All Questions

0

1

0

+124

Geometry

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

Pythagorearn 2 hours ago

0

1

0

+124

math problem

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 $BXA$.

Pythagorearn 2 hours ago

0

1

0

+124

help math

A rectangle is inscribed in a circle of radius $5$ cm. If the area of the rectangle is equal to 24, what is the perimeter of the rectangle? Express your answer as a decimal to the nearest tenth.

Pythagorearn 3 hours ago

0

1

0

+38

The perimeter of a rectangle is 40 and the length of one of its diagonals is 16. Find the area of the rectangle.

Ranger897 3 hours ago

0

1

0

+38

Homework Help Please :P

In a rhombus, all the side lengths are 12, and one of the angles is equal to 120 degrees Find the area of the rhombus.

Ranger897 5 hours ago

0

1

0

+1509

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 ..

bader 7 hours ago

0

1

0

+1509

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 $\overline{QN}\perp\overline{PR}$, $QN = 15$, and $PR = 20$, read more ..

bader 8 hours ago

+1

1

0

+7

Pythagorean Theorem Proof!

According to Google, there are over 371 proofs for the pythagorean theorem.
My challenge is for you to name as many as could possible name.
I already know a few common ones, so I challenge you guys to read more ..

NotThatSmart 10 hours ago

-1

1

+1509

Geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

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bader Apr 26, 2024, 6:00:10 PM

0

1

0

+1509

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

bader Apr 26, 2024, 4:12:24 PM

0

1

+4

Help pls

If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.

0.74 units 1.17 units 1.64 units 2.14 units

●

PlsAnswer Apr 26, 2024, 4:06:13 PM

0

1

0

+1509

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

bader Apr 26, 2024, 2:52:20 PM

0

1

0

+1509

Geometry

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 $ABD$.

bader Apr 26, 2024, 2:52:09 PM

0

1

0

+1105

help 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 26, 2024, 2:14:45 PM

0

1

0

+1105

help with algebra

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

parmen Apr 26, 2024

0

1

0

+1105

help algebra

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 $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

parmen Apr 26, 2024

0

1

0

+1105

help algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

parmen Apr 26, 2024

0

1

+1105

help algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

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parmen Apr 26, 2024

0

1

0

+20

Four points form the vertices of a square. Find the area of the square if the points are (2,b), (0,a), (5,c), and (7,d).

RedDragon1 Apr 26, 2024

0

2

1

+785

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

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ABJeIIy Apr 26, 2024

0

1

0

+785

Algebra

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 (-2,8), (0,0), and (2,8).

ABJeIIy Apr 26, 2024

0

1

0

+785

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

ABJeIIy Apr 26, 2024

0

1

0

+785

Algebra

Find all real values of $p$ such that
(x+1)(x-2p)
has a minimum value of 0 over all real values of $x$.

ABJeIIy Apr 26, 2024

0

1

0

+785

help Algebra

Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$

ABJeIIy Apr 25, 2024

0

1

+785

Algebra

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

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ABJeIIy Apr 25, 2024

0

1

0

+785

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

ABJeIIy Apr 25, 2024

0

1

+12

Geometry

Can you solve these?
1.

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

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wendigo Apr 25, 2024

0

1

+679

help with functions

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

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LiIIiam0216 Apr 25, 2024

0

1

+679

Algebra problem

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

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LiIIiam0216 Apr 25, 2024

0

1

0

+679

help algebra

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

LiIIiam0216 Apr 25, 2024

0

1

0

+679

help with algebra

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

LiIIiam0216 Apr 25, 2024

0

1

0

+679

help need help

Find the value of $v$ such that $\frac{-21-\sqrt{201}}{10}$ a root of $5x^2+21x+v = 0$.

LiIIiam0216 Apr 25, 2024

0

1

0

+124

HELP

The roots of the quadratic equation are and . What is ?

Lilliam0216 Apr 25, 2024

0

1

0

+124

Sums

How many unique sums can be formed by adding any three different numbers from the set {4,6,8,10,12,...,154}?

Pythagorearn Apr 25, 2024

0

1

0

+679

help help

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2ab - 12a + 3a + 3b - 8b - ab + ___

LiIIiam0216 Apr 25, 2024

0

1

0

+679

help me

Simplify \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9}.

LiIIiam0216 Apr 25, 2024

0

1

0

+679

need help

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

LiIIiam0216 Apr 25, 2024

0

1

0

+124

pls help

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

Lilliam0216 Apr 25, 2024

0

1

0

+679

Algebra

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 ..

LiIIiam0216 Apr 25, 2024

0

1

0

+679

help help

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 ..

LiIIiam0216 Apr 25, 2024

0

2

0

+679

help me

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

LiIIiam0216 Apr 25, 2024

0

1

0

+679

need help

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

LiIIiam0216 Apr 25, 2024

0

1

0

+124

IDK WHAT TO DO

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?

Lilliam0216 Apr 25, 2024

0

1

+785

Algebra

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

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ABJeIIy Apr 25, 2024

0

1

+785

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

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ABJeIIy Apr 25, 2024

0

1

0

+785

Algebra

The roots of Ax^2+Bx+1 are the same as the roots of (x - 2)(x + 2). What is A+B?

ABJeIIy Apr 25, 2024

0

1

0

+785

Algebra

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

ABJeIIy Apr 24, 2024

0

2

0

+785

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

ABJeIIy Apr 24, 2024

0

1

+785

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?

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ABJeIIy Apr 24, 2024

0

1

0

+785

Algebra

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

ABJeIIy Apr 24, 2024

0

1

0

+785

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

ABJeIIy Apr 24, 2024

0

1

0

+785

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

ABJeIIy Apr 24, 2024

0

1

0

+182

Algebra

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

ABJelly Apr 24, 2024

0

1

0

+1791

coordinates

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

tomtom Apr 24, 2024

0

1

0

+1791

coordinates

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

tomtom Apr 24, 2024

0

2

0

+1791

Coordinates

Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.

tomtom Apr 24, 2024

0

1

0

+1791

coordinates

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

tomtom Apr 24, 2024

0

1

+1791

help with coordinates

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

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tomtom Apr 24, 2024

0

1

0

+124

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 ..

Pythagorearn Apr 24, 2024

0

1

+124

pls help

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?

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Lilliam0216 Apr 24, 2024

0

1

0

+124

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.

Pythagorearn Apr 24, 2024

0

1

+679

need 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?

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LiIIiam0216 Apr 24, 2024

0

1

+124

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.

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Pythagorearn Apr 24, 2024

0

1

0

+124

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

Pythagorearn Apr 24, 2024

0

1

0

+4

HELP ME PLS

a.Given the polynomial function y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
a. Use the definition of derivative to differentiate y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
b. Find the points on the graph where the tangent line is horizontal read more ..

aoas123 Apr 24, 2024

0

2

0

+124

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 ..

Pythagorearn Apr 23, 2024

0

1

+11

PLEASE HELP

I could use the help

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justtryinpass Apr 23, 2024

0

1

0

+124

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 $EFGH$

Pythagorearn Apr 23, 2024

0

1

+124

Geometry

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

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Pythagorearn Apr 23, 2024

0

1

0

+679

help plz

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 23, 2024

0

1

0

+679

help counting

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 23, 2024

0

1

+679

help help

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 ..

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LiIIiam0216 Apr 23, 2024

0

2

1

+679

need help quick

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 ..

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LiIIiam0216 Apr 23, 2024

0

2

0

+466

help geo

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 ..

booboo44 Apr 23, 2024

0

2

0

+466

help plz

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 ..

booboo44 Apr 23, 2024

0

1

+910

Geometry

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 ..

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Akhain1 Apr 23, 2024

0

2

1

+910

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 $a + b$.

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Akhain1 Apr 23, 2024

0

2

1

+910

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.

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Akhain1 Apr 23, 2024

0

1

0

+679

i need help

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

LiIIiam0216 Apr 23, 2024

0

2

1

+124

All the other answers are wrong :(

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?

●

Lilliam0216 Apr 23, 2024

+1

2

1

+910

Geometry

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

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Akhain1 Apr 23, 2024

0

1

+679

need help

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

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LiIIiam0216 Apr 23, 2024

0

2

0

+910

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 23, 2024

0

2

0

+679

need help

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

LiIIiam0216 Apr 23, 2024

0

1

+124

pls 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 12 steps, how many different points could Franklin end up at?

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Lilliam0216 Apr 23, 2024

0

1

0

+679

help me

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

LiIIiam0216 Apr 23, 2024

0

1

+124

Rlly confusing

Find the number of ways of choosing three circles below, so that no two circles are next to each other.
There are 12 circles, in the shape of a circle.
[asy]
unitsize(1 cm);
int i;
for (i = 0; i <= 11; ++i) {
draw(Circle(2*dir(360/12*i),0.3));<#> read more ..

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Lilliam0216 Apr 23, 2024

0

3

0

+4

stat help

You may need to use the appropriate technology to answer this question.
The competitive advantage of small American factories such as Tolerance Contract Manufacturing lies in their ability to produce parts with highly narrow requirements, or tolerances, read more ..

loook Apr 23, 2024

0

1

+785

Quadratic

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

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ABJeIIy Apr 23, 2024

0

1

+785

help plz

Find the coordinates of the center of the circle.

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ABJeIIy Apr 23, 2024

0

2

1

+785

Parabola

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

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ABJeIIy Apr 23, 2024

0

2

1

+785

need help

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = 2.$ If $(4,7)$ lies on the graph, find another point on the graph.

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ABJeIIy Apr 23, 2024

+1

2

3

+16

pls help me

Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12

●●●

gaberiellz Apr 23, 2024

0

2

1

+124

Geometry

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

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Pythagorearn Apr 23, 2024

0

2

1

+124

Geometry

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

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Pythagorearn Apr 23, 2024

0

1

+124

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 ..

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Pythagorearn Apr 22, 2024

0

2

0

+124

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 ..

Pythagorearn Apr 22, 2024

0

2

1

+14

pre-calc question- please help

Convert the function into rectangular form. Show all work for credit.

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FireflySky Apr 22, 2024

0

2

0

+124

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.

Pythagorearn Apr 22, 2024

0

2

1

+124

Geometry

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

●

Pythagorearn Apr 22, 2024

+1

2

1

+124

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 ..

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Pythagorearn Apr 22, 2024

0

1

0

+785

Algebra

Fill in the blanks to make a true equation:
1/(n(n + 3)(n + 5)) = __/n + ___/(n + 3) + ___/(n + 5)

ABJeIIy Apr 22, 2024

0

2

0

+785

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 12}

ABJeIIy Apr 22, 2024

0

1

0

+785

Algebra

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

ABJeIIy Apr 22, 2024

0

2

0

+124

Geometry

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

Pythagorearn Apr 22, 2024

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+124

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 $BX$?

Pythagorearn Apr 22, 2024

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3

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+124

Geometry

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

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Pythagorearn Apr 22, 2024

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+124

Geometry

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

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Pythagorearn Apr 22, 2024

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+124

Geometry

Find the circumradius of triangle ABC.

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Pythagorearn Apr 22, 2024

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2

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+124

Geometry

Find the inradius of triangle ABC.

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Pythagorearn Apr 22, 2024

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+124

Geometry

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 ..

Pythagorearn Apr 22, 2024

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2

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+124

Geometry

In triangle $ABC$, $AB = 7$, $AC = 17$, and the length of median $AM$ is $12$. Find the area of triangle $ABC$.

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Pythagorearn Apr 22, 2024

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1

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+124

Geometry

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 $AD$.

Pythagorearn Apr 22, 2024

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+124

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 $AB$?

Pythagorearn Apr 22, 2024

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+124

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

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Pythagorearn Apr 22, 2024

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+124

Geometry

Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.

Pythagorearn Apr 22, 2024

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+124

Geometry

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 of6 from one wall, and a distance of 6 from the other wall. Find the radius of read more ..

Pythagorearn Apr 22, 2024

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+124

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 10$ and $WX = 8,$ find $YZ.$

Pythagorearn Apr 22, 2024

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2

+4

Geometry (Inradius and Incircles)

1) I is the incenter of triangle ABC. If angle ABC = 78^\circ$ and angle ACB = 47^\circ,$ find angle BID, in degrees.

2) Find angle read more ..

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Pythagoream Apr 21, 2024

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+910

Geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

Akhain1 Apr 21, 2024

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2

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+910

Geometry

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 EBF is 1, and the area of triangle BCE is 2. Find the area of parallelogram ABCD.

Akhain1 Apr 21, 2024

-1

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+910

Geometry

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

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Akhain1 Apr 21, 2024

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2

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+910

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 PRS is 27, and the area of triangle PQR is 75. Find the area of trapezoid PQRS read more ..

Akhain1 Apr 21, 2024

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1

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+910

Geometry

In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 2:1, and let N be the point on \overline{EH} such that HN:NE = 3:8. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and \overline{GN} read more ..

Akhain1 Apr 21, 2024

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2

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+910

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 $[ABC] = 14$. read more ..

Akhain1 Apr 21, 2024

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2

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+910

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 21, 2024

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2

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+910

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 21, 2024

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1

+910

help geometry

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees? read more ..

hasAquestion ●

Akhain1 Apr 21, 2024

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+383

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all the freshmen are standing together?

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magenta Apr 21, 2024

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