All Questions

+128

Geometry

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

Pythagorearn 4 hours ago

+128

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 5 hours ago

+128

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 5 hours ago

+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 6 hours ago

+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 7 hours ago

Apr 26, 2024

+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 9 hours ago

+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 11 hours ago

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 Apr 26, 2024, 8:21:46 PM

-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

+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

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

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

+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

+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

+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

+1105

help with algebra

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

parmen Apr 26, 2024

+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

+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

+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

+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

+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

+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

+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

+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

Apr 25, 2024

+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

+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

+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

+12

Geometry

Can you solve these?
1.

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

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wendigo Apr 25, 2024

+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

+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

+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

+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

+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

+124

HELP

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

Lilliam0216 Apr 25, 2024

+128

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

+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

+679

help me

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

LiIIiam0216 Apr 25, 2024

+679

need help

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

LiIIiam0216 Apr 25, 2024

+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

+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

+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

+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

+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

+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

+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

+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

+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

Apr 24, 2024

+785

Algebra

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

ABJeIIy Apr 24, 2024

+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

+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

+785

Algebra

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

ABJeIIy Apr 24, 2024

+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

+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

+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

+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

+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

+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

+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

+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

+128

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

+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

+128

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

+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

+128

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

+128

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

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

Apr 23, 2024

+128

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

+11

PLEASE HELP

I could use the help

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justtryinpass Apr 23, 2024

+128

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

+128

Geometry

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

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Pythagorearn Apr 23, 2024

+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

+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

+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

+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

+466

help geo

booboo44 Apr 23, 2024

+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

+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

+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

+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

+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

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