

halp!

Joanna has seven beads that she wants to assemble into a bracelet. Five of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

faiafronk Mar 24, 2024

0

5

0

+357

Need help

falafronk Mar 24, 2024

0

6

0

+357

Help Probability

Raina places the following balls into a bag. She draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 6 orange balls and 6 purple read more ..

falafronk Mar 24, 2024

0

2

1

+854

Square

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

Akhain1 Mar 24, 2024

0

4

0

+1465

Triangle

bader Mar 24, 2024

0

4

1

+1465

Geometry

Points $T$ and $U$ lie on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PT}$ and $\overline{PU}$ are tangent to the circle. If $\angle TOP = 45^{\circ}$, then what is the measure of minor arc $TU$, in deg read more ..

Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is spades or an Ace, the second card is red, and the third card is a nine.

bader Mar 24, 2024

0

4

0

+357

Probability

falafronk Mar 24, 2024

0

3

1

+357

Counting

Syd chooses two different primes, and multiplies them. If both primes are greater than 4, and the resulting product is less than 600, then how many different products could Syd have ended up with?

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word ARCH?
A
RRR read more ..

falafronk Mar 24, 2024

0

6

0

+357

help counting

falafronk Mar 24, 2024

0

3

+64

PLEASE HELP ASAP!!!!

Let

Evaluate (This sum has terms, one for the result when we input each integer from to into .)

CPhill ●●●

SilviaJendeukie Mar 24, 2024

0

4

1

+357

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

falafronk Mar 24, 2024

0

6

0

+357

Counting

falafronk Mar 24, 2024

0

4

0

+357

Probability

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
There are two queens, two kings, and two aces.

falafronk Mar 24, 2024

0

4

0

+357

Probability

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

falafronk Mar 24, 2024

0

5

1

+60

math problem

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

Let $x$ and $y$ be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

nathanl6656 Mar 24, 2024

0

7

0

+60

Algebra

nathanl6656 Mar 24, 2024

0

4

1

+1763

help with coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
\[PA^2 + PB^2 + PC^2 = 3PQ^2 + k.\]
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

tomtom Mar 24, 2024

0

4

1

+1763

help! coordinates

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.

tomtom Mar 24, 2024

0

3

1

+1763

help coordinates

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
\[x^2 + y^2 = 4x - 8y + 17x - 5y + 25,\]
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

tomtom Mar 24, 2024

0

5

0

+1763

Coordinates

tomtom Mar 24, 2024

0

4

1

+458

Pyramid

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid.

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

booboo44 Mar 24, 2024

0

4

0

+458

Prism

booboo44 Mar 24, 2024

0

5

0

+357

need help

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

falafronk Mar 24, 2024

0

5

0

+357

help pyramid

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G$, $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $ABCD$ is $18.$ Find the volume of pyramid $DEFG$.

falafronk Mar 24, 2024

0

4

0

+357

Prism

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $1.$ Also, the sum of all the edges of the prism is $2.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

falafronk Mar 24, 2024

0

5

0

+1002

Angles

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

kittykat Mar 24, 2024

0

7

0

+1002

Polygon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

kittykat Mar 24, 2024

0

6

0

+1002

Angles

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

kittykat Mar 24, 2024

0

2

0

+1030

Triangle

In triangle $ABC,$ $AC = BC$ and $\angle ACB = 90^\circ.$ Points $P$ and $Q$ are on $\overline{AB}$ such that $P$ is between $A$ and $Q$ and $\angle QCP = 45^\circ.$ If cos ACP = 2/3, then find cos BCQ.

blackpanther Mar 24, 2024

0

2

0

+1030

Triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

blackpanther Mar 24, 2024

0

2

0

+1030

geometry problem

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

blackpanther Mar 24, 2024

0

2

0

+1037

help with triangle

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

parmen Mar 24, 2024

0

2

0

+1037

Triangle

In triangle ABC, the angle bisector of angle BAC meets BC at D. If angle BAC=60 degrees, angle ABC=60 degrees and AD=24 then find the area of triangle ABC.

parmen Mar 24, 2024

0

3

0

+1037

Pyramid

A right pyramid has a square base. The area of each triangular face is one-third the area of the square face. If the total surface area of the pyramid is $432$ square units, then what is the volume of the pyramid in cubic units? read more ..

parmen Mar 24, 2024

0

4

0

+357

Circles

Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. Find $SW$.

falafronk Mar 24, 2024

0

3

0

+357

Circles

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the radius of the circle.

falafronk Mar 24, 2024

0

2

0

+357

Angle bisector

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle such that $AC = 4$ and $BC = 4.$ The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$

falafronk Mar 24, 2024

0

5

1

+70

last one for the month

Semicircles are constructed on AB, AC,and BC. A circle is tangent to all three semicircles. Find the radius of the circle.
read more ..

In triangle ABC, point X is on side BC such that AX = 13, BC = 10, CX = 4, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.
(no diagram)

faiafronk Mar 24, 2024

0

4

1

+70

trianlge ABC