All Questions +0 238379 Questions

The longer leg of a right triangle is two times as long as the shorter leg. What is the area of this triangle?

BlackoutMiIkshake 9 hours ago

0

1

2

+930

Geometry

In the diagram below, if AD=30, what is BC?

cooIcooIcooI17 Sep 14, 2026

0

1

+930

Geometry

If \frac{AE}{DE} = 3, what is \frac{AD}{BC}?

cooIcooIcooI17 Sep 14, 2026

0

1

+930

Geometry

If ST = 2, QS = 4, and QT = 5, find PQ.

cooIcooIcooI17 Sep 11, 2026

0

2

1

+930

geometry

In the diagram below, ABCD is a square with side length 1, and the area of triangle CEF is 1/2. Compute the area of triangle AEF.

cooIcooIcooI17 Sep 11, 2026

0

1

+1867

Geometry

The area of square ABCD is 36. E is a point on \overline{CD} such that CE=2ED. F is the intersection of AB and CD. Find [DEF].

ABJeIIy Sep 7, 2026

0

1

5

+835

Geometry

In \triangle ABC, shown here, \overline{AB} and \overline{AC} have each been divided into four congruent segments. What fraction of triangle ABC is shaded? Express your answer as a common fraction.

maximum Sep 4, 2026

0

1

+835

Geometry

In the diagram, BD = 2 \cdot CD and CF = FB. Find the length AE.

maximum Sep 4, 2026

0

1

+835

Geometry

In the diagram, \triangle ABC \cong \triangle BFA. Find \frac{AB}{BC}.

maximum Sep 4, 2026

0

1

+835

Geometry

In the diagram below, we have DE = 3 \cdot EC and AB = DC = 20. Find the length FG.

maximum Sep 4, 2026

0

1

+1042

Geometry

Triangles ADE, CDE, and BCE are all equilateral triangles with area 1, and H is the midpoint of \overline{BC}. Find the area of the blue region.

gnistory Sep 4, 2026

0

1

+1042

Geometry

Right triangle ABC has side lengths AB=1, BC = 3, and AC = \sqrt{10}. Square XYZW is inscribed in triangle ABC with X and Y on \overline{BC}, W on \overline{AC}, and Z on \overline{AB}. What is the area of the square?

gnistory Sep 4, 2026

0

1

+1042

Geometry

We know \angle B=\angle C, BE=5, and AB=8. If [ACB]=80, what is [CED]?

gnistory Sep 4, 2026

0

1

+1042

Geometry

Right triangles ABC, ADE, EFG, and GHC are all similar. Also, [ADE] = 1, [EFG] = 4, and [GHC] = 9. Find the area of the red region.

gnistory Sep 4, 2026

0

1

+1348

Geometry

We know \angle B=\angle C. Given AB=50, BE=20, DA=35, and CE=51, find DE.

AnswerscorrectIy Sep 4, 2026

0

1

+1348

Geometry

In triangle ABC, shown here, \overline{AB} and \overline{AC} have each been divided into three congruent segments. What fraction of triangle ABC is shaded? Express your answer as a common fraction.

AnswerscorrectIy Sep 4, 2026

0

1

+1348

Geometry

In the diagram below, ADEF is a square with side length 4. If AC = 16, what is BD?

AnswerscorrectIy Sep 4, 2026

0

1

+1348

Geometry

In rectangle BCDF below, [ABE] = 2 and [BEF] = 3. Find [ACDE].

AnswerscorrectIy Sep 4, 2026

0

1

+930

Geometry

In rectangle BCDF below, [ABE] = 2 and [BEF] = 3. Find [BCDF].

cooIcooIcooI17 Aug 25, 2026

0

1

+930

Geometry

In the diagram below, M is the midpoint of \overline{AB} and $\angle ACN \cong \angle XCN$.
Find MN.

cooIcooIcooI17 Aug 25, 2026

0

1

+930

Geometry

D is on side \overline {AB} of \triangle ABC. We know $\triangle ABC \sim \triangle ACD$ and we know all the marked side lengths. What is the length AB?

cooIcooIcooI17 Aug 25, 2026

0

1

+930

Geometry

In the diagram below, \overline{BC} and \overline{DE} are parallel. Find y.

cooIcooIcooI17 Aug 25, 2026

0

1

+930

Geometry

In the diagram, \overline{AB} \parallel \overline{CD}. Select the two products of lengths that must be equal.

cooIcooIcooI17 Aug 25, 2026

0

1

+701

Geometry

Find SR and QR. Enter them in the boxes below, in that order.

Pythagorearn Aug 24, 2026

0

1

+133

Geometry

D is on side \overline {AB} of triangle ABC. We know \triangle ABC \sim \triangle ACD. What is the length AB?

Jyrgernry Aug 24, 2026

0

1

+133

Geometry

In the diagram, if AC = 35, then what is AD?

Jyrgernry Aug 24, 2026

0

1

+133

Geometry

In the diagram below, we have \overline{QR}\parallel\overline{ST}, and PT = 10. Find PR.

Jyrgernry Aug 24, 2026

0

1

+133

Geometry

In rectangle ABCD, [ABE] = [BEF] = [BFC]. Compute AE/ED.

Jyrgernry Aug 24, 2026

0

1

+133

Geometry

In rectangle ABCD, [AEP]/[DFP] = 5. Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

Jyrgernry Aug 21, 2026

0

1

+133

Geometry

In the diagram, ABCD is a rectangle, BEFG is a square, and F lies on \overline{CE}. Find AD.

Jyrgernry Aug 21, 2026

0

1

+133

Geometry

Jyrgernry Aug 21, 2026

0

52

1

+248

Geometry

Find [YBC]/[ZYC].

In the diagram below, E lies on \overline{BD}, [ADP] = 3, [BCE] = 12, and [CDE] = 4. Compute [BCE].

BlackoutMiIkshake Aug 20, 2026

0

1

+248

Geometry

Rectangle ADEH$ is divided into rectangles ABGH, BCFG, and CDEF. If AC = 15, GF = 20, [ABCH] = 8, and [CDEF] = 30, find [BCFG].

BlackoutMiIkshake Aug 20, 2026

0

1

+248

Geometry

A point in a square is connected to the midpoints of its sides, dividing the square into four regions. The areas of three of the regions are 2, 2, and 2. Find the area of the fourth region.

BlackoutMiIkshake Aug 20, 2026

0

1

+248

Geometry

In the diagram, PR = 12, QS = 10, [PQR] = 15, and [ARS] = 18. Find [AQR].

BlackoutMiIkshake Aug 20, 2026

0

2

1

+701

Geometry

In the diagram below, we have BE = 7, AC = 3, and [CBDE]=15. What is [CDA]?

Pythagorearn Aug 20, 2026

0

1

+701

Geometry

A square is divided into five rectangles, and all the rectangles have the same area. Given that [ABC] = 1, find the side length of the square.

Pythagorearn Aug 20, 2026

0

17

1

+701

Geometry

Given that [ABC] = 10, find [BCD].

Pythagorearn Aug 20, 2026

0

1

+701

Geometry

Triangle ABC is acute. Point D lies on \overline {AC} so that \overline {BD}\perp \overline {DE}, and point E lies on \overline {AB} such that \overline {CE}\perp\overline {BE}. Find the value of AE if CB = 10, PB = 20, and DB = 30.

Pythagorearn Aug 20, 2026

0

2

1

+930

Geometry

Triangles RST and XYZ are congruent. Point P lies on \overline{ST}, and point W lies on \overline{YZ}. Select all the true statements.
If RP = WY, then RSP = XYT
If RP perp XW and ST perp RS, then RSP cong XWP
if read more ..

cooIcooIcooI17 Aug 6, 2026

0

2

1

+701

Geometry

In the diagram, \overline{AD} bisects \angle BAC.
By adding one more condition, we can prove that triangles ABD and ACD are congruent. Which of the following could be that condition? Select all that apply.
AB read more ..

Pythagorearn Aug 6, 2026

0

2

1

+701

Geometry

Triangle ABC is congruent to triangle DEF, but triangle ABC is not congruent to triangle DFE. Which of the following relationships cannot hold?
AB + BC = EF + DE
BC * EF = AD * BE
AC + AD = EF + BC read more ..

Pythagorearn Aug 6, 2026

0

2

1

+701

Geometry

Let x be the measure of \angle DCE (in degrees) in the diagram below (not drawn to scale). Find $x.$

Pythagorearn Aug 6, 2026

0

2

1

+701

Geometry

A robot moved $10$ meters towards north. It then turned $44^\circ$ to its right and moved another $10$ meters. It then turned $68^\circ$ to its right and moved $20$ meters. It then turned $38\circ$ to its right and moved $30$ meters. Last, it turned read more ..

Pythagorearn Aug 6, 2026

0

2

1

+1042

Geometry

In triangle ABC, the angles \angle A, \angle B, \angle C form an arithmetic sequence. If \angle A + \angle B = 21^\circ, then what is \angle C, in degrees?

gnistory Aug 6, 2026

0

2

1

+1042

Geometry

In the diagram, what is the measure of \angle ACB in degrees?

gnistory Aug 6, 2026

0

2

1

+1042

Geometry

What is x in the diagram below?

gnistory Aug 6, 2026

0

2

1

+1348

Geometry

Find x given the angle measures shown.

AnswerscorrectIy Aug 6, 2026

0

2

1

+1348

Geometry

Given that \ell \parallel m, find \angle XYZ + \angle XZY.

AnswerscorrectIy Aug 6, 2026

0

2

1

+1348

Geometry

Lines $AB$ and $CD$ intersect at a point $O$ in such a way that the measure of $\angle AOC$ is $3$ times the measure of angle $x$. What is the measure of $\angle AOB$?

AnswerscorrectIy Aug 6, 2026

0

2

1

+1348

Geometry

Suppose instead of measuring an angle the "regular" way, we go around the "long" way, as shown in the diagram.
What is the measure of the "long" way around angle?

AnswerscorrectIy Aug 6, 2026

0

2

1

+1348

Geometry

Line \ell is shown below. The line y = 2x + k has a distance of 3 from line y = 5x + k. Find all possible values of k.

AnswerscorrectIy Aug 6, 2026

0

3

1

+1548

Math

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

learnmgcat Jun 18, 2026

0

2

1

+1548

Math

In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

learnmgcat Jun 18, 2026

0

2

1

+1548

Math

Hi everyone,
I am currently analyzing the mathematical patterns and probability distributions behind single-player puzzle levels to better understand game balancing. Specifically, I'm looking at how decision trees affect a player's winning probability read more ..

learnmgcat Jun 18, 2026

+1

2

3

+5

Help with Math Logic: Calculating Winning Probabilities in Solo Strategy Games?

Fill in the blanks to make the statement true. Each number can be used at most once.
The function f(x) = sqrt(___) - 1/(x - ___)^2 has domain [___, ___] and range [___, ___].

tetrisgameaz Jun 17, 2026

0

3

+990

help

The average distance of Mercury from the Sun is 36 million miles. The distance varies by 7.5 million miles.
The minimum distance of Mercury from the Sun is ____ Text entry field 1 of 2 Enter answer here million miles, and the maximum read more ..

booboo44 May 21, 2026

+1

2

+5

help

Bosco ●●

esthergalvez38 May 19, 2026

0

5

1

+4

4*4

Fill in the blanks to make a true statement.
The quadratic y = ax^2 + bx + c is plotted above. If a = ___, b = ___, and c = ___, then the discriminant of the quadratic is ___.

Melo.100 May 18, 2026

0

2

+990

help

Fill in the blanks to make a true statement.
The roots of the quadratic ___x^2 + ___x + ___ are ___ and ___.
Expanding (x + ___)(x + ___), we get x^2 + ___ x + ___.
Completing the square on read more ..

booboo44 May 15, 2026

0

2

1

+1056

help

Fill in the blanks to make a true statement.
The roots of ___x^2 + ___x + ___ are ___ and ___.
Expanding (x + ___)(x + ___), we get x^2 + ___ x + ___.
Completing the square on x^2 + ___x + ___, read more ..

Hi6942O May 15, 2026

0

2

+1056

help

Find all numbers N between 800 and 900 for which the equation x^2 + 50x = N^2 has integer solutions.

Hi6942O May 14, 2026

0

3

1

+1056

help

Fill in the blanks, so that the resulting expression can be factored as the product of two linear expressions:
12xy
8x
-5y read more ..

Hi6942O May 14, 2026

0

5

1

+990

help

Fill in the blanks with rational numbers.
\frac{1}{\sqrt{2}} + \sqrt{5} + \sqrt{7} = ___ \sqrt{2} + ___ \sqrt{5} + ____ \sqrt{7} + ____ \sqrt{10} + ___ \sqrt{14} + ____ \sqrt{35} + ____ \sqrt{70}
\frac{1}{\sqrt{2}} + \sqrt{3} read more ..

booboo44 May 14, 2026

0

5

1

+990

help

Fill in the blank with rational numbers
\frac{1}{2} + \sqrt{5} = ___ + ___ \sqrt{5}
\frac{1}{2} + \sqrt[3]{5} = ____ + ___ \sqrt[3]{5} + ___ \sqrt[3]{25}
\frac{1}{2} + \sqrt[3]{25} = ____ + ___ \sqrt[3]{5} + ___ \sqrt read more ..

booboo44 May 13, 2026

0

4

1

+990

help

Fill in the blanks, so that all the quadratic equations have integer roots.

booboo44 May 13, 2026

0

3

1

+990

help

You are told that the quadratic expression Ax^2 + Bx + C factors into linear factors with integer coefficients. Which of the following quadratic expressions must also factor, into linear factors with integer coefficients? Select all that ap read more ..

booboo44 May 13, 2026

0

2

1

+1348

help

The region R is shown below.
Which expressions have a minimum value, over all points (x,y) in R? Select all that apply.

AnswerscorrectIy May 12, 2026

0

3

1

+990

help

The region R is shown below. Find the smallest possible value of 5x + 9y over all points (x,y) in R.

booboo44 May 8, 2026

0

3

1

+215

help

Select all the points that satisfy y < 2x - 3.

Boseo May 7, 2026

0

3

1

+215

help

For 0 \le x \le 1, the function f(x) satisfies the relations f(x/x + 1) = f(x) and f(1 - x) = f(x). What is the value of f(2/3) + f(2/5)?

Boseo May 6, 2026

0

3

1

+1548

help

Line \ell is shown below. The line through P that is perpendicular to \ell intersects \ell at Q. Find the coordinates of Q.

learnmgcat May 2, 2026

0

3

2

+1548

help

Fill in the blanks to make a true statement.
The line x + y = 1 is perpendicular to the line x - y = 2, and passes through the point (1,___).

learnmgcat May 2, 2026

0

4

1

+1548

help

Fill in the blanks to make a true statement.
The line x + y = 1 is parallel to the line x + y = 2, and passes through the point (1,___).

learnmgcat May 1, 2026

0

2

+248

help

Here is a summary of some inequality rules.
Fill in the blanks to complete the rules. (The first rule is already complete.)
a + b < c + d
a + c > b + d
a + d > b + c read more ..

BlackoutMiIkshake Apr 30, 2026

0

4

1

+133

help

Write a simplified equation for the set of points that are exactly twice as far from (12,0) as they are from (0,0).

Jyrgernry Apr 28, 2026

0

3

5

+133

help

Fill in the blanks to make a true statement.
The equation of the line passing through ___ and ___ is given by y = ___ x + ___
(-1,-3), (2,-2)

Jyrgernry Apr 27, 2026

0

2

1

+133

help

Ichbineule ●

Jyrgernry Apr 27, 2026

0

3

2

+133

Help

Select two points so that the distance between them is equal to 2 sqrt(5).
(0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)

Select all the points that lie below the line y = -\frac{1}{3} x
(0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)

Jyrgernry Apr 27, 2026

0

2

1

+133

help

Select two points so that the $y$-intercept of the line passing through them is $(0,-5)$.
(0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)

Jyrgernry Apr 27, 2026

0

3

1

+133

help

Select two points so that the slope between them is -3.
(0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)

Jyrgernry Apr 27, 2026

0

3

1

+133

help

Select all the points that lie on the line y = \frac{1}{2} x + 3.
(0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)

Jyrgernry Apr 27, 2026

0

4

1

+133

help

Fill in the blanks to make a true statement.
The variables x and y are inversely proportional. If x = 1, then y = 2. And if x = 2, then y = ___.

Jyrgernry Apr 27, 2026

0

2

+133

help

Fill in the blanks to make a true statement.
The variables x and y are inversely proportional. If x = 1, then y = 2. And if x = 2, then y = ___.

Jyrgernry Apr 24, 2026

0

5

2

+1844

help

Fill in the blanks to make a true statement.
If we increase a by 10%, then we obtain b. If we increase b by 10%, then we obtain c. Overall, we can obtain c by increaseing a by ___ %.

blackpanther Apr 23, 2026

0

4

2

+1844

help

Fill in the blanks to make an equation that is linear in disguise, and has a solution.
sqrt(2x - 3) + __x + ___ = ___x - ___ + ____
8 9 10 11 12 13 14 15 16 17 18 19 20

blackpanther Apr 23, 2026

0

6

1

+1844

help

Fill in the blanks to make a true statement.
The variables $x$ and $y$ are inversely proportional. If $x = 1$, then $y = 1$. And if $x = 2$, then $y = 2$.
The variables ___ and ___ are proportional. read more ..

blackpanther Apr 23, 2026

0

2

1

+1844

help

Fill in the blanks to make a true statement.
The variables $x$ and $y$ are inversely proportional. If $x = 1$, then $y = 1$. And if $x = 2$, then $y = 2$.
The variables ___ and ___ are proportional. read more ..

blackpanther Apr 23, 2026

0

4

2

+1056

help

Fill in the blanks to make a true statement.
Gabriella drives for 40 miles at 60 miles per hour, 20 miles at 40 miles per hour, and 10 miles at 56 miles per hour. Her overall average speed is 40 miles read more ..

Hi6942O Apr 23, 2026

0

2

1

+1056

help

Fill in the blanks to make a true statement.
Gabriella drives for 40 miles at 60 miles per hour, 20 miles at 40 miles per hour, and 10 miles at 56 miles per hour. Her overall average speed is 40 miles read more ..

Hi6942O Apr 23, 2026

0

4

2

+133

help

The graph of y = f(x) is shown below.
Find f(f(1))+f(f(2))+f(f(3))+\dots+f(f(8))+f(f(9)).

Jyrgernry Apr 23, 2026

0

4

1

+133

help

The complete graph of the function f(x) is shown below. How many values of x satisfy f(f(x)) = 2?

Jyrgernry Apr 22, 2026

0

3

1

+133

help

The graph of y = p(x) is shown below.
Find p(1.5).

Jyrgernry Apr 22, 2026

0

2

1

+133

help

A local charity fundraiser is distributing care packages. On Monday, they distributed some number of packages. On Tuesday, they distributed one more than they did on Monday. This new amount is exactly 3/5 of what they would have distributed if they had read more ..

Jyrgernry Apr 22, 2026

0

4

1

+21

help

The point $(p,9)$ lies on line $k$ shown here. What is the value of $p$?

Jyrgerhry Apr 22, 2026

0

4

1

+1944

help

This graph shows the linear relationship between the time in seconds, $x$, for Caroline's walk and the distance in meters, $y$, Caroline is from her starting point. The graph passes through the point $(20,10)$. According to the graph, how many meters will read more ..

tomtom Apr 22, 2026

0

2

1

+133

help

Let $A(9,3)$, $B(9,10)$ and $C(k,10)$ be points in the Cartesian coordinate plane. What is the smallest value for $k$ such that the distance from $A$ to $C$ is 1 unit?

Jyrgernry Apr 22, 2026

0

3

1

+133

help

Wanda is trying to locate the Fermat point $P$ of $\triangle ABC$, where $A$ is at the origin, $B$ is at $(2,1)$, and $C$ is at $(-5,1)$ (the Fermat point is the point such that the sum of its distances from the vertices of a triangle is minimized). She read more ..

Jyrgernry Apr 22, 2026

0

4

1

+133

help

In the diagram, $\triangle PQR$ is right-angled at $Q$, $PQ$ is horizontal and $QR$ is vertical. What are the coordinates of $Q$? Type your answer in the form (a,b) (no spaces) where a and b are real numbers.

Jyrgernry Apr 22, 2026

0

2

1

+133

help

What is the circumference of the circle with center at P and passing through Q? Express your answer in terms of \pi.
P = (0,0) and Q = (1,1).

Jyrgernry Apr 22, 2026

0

3

2

+133

help

The graphs of four functions, labelled (2) through (5), are shown below. Note that the domain of function (3) is $$\{-5,-4,-3,-2,-1,0,1,2\}.$$ Find the product of the labels of the functions which are invertible.

Jyrgernry Apr 22, 2026

0

4

1

+2741

help

If f(x), whose graph is shown below, is defined on 1 \le x \le 6, what is the maximum value of $f^{-1}(x)$?

LiIIiam0216 Apr 22, 2026

0

3

1

+2741

help

Fill in the blanks so that the resulting system does not have a unique solution.
8x + 12y = ___
8x + 12y = ___
14x + 16y = ___ read more ..

LiIIiam0216 Apr 22, 2026

0

4

1

+2741

help

Fill in the blanks to make the equation true.
15a^4 - 5a^4 b - ___ + 20a^2 = 12a^2 b - 8b^4 - 4^b + ___
4a^2 b^2 12ab^2 18a^2 5a^2 b^3 16b^2

LiIIiam0216 Apr 22, 2026

0

4

1

+1348

help

The graph of y = f(x) is shown below.
The graphs of y = f(x) and y = f(x - 3) intersect at one point. What is the sum of the coordinates of that point?

AnswerscorrectIy Apr 22, 2026

0

5

1

+1867

help

The graph of y = f(x) is shown below, where f(x) = ax^2 + bx + c.
Find f(15).

ABJeIIy Apr 22, 2026

0

5

1

+1867

help

im doing math finding intercepts rise over run and slope in school and im trying to find out the process of how to find the slope and rise over run from an equation. im trying to do it on my own and not calculate or cheat. as we have EOC soon and i wanna read more ..

ABJeIIy Apr 22, 2026

0

7

2

+4

need help learning please

The graph of f(x)=ax^3+bx^2+cx+d is shown below. What is the value of 8a-14b+6c-5d?

huntsigh Apr 22, 2026

0

5

1

+133

Algebra

Let f(x) and g(x) be two linear functions. The graphs of $f(x)$ and $g(x)$ are shown below.
Evaluate f(1) + g(1) + f(g(1)) + g(f(1)).

Jyrgernry Apr 22, 2026

0

3

1

+133

Algebra

The graph of y = f(x) is shown below.
For a constant a, let g(x) = f(x + a). Find the constant a so that $g(x)$ and $g^{-1}(x)$ are the same function.

Jyrgernry Apr 22, 2026

0

9

1

+133

Algebra

The graph of the invertible function y = f(x) is shown below.
If f(a)=b and f(b)=4, then what is the value of $a-b$?

Jyrgernry Apr 22, 2026

0

7

1

+133

Algebra

An artist is designing a unique geometric trophy base using a flat sheet of acrylic. The base is composed of several distinct sections that need to be cut from the same material. To calculate the total cost of materials, the artist needs to find the total read more ..

Jyrgernry Apr 22, 2026

0

6

1

+21

The Custom Trophy Base

The equation of the circle below can be expressed in the form x^2 + Ay^2 + Bx + Cy + D = 0. Find A+B+C+D.

Jyrgerhry Apr 22, 2026

0

3

1

+1348

help

In the coordinate plane, one circle is centered at (0,-1), and another circle is centered at (-3,2), as shown below. The two circles are internally tangent.
The equation of the smaller circle can be expressed in the form x^2 + read more ..

AnswerscorrectIy Apr 22, 2026

0

5

1

+1348

help

The graph of y = \frac{x + A}{Bx + C}, where $A,B,$ and $C$ are integers, is shown below. What is $A + B + C$?

AnswerscorrectIy Apr 22, 2026

0

3

1

+701

help

The complete graph of f(x) is shown below, which consists of five line segments. Find the sum of all values of x that satisfy f(x) = x + 1.

Pythagorearn Apr 22, 2026

0

3

1

+701

help

The complete graph of f(x) is shown below, which consists of five line segments. Find the sum of all values of x that satisfy f(x) = 1.8.

Pythagorearn Apr 22, 2026

0

2

1

+701

help

The complete graph of f(x) is shown below.
Find the sum of all integers n for which the equation f(x)=n has exactly 6 solutions.

Pythagorearn Apr 22, 2026

0

2

1

+701

help

The complete graph of f(x) is shown below.
For a real number k, let g(k) be the number of solutions to the equation f(x)=k. What is the average of all distinct values in the range of g(k)?

Pythagorearn Apr 22, 2026

0

2

1

+1042

help

The complete graph of f(x) is shown below.
For a real number y, let g(y) be the number of solutions to the equation f(x)=y. What is the average of all distinct values in the range of g(y)?

gnistory Apr 21, 2026

0

3

1

+1042

help

The graph of the quadratic function f(x) is shown below
Let g(x)=-f(x) and h(x)=f(-x). Let $a$ be the number of points where the graphs of $y=f(x)$ and $y=g(x)$ intersect, and let $b$ be the number of points where the graphs read more ..

gnistory Apr 21, 2026

0

2

1

+1042

help

The graph of f(x)=ax^2+bx+c is shown below. What is the value of a+b+2c?

gnistory Apr 21, 2026

0

2

1

+1042

help

The graph of f(x) is shown. What are the possible values of f(x) - x for -3 \le x \le 3? Enter your answer using interval notation.

gnistory Apr 21, 2026

0

2

1

+701

help

The graph of G(x) is shown below. Compute G(G(G(G(G(1))))).

Pythagorearn Apr 21, 2026

0

2

1

+701

help

The graph of f(x) is shown below, where f(x) is a quadratic function. What is the sum of all $x$ such that $f(f(f(x)))=-3$ ?

Pythagorearn Apr 21, 2026

0

3

1

+701

help

For -1 \le x \le 1, let f(x) = 1 - \sqrt{1 - x^2}. The graph of f(x) is shown below.
The graphs of y = f(x) and y = f(x + 1) enclose a region. What is the area of that region, rounded to the nearest hundredth?

Pythagorearn Apr 21, 2026

0

4

1

+701

help

The graph of f(x) is shown below, which consists of five line segments.
Let a be the largest negative integer such that the function g(x) = f(x) + ax is invertible. Let $b$ be the smallest positive integer such that the function read more ..

Pythagorearn Apr 21, 2026

0

2

1

+1661

help

The graph of f(x) is shown below.
Mrs. Levans writes the number 3 on her pinky finger. She then applies $f$ to $3$ and writes the output on her ring finger. If Mrs. Levans continues this process of applying f and writing read more ..

kittykat Apr 21, 2026

0

2

1

+1661

help

The graph of y = f(x) is shown below.
Find the sum of all integers x, 0\le x\le 8, such that f(x) > x.

kittykat Apr 21, 2026

0

3

1

+1661

help

The graph of y = f(x) is shown below.
Find f(f(1))+f(f(2))+f(f(3))+\dots+f(f(8))+f(f(9)).

kittykat Apr 21, 2026

0

3

1

+215

help

The complete graph of the function f(x) is shown below. How many values of x satisfy f(f(x)) = 2?

Boseo Apr 21, 2026

0

3

1

+215

help

The graph of y = p(x) is shown below.
Find p(1.5).

Boseo Apr 21, 2026

0

4

1

+215

help

The graph of y = f(x) is shown below.
Find f(3).

Boseo Apr 21, 2026

0

3

1

+930

help

The graph of y = f(x) is shown below, where f(x) = ax^2 + bx + c.
Find f(15).

cooIcooIcooI17 Apr 21, 2026

0

2

1

+930

help

The graph of y = f(x) is shown below.
The graphs of y = f(x) and y = f(x - 3) intersect at one point. What is the sum of the coordinates of that point?

cooIcooIcooI17 Apr 21, 2026

0

2

1

+930

help

The complete graphs of the functions f(x) and g(x) are shown below.
What is the largest value of $f(x)-g(x)$?

cooIcooIcooI17 Apr 21, 2026

0

2

1

+248

help

The graph of y = f(x) is shown below.
What is f(-2.33)+f(-0.81)+f(0.81)+f(2.33)?

BlackoutMiIkshake Apr 21, 2026

0

3

1

+248

help

The graph of y = g(x) is shown below.
What is the value of g(g(-1))?

BlackoutMiIkshake Apr 21, 2026

0

2

1

+248

help

The graph of y = h(x) is shown below.
Find the sum of all integers x, 0\le x\le 8, such that h(x) > x.

BlackoutMiIkshake Apr 21, 2026

0

5

1

+1844

help

The graph of the invertible function y = f(x) is shown below.
If f(a)=b and f(b)=4, then what is the value of $a-b$?

blackpanther Apr 21, 2026

0

5

1

+1844

help

The graph of y = f(x) is shown below.
For a constant a, let g(x) = f(x + a). Find the constant a so that $g(x)$ and $g^{-1}(x)$ are the same function.

blackpanther Apr 21, 2026

0

4

1

+1844

help

Let f(x) and g(x) be two linear functions. The graphs of $f(x)$ and $g(x)$ are shown below.
Evaluate f(1) + g(1) + f(g(1)) + g(f(1)).

blackpanther Apr 21, 2026

0

4

1

+1042

help

The graph of f(x)=ax^3+bx^2+cx+d is shown below. What is the value of 8a-14b+6c-5d?

gnistory Apr 21, 2026

0

2

1

+1042

help

The graph of x = ay^2 + by + c is shown below. Find a+b

gnistory Apr 21, 2026

0

3

1

+1042

help

The graph of x = ay^2 + by + c is shown below. Find $c$.

gnistory Apr 21, 2026

0

5

1

+1056

help

The graph of $y=ax^2+bx+c$ is shown below, where $a$, $b$, and $c$ are integers. Find $a-b$.

Hi6942O Apr 21, 2026

0

2

1

+1056

help

The graph of $y=ax^2+bx+c$ is shown below, where $a$, $b$, and $c$ are integers. Find $a$.

Hi6942O Apr 21, 2026

0

3

1

+1056

help

The graph of $y = ax^2 + bx + c$ is shown below.
The zeros of the quadratic $ax^2 + bx + c$ are at $x=m$ and $x=n$, where $m>n$. What is $m-n$?

Hi6942O Apr 21, 2026

0

4

1

+1757

help

The complete graph of the function $f(x)$ is shown below. How many values of $x$ satisfy $f(f(x)) = 3$?

parmen Apr 21, 2026

0

3

1

+1757

help

The complete graph of the function $y = f(x)$ is shown below. Find the maximum value of $f^{-1}(x)$.

parmen Apr 21, 2026

0

2

1

+1757

help

The complete graph of $y = f(x)$ is shown below. Find the maximum value of $f^{-1}(x)$.

parmen Apr 21, 2026

0

3

1

+1661

help

Below is a portion of the graph of a function, $y=g(x)$:
What is the value of $g(g(-1))$?

kittykat Apr 21, 2026

0

3

1

+1661

help

Below is a portion of the graph of a function, $y=u(x)$:
What is the exact value of $u(-2.33)+u(-0.81)+u(0.81)+u(2.33)$ ?

kittykat Apr 21, 2026

0

3

1

+1661

help

The graphs of two functions, $p(x)$ and $q(x),$ are shown here on one set of axes:
If $q(p(x))$ is evaluated at $x=-4,$ $-3,$ $-2,$ $-1,$ $0,$ $1,$ $2,$ $3,$ $4,$ what is the sum of the nine values obtained in this way?

kittykat Apr 21, 2026

0

3

1

+1661

help

The graphs of four functions, labelled (2) through (5), are shown below. Note that the domain of function (3) is $$\{-5,-4,-3,-2,-1,0,1,2\}.$$ Find the product of the labels of the functions which are invertible.

kittykat Apr 21, 2026

0

4

1

+1661

help

If f(x), whose graph is shown below, is defined on 1 \le x \le 6, what is the maximum value of $f^{-1}(x)$?

kittykat Apr 21, 2026

0

3

1

+1661

help

The equation of the line shown can be written as $y=mx+b$. Find $mb$.
The line is y = x.

kittykat Apr 21, 2026

-1

3

1

+502

help

If the intersection point of lines $l$ and $m$ can be expressed in simplified form as $\left(-\frac{a}{b},\frac{c}{d}\right)$, what is $a + b + c + d$?

The lines are y = 3x + 1 and y = -2x + 8.

ikleyn Apr 21, 2026

0

4

1

+1661

help

The two lines shown intersect at the point (a,b). Find ab.
The lines are y = 3x + 4 and y = 8 - 7x.

kittykat Apr 21, 2026

0

2

1

+1661

help

Three squares of a 5 \times 5 grid are colored. Two colorings are conisdered equivalent if one coloring can be rotated to form the other coloring, such as the two colorings below, and the grid can be reflected as well. We also want the three read more ..

kittykat Apr 21, 2026

0

2

1

+1042

help

A number is chosen at random from among all 9-digit numbers that use each of the digits 1 through 9 exactly once. What is the probability that this number is a multiple of 2?

gnistory Apr 21, 2026

0

4

1

+1042

help

Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<read more ..

gnistory Apr 21, 2026

0

6

1

+226

help

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, read more ..

HumanBemg Apr 21, 2026

0

5

1

+226

help

Two chords with length r are drawn on a circle of radius r. What is the maximum possible distance between their endpoints?

HumanBemg Apr 21, 2026

0

6

1

+133

help

William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:

* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every read more ..

Jyrgernry Apr 21, 2026

0

4

1

+133

help

Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

Jyrgernry Apr 21, 2026

0

4

1

+930

help

Mrs. Monstrous Millie wants to throw a party for a group of monsters and aliens. The monsters each have 5 heads with 7 ears on each head, and the aliens each have 5 heads with 3 ears on each head. As party favors, Mrs. Millie wants to give each guest a read more ..

cooIcooIcooI17 Apr 21, 2026

0

3

1

+930

help

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

cooIcooIcooI17 Apr 21, 2026

0

5

1

+133

helpme

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

Jyrgernry Apr 21, 2026

0

11

1

+133

help

The triangle with vertices at (1,0), (0,1), and (k,k) has area 1/2. Find k.

Jyrgernry Apr 21, 2026

0

4

1

+930

help

Distinct prime numbers p, q, and r satisfy the equation p(q + r) = 16. Which of the following prime numbers must either q or r be equal to?
2 3 5 7 11

cooIcooIcooI17 Apr 20, 2026

0

2

+930

help

In triangle ABC, let D be a point on side BC. Select all the true statements.
If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector read more ..

cooIcooIcooI17 Apr 20, 2026

0

4

1

+701

help

All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?

Pythagorearn Apr 20, 2026

0

5

1

+701

help

In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.

Pythagorearn Apr 20, 2026

0

7

1

+275

help

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

CInsbstnkng Apr 20, 2026

0

3

1

+275

help

In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

CInsbstnkng Apr 20, 2026

0

8

0

+226

help

HumanBemg Apr 20, 2026

-1

11

0

+226

help

Semicircles are drawn on diameters \overline{AB} and \overline{CD}, as shown below. Find AB.

HumanBemg Apr 20, 2026

0

9

0

+701

Help

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

Pythagorearn Apr 20, 2026

0

9

0

+701

help

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

Pythagorearn Apr 20, 2026

0

5

0

+248

Help

The graph of y = p(x)/q(x) is shown below, where p(x) and q(x) are quadratic. (Assume that the grid lines are at integers.)
The horizontal asymptote is x = 0 and the only vertical asymptote is y = 0. Find p(3)/q(3)

BlackoutMiIkshake Apr 20, 2026

0

6

0

+248

Help

Triangle ABC is rotated clockwise about A to triangle $AB'C',$ as shown in the diagram. We know the length of the path taken by vertex $B$ is $6.$ What is the length of the path taken by vertex $C?$

BlackoutMiIkshake Apr 20, 2026

0

7

0

+248

Help

Two circles C_1 and C_2 are shown below. Find the radius of the circle that is externally tangent to both $C_1$ and $C_2,$ and tangent to the $x$-axis.

BlackoutMiIkshake Apr 20, 2026

0

11

0

+1844

help

Triangle PQR is rotated clockwise about P to triangle PQ'R', as shown in the diagram. We know the length of the path taken by vertex Q is the same as the length of the path takesn by P. What is the length of the path taken by vertex R?

blackpanther Apr 20, 2026

0

5

0

+1844

help

Line \ell is shown below. The line y = 2x + k has a distance of 3 from line y = 5x + k. Find all possible values of k.

blackpanther Apr 20, 2026

0

7

0

+1042

help

Two tangent circles are shown below. One common external tangent is the x-axis. The equation of the other external common tangent has the form y = mx + b. What is m?

gnistory Apr 20, 2026

0

10

0

+1042

help

Let theta be an acute angle such that sin 2 theta = sin 3 theta + sin 4 theta. What is the measure of theta in degrees?

gnistory Apr 20, 2026

0

2

1

+1348

Help

Let alpha be an angle in the third quadrant such that tan alpha = 4. Find cot alpha.

Triangle PQR is equilateral. Find AQ.
PQR has side length 4, and A is on side PR so that AP = 1.

AnswerscorrectIy Apr 20, 2026

0

3

1

+1348

help

In triangle ABC, \sin A = \frac{4}{5} and \tan C = 1. Find \cos B.

AnswerscorrectIy Apr 20, 2026

0

5

1

+64

Help

ABCDEFGH is a regular octagon. Find the ratio of the area of the red triangle to the area of the blue square.

NotThatSmartTwo Apr 20, 2026

0

8

1

+64

help me

A spherical orange is cut into 8 congruent slices. If the volume of the orange was 8, then what is the volume of each slice?

NotThatSmartTwo Apr 20, 2026

0

3

1

+1056

Geometry

In unit square ABCD, E and F are the midpoints of \overline{AD} and \overline{AB}, respectively. The square is then folded along the edges of triangle CEF, so that triangles AEF, CDE, BCF, cover triangle CEF. read more ..

Hi6942O Apr 20, 2026

0

5

1

+1056

Geometry

Triangular pyramid BCDG is cut from cube ABCDEFGH. The triangular pyramid is then placed on a surface with triangle BCD as the base. Given that the side length of the cube is $12,$ find the height of the pyramid.

Hi6942O Apr 20, 2026

0

3

1

+930

Geometry

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

cooIcooIcooI17 Apr 20, 2026

0

2

1

+930

Geometry

3 kinds of candies: fruit, milk and chocolate were placed into 3 boxes. The number of fruit candies is more than the number of chocolate candies and the number of milk candies is half of fruit candies. There are 390 candies in total. Given that the read more ..

cooIcooIcooI17 Apr 20, 2026

0

4

1

+21

Help

Étienne and Hans were collecting vintage stamps. Étienne gave 1/4 of his stamps to Hans. Hans then gave 1/3 of his total stamps to Étienne. After these exchanges, Étienne had 4 times as many stamps as Hans. If the number of stamps Étienne gave read more ..

Jyrgerhry Apr 20, 2026

0

6

1

+21

Math

Fill in the blanks to make an equation that is linear in disguise, and has a solution.
sqrt(2x - 3) + __x + ___ = ___x - ___ + ____
8 9 10 11 12 13 14 15 16 17 18 19 20

Jyrgerhry Apr 20, 2026

0

2

+312

Algebra

Fill in the blank to make an equation that is linear in disguise, and has a solution.
sqrt(2x - 3) + __x + ___ = ___x - ___ + ____
8 9 10 11 12 13 14 15 16 17 18 19 20

AUnVerifedTaxPayer Apr 18, 2026

0

4

1

+312

Algebra

Fill in the blanks to make the equation true.
___ + ___ = ___
x^4 - 2x^3 + 3x
x^4 + 3x + 1 read more ..

AUnVerifedTaxPayer Apr 18, 2026

0

4

1

+312

Algebra

The large square below is made-up of seven identical rectangles and three identical squares. The height of each of the seven rectangles is h. What is the area of each of the seven rectangles? (Give your answer in terms of h.)

AUnVerifedTaxPayer Apr 17, 2026

0

3

1

+312

Geometry

Fill in the blanks to make the equation true.
(___)^{-1/3} = (___)^{-1/2}
-72 -45 -9 -4 -18 -27 -64 -16 -25

AUnVerifedTaxPayer Apr 17, 2026

0

2

1

+1056

Algebra

Fill in the blanks to make the equation true.
sqrt(___) + sqrt(___) = sqrt(___)
12 28 42 60 4 9 18 27 56 8 16 50 25 40 1 44

Hi6942O Apr 16, 2026

0

6

1

+1056

Algebra

Fill in the blanks to make an expression that is constant (which does not depend on x).
___^(-2) * ___^4 * ____^5
-3 - x - 2 - x + 4 - 2 + x + 6 - x - 8 + 4x + 3 + 5x

Hi6942O Apr 16, 2026

0

3

1

+1056

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 $a + b$.

Hi6942O Apr 16, 2026

0

3

1

+701

Geometry

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

Pythagorearn Apr 13, 2026

0

2

+12

number theory

Let ABCDE be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 90^{\circ},$ then what is the degree measure of $\angle E$?

BatchOfQuestions Apr 13, 2026

0

3

+248

CPhill i need answer

An equilateral triangle, a regular heptagon, a square, a 20-gon, a regular pentagon, a regular hexagon, and a regular n-gon, all with the same side length also completely surround a point. Find n.

BlackoutMiIkshake Apr 7, 2026

0

2

1

+248

help Cphill

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 ..

BlackoutMiIkshake Apr 7, 2026

0

2

+248

help help

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[ABD]=8$ and $[PBC]=8$, then what is $[PAB]$?

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

plz help

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[PBC] = 15$ and $CD = 3 \cdot AD,$ what is $[ABCD]$?

BlackoutMiIkshake Apr 7, 2026

0

5

1

+248

helphelphelp

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 $k?$

BlackoutMiIkshake Apr 7, 2026

0

3

1

+248

i need help CPhil

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

plz help

Point P lies in regular hexagon ABCDEF such that [ABP ] = 3, [CDP] = 3, and [EFP] = 3. Compute [BCP].

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

help me Cphil

Regular hexagon ABCDEF is inscribed in rectangle PQRS. If [AFP] = 20 and [ABC] = 25, then find [ABCDEF].

BlackoutMiIkshake Apr 7, 2026

0

6

1

+248

Cphil help me

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 $BD$?

BlackoutMiIkshake Apr 7, 2026

0

3

1

+248

CPhill help me

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 $DE$?

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

help me now

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.

BlackoutMiIkshake Apr 7, 2026

0

3

1

+248

help help

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

help me now

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 $BX$?

BlackoutMiIkshake Apr 7, 2026

0

3

1

+248

need help

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

BlackoutMiIkshake Apr 7, 2026

0

3

2

+248

help help help help

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 $BD$?

BlackoutMiIkshake Apr 7, 2026

0

5

1

+248

need help now

Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<read more ..

BlackoutMiIkshake Apr 7, 2026

0

5

1

+248

Need help

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, read more ..

BlackoutMiIkshake Apr 7, 2026

0

4

1

+248

help geometry

Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

BlackoutMiIkshake Apr 7, 2026

0

2

1

+248

help mee

In triangle ABC, let D be a point on side BC. Select all the true statements.
If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector read more ..

BlackoutMiIkshake Apr 7, 2026

0

6

1

+248

help geo

In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.

BlackoutMiIkshake Apr 7, 2026

0

8

1

+248

Help help

In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

BlackoutMiIkshake Apr 6, 2026

0

69

1

+248

Plz help

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

BlackoutMiIkshake Apr 6, 2026

0

4

1

+248

help me help

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

BlackoutMiIkshake Apr 6, 2026

0

6

1

+248

help CPhill

Triangular pyramid BCDG is cut from cube ABCDEFGH. The triangular pyramid is then placed on a surface with triangle BCD as the base. Given that the side length of the cube is $12,$ find the height of the pyramid.

BlackoutMiIkshake Apr 6, 2026

0

4

1

+226

help me now

In unit square ABCD, E and F are the midpoints of \overline{AD} and \overline{AB}, respectively. The square is then folded along the edges of triangle CEF, so that triangles AEF, CDE, BCF, cover triangle CEF. read more ..

HumanBemg Apr 6, 2026

0

6

1

+226

help me CPhill

A spherical orange is cut into 8 congruent slices. If the volume of the orange was 8, then what is the volume of each slice?

HumanBemg Apr 6, 2026

0

12

0

+226

Help CPhill

HumanBemg Apr 6, 2026

+1

2

1

+21

Area

What is the area of this figure?

what is the area of this figure

Jyrgerhry Apr 5, 2026

0

4

1

+16

Hey CPhill please help me

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.

BlackoutMilkshake Apr 4, 2026

0

2

1

+12

Algebra

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 $WXYZ$?

BatchOfQuestions Apr 4, 2026

0

4

1

+12

Geometry

NotThatSmart ●

BatchOfQuestions Apr 4, 2026

+1

2

1

+2029

hello

just poppin and sayin hi
i see u online CPhill :)

ABCDEFGH is a regular octagon. Find the ratio of the area of the red triangle to the area of the blue square.

NotThatSmart Apr 4, 2026

0

3

2

+1757

Geometry

In triangle ABC, \sin A = \frac{4}{5} and \tan C = 1. Find \cos B.

parmen Mar 25, 2026

0

3

+1661

Geometry

Triangle PQR is equilateral. Find AQ.
PQR has side length 4, and A is on side PR so that AP = 1.

kittykat Mar 24, 2026

0

4

1

+1661

Geometry

Let alpha be an angle in the third quadrant such that tan alpha = 4. Find cot alpha.

kittykat Mar 23, 2026

0

2

+1661

Geometry

Let theta be an acute angle such that sin 2 theta = sin 3 theta + sin 4 theta. What is the measure of theta in degrees?

kittykat Mar 19, 2026

0

2

3

+1661

Geometry

Two tangent circles are shown below. One common external tangent is the x-axis. The equation of the other external common tangent has the form y = mx + b. What is m?

kittykat Mar 19, 2026

0

2

+1661

Geometry

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

kittykat Mar 18, 2026

0

2

+1661

Geometry

Line \ell is shown below. The line y = 2x + k has a distance of 3 from line y = 5x + k. Find all possible values of k.

kittykat Mar 18, 2026

0

3

+1661

Geometry

Triangle PQR is rotated clockwise about P to triangle PQ'R', as shown in the diagram. We know the length of the path taken by vertex Q is the same as the length of the path takesn by P. What is the length of the path taken by vertex R?

kittykat Mar 17, 2026

0

3

+930

Geometry

Hi i offten face difficulties in coverting number into words. is there any reliable solution to this. or any advice.
Thanks.

cooIcooIcooI17 Mar 16, 2026

0

4

2

+4

How to convert numbers to words?

Two circles C_1 and C_2 are shown below. Find the radius of the circle that is externally tangent to both $C_1$ and $C_2,$ and tangent to the $x$-axis.

jamesright22 Mar 10, 2026

0

3

2

+1661

Geometry

Triangle ABC is rotated clockwise about A to triangle $AB'C',$ as shown in the diagram. We know the length of the path taken by vertex $B$ is $6.$ What is the length of the path taken by vertex $C?$

kittykat Mar 5, 2026

0

4

3

+1661

Geometry

kittykat Mar 2, 2026

0

5

1

+1757

Geometry

Find XY if UV = 12

In the figure, triangles ABC$ and ACD are similar. What is \angle B in degrees?

parmen Feb 28, 2026

0

17

1

+1757

Geometry

A spherical orange is cut into 8 congruent slices. If the volume of the orange was 8, then what is the volume of each slice?

parmen Feb 27, 2026

0

5

1

+1661

Geometry

In unit square ABCD, E and F are the midpoints of \overline{AD} and \overline{AB}, respectively. The square is then folded along the edges of triangle CEF, so that triangles AEF, CDE, BCF, cover triangle CEF. read more ..

kittykat Feb 26, 2026

0

5

3

+1661

Geometry

Triangular pyramid BCDG is cut from cube ABCDEFGH. The triangular pyramid is then placed on a surface with triangle BCD as the base. Given that the side length of the cube is $12,$ find the height of the pyramid.

kittykat Feb 24, 2026

0

5

3

+1661

Geometry

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

kittykat Feb 24, 2026

+1

4

1

+226

Geometry

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

HumanBemg Feb 20, 2026

0

9

1

+226

Geometry

Hi friends,
it's been a couple of years since I've last been here, nice to see you guys are still around. Today please, I just need clarification on a solution. I hope supplying pictures will be okay.
This is the drawing: read more ..

HumanBemg Feb 20, 2026

+1

16

1

+5

Triangle ratios

Compute \angle AGD, in degrees.

Urimagic Feb 6, 2026

0

4

2

+990

Math

Find the radius of the quarter-circle.

booboo44 Jan 28, 2026

-2

5

2

+990

Math

Prove that for all numbers N;

booboo44 Jan 28, 2026

+1

3

2

+123

Proof

Evaluate the derivative:
Using this derivative, find the slope of the graph at the x-values of 1, 2, and 3.

nerdboy Jan 28, 2026

0

4

1

+123

Easy Derivatives

nerdboy Jan 27, 2026

+1

8

2

+123

Beginner limit

Evaluate the limit:

nerdboy Jan 27, 2026

+1

4

1

+123

Beginning Integral

Evaluate

Two quarter-circles are drawn inside a unit square. A smaller square is inscribed in the two quarter-circles. Find the area of the smaller square.

nerdboy Jan 27, 2026

0

3

4

+1661

Math

The circle below centered at $O$ has a radius of $5.$ Find $CD.$

kittykat Jan 26, 2026

0

6

1

+1661

Math

Semicircles are drawn on diameters \overline{AB} and \overline{CD}, as shown below. Find AB.

kittykat Jan 26, 2026

0

4

1

+1661

Math

In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

kittykat Jan 26, 2026

+1

3

+990

Math

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

booboo44 Jan 23, 2026

0

3

2

+990

Math

In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.

booboo44 Jan 22, 2026

0

4

1

+990

Math

All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?

booboo44 Jan 22, 2026

0

4

+1944

Math

In triangle ABC, let D be a point on side BC. Select all the true statements.
If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector read more ..

tomtom Jan 17, 2026

0

5

1

+1944

Math

Bekah has three brass house number digits: 2, 3, 4, 5, and 6. How many distinct numbers can she form using one or more of the digits, if her number must be divisible by 4?

tomtom Jan 17, 2026

0

6

1

+404

Math

Ms. Lee has 12 boxes of crayons. Next year, she plans to buy 250% more boxes. How many boxes will she have in all?
Responses
15 boxes
15 boxes read more ..

Stanry Jan 16, 2026

0

9

1

+4

Ms. Lee has 12 boxes of crayons. Next year, she plans to buy 250% more boxes. How many boxes will she have in all? Responses 15 boxes 15 bo

To win a game with a fair coin, you must flip n+1 heads in a row, where $n$ is the total number of tails flipped so far. So if your first flip is heads, you win and the game is over; if your first flip is tails but your next two in a row are heads, you read more ..

emmaisthebest Jan 16, 2026

0

2

+1348

Math

A train engine and carriages have a total mass of 750 tons
Its brakes fail, and it crashes into the barrier in the terminus with a force of 1,687,500 N.
The barrier stops the train in 15 s.
Calculate the velocity of the train in km/h just read more ..

AnswerscorrectIy Jan 15, 2026

+1

36

1

+123

Easy Physics Problem

The sum of the prime numbers from 1-10, 11-20, 21-30, 31-40, and 41-50 are multiplied together with 997. What is the remainder when this result is divided by 97?

nerdboy Jan 14, 2026

+2

23

1

+123

Modulo

Distinct prime numbers p, q, and r satisfy the equation p(q + r) = 16. Which of the following prime numbers must either q or r be equal to?
2 3 5 7 11

nerdboy Jan 14, 2026

0

27

2

+248

Math

ElectricPavlov ●●

BlackoutMiIkshake Oct 24, 2025

0

29

1

+248

Math

The triangle with vertices at (1,0), (0,1), and (k,k) has area 1/2. Find k.

Mrs. Monstrous Millie wants to throw a party for a group of monsters and aliens. The monsters each have 5 heads with 7 ears on each head, and the aliens each have 5 heads with 3 ears on each head. As party favors, Mrs. Millie wants to give each guest a read more ..

BlackoutMiIkshake Oct 24, 2025

-1

30

1

+248

Math

Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

BlackoutMiIkshake Oct 24, 2025

0

31

1

+248

Math

Bosco ●

BlackoutMiIkshake Oct 22, 2025

0

24

2

+248

Math

William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:

* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every read more ..

Two chords with length r are drawn on a circle of radius r. What is the maximum possible distance between their endpoints?

BlackoutMiIkshake Oct 22, 2025

+1

24

1

+248

Math

asinus ●

BlackoutMiIkshake Oct 22, 2025

+1

7

1

+248

Math

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, read more ..

Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<read more ..

BlackoutMiIkshake Oct 21, 2025

-1

7

1

+248

Math

A number is chosen at random from among all 9-digit numbers that use each of the digits 1 through 9 exactly once. What is the probability that this number is a multiple of 2?

BlackoutMiIkshake Oct 21, 2025

0

5

2

+248

Math

Bosco ●●

BlackoutMiIkshake Oct 20, 2025

0

7

1

+248

Math

Three squares of a 5 \times 5 grid are colored. Two colorings are conisdered equivalent if one coloring can be rotated to form the other coloring, such as the two colorings below, and the grid can be reflected as well. We also want the three read more ..

Selma multiplies the number 9 the two-digit number \overline{AB}, and the three-digit number \overline{CDE}. She finds that the product of all three numbers is the five-digit number 41409. Compute the sum \overline{AB} + \overline{CDE}. read more ..

BlackoutMiIkshake Oct 20, 2025

0

6

1

+248

Math

Given a positive integer N, a multiplication decomposition of N is a sequence of positive integers (d_1, d_2, \dots, d_k) such that
* d_1 \neq 1,
* d_i divides d_{i + 1} for 1 \le i \le k - 1, and
* d_1 d_2 \dotsm d_k = N.
The last read more ..

BlackoutMiIkshake Oct 20, 2025

0

12

1

+248

Math

A traffic light runs repeatedly through the following cycle: green for 40 seconds, then yellow for 5 seconds, then red for 35 seconds, which repeats indefinitely. Oliver picks a random time and watches the light for 75 seconds. What is the probability read more ..

BlackoutMiIkshake Oct 20, 2025

0

5

2

+248

Math

Consider a cube with side length 1, together with 14 congruent spheres each of radius r, with 8 of the spheres centered at the 8 vertices of the cube and the remaining $6$ spheres centered at the centers of the $6$ faces of the cube. Suppose $r$ is chosen read more ..

BlackoutMiIkshake Oct 20, 2025

0

15

1

+248

Math

What is the units digit of 1^1 + 2^2 + 3^4 + 4^8?

BlackoutMiIkshake Oct 20, 2025

0

5

2

+248

Math

A square has two of its vertices at (12, 34) and (-98, 56),$ and another vertex at (a, b). What is the sum of all possible values of the area of the square?

BlackoutMiIkshake Oct 18, 2025

0

12

1

+248

Math

At Patty the panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and papaya popsicles. If Prajwal the porcupine, Petunia the peacock, and Pete read more ..

BlackoutMiIkshake Oct 18, 2025

0

13

1

+248

Math

In a rectangular prism, the surface area is 24 and the sum of the lengths of all twelve edges is 24. What is the volume of the prism?

BlackoutMiIkshake Oct 17, 2025

0

4

1

+248

Math

For how many prime numbers p less than 100 is the sum of p's digits less than or equal to 2?

BlackoutMiIkshake Oct 17, 2025

0

11

1

+248

Math

In the game Nerdle, a player tries to guess a true equation made up of $8$ symbols, each of which is either $+,$ $-,$ $*,$ $/,$ $=,$ or one of the digits from $0$ to $9.$ A square turns teal if the symbol is correct and in the correct location, magenta read more ..

BlackoutMiIkshake Oct 17, 2025

0

10

1

+248

Math

Define the importance of a point (x, y) on the coordinate plane to be x^2 + y^2. There exist some points with positive, integer $x$- and $y$-coordinates whose importances are 5. Find the area of the convex polygon determined by those points.

BlackoutMiIkshake Oct 17, 2025

0

12

1

+248

Math

A set of 16 positive integers has mean, median, and unique mode all equal to 5. What is the largest possible value of one of the numbers in the set?

BlackoutMiIkshake Oct 17, 2025

0

8

2

+248

Math

Haoyu gives Mingze and Yihan two different positive integers, and tells them that the product of their numbers is less than 1000. They are also aware that they have two different positive integers. They have the following conversation:
Mingze: read more ..

BlackoutMiIkshake Oct 17, 2025

0

13

1

+248

Math

Sunita and Mohammed play a game where they start with a pile of candy and take turns eating a prime number of pieces of candy from the pile. A player who leaves 0 or 1 candies in the pile after their move wins. If Sunita and Mohammed both play perfectly read more ..

BlackoutMiIkshake Oct 17, 2025

0

13

1

+248

Math

The shaded region below has area a+b\pi where a and b are positive integers. What is a+b? (You may assume the boundary of each region is made up of straight lines and circular arcs, and the squares of the grid have side length $1.$) read more ..

BlackoutMiIkshake Oct 17, 2025

0

5

1

+248

Math

Jason is driving from his home to his office, which is 20 miles away. He normally drives at a constant speed of 60 miles per hour for the whole trip. However today, 15 minutes into his drive, his car breaks down. He calls a taxi, and it arrives 20 minutes read more ..

BlackoutMiIkshake Oct 17, 2025

0

9

2

+248

Math

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 $BD$?

BlackoutMiIkshake Oct 17, 2025

0

16

1

+930

Math

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

cooIcooIcooI17 Oct 16, 2025

0

6

1

+930

Math

cooIcooIcooI17 Oct 16, 2025

0

13

1

+16

Math

Area of compound figure

BlackoutMilkshake Oct 15, 2025

0

5

1

+16

Math

area of compound figure

I need help. What's the answer?

BlackoutMilkshake Oct 15, 2025

0

8

1

+16

Math

We define a formula that calculates both and . What formula would you create (or use)?

BlackoutMilkshake Oct 15, 2025

0

20

1

+4

Math

For a positive integer n, let
a_n = 1 + \sqrt{\frac{1}{n}} - \sqrt{\frac{1}{n + 1}
Compute the product a_1 a_2 a_3 \dotsm a_{99}.

CharlieMathematical Oct 11, 2025

0

10

1

+1844

Math

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

blackpanther Oct 7, 2025

0

8

1

+1844

Math

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up four times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.

blackpanther Oct 7, 2025

+1

12

2

+275

Math

In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

CInsbstnkng Oct 7, 2025

-1

7

4

+275

Math

Some context:
Currently, I am in 9th grade and taking Calculus BC.
I can understand competition math problems and what they are asking for but I don't really have a sense for solving them.
I should have started preparing earlier and read more ..

CInsbstnkng Oct 7, 2025

+1

27

3

+5

AMC 10 I want to make AIME - PLEASE HELP

I’ve been working on this series and I’m not sure if I’m approaching it the right way:
At first glance it looks like it might behave similar to the alternating harmonic series, but the sine term is throwing me off. I’m wondering whether this read more ..

OOOOOOOO Oct 6, 2025

0

18

4

+4

Stuck on a Tricky Series Problem

Let M⊂R∞×∞\mathcal{M} \subset \mathbb{R}^{\infty \times \infty}M⊂R∞×∞ be the set of all improperly convergent matrices whose entries are defined by the double integral:
Mij=∫0∞∫0∞sin⁡(ix)cos⁡(jy)x2+y2+ij dx dyM_{ij} = \int_0^{\infty} \int_0^{\infty} read more ..

skylerclooney Oct 1, 2025

0

48

2

+4

plz help im cooked

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

fof.urmum Sep 28, 2025

0

7

30

3

+1348

Math

Bosco ●●●

AnswerscorrectIy Aug 25, 2025

0

8

32

1

+1348

Math

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(x^3)$ are drawn, at how many points do they intersect?

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 $ABC.$

AnswerscorrectIy Aug 25, 2025

0

7

36

1

+990

Math

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 $BX$?

booboo44 Aug 23, 2025

0

6

38

1

+990

Math

Bosco ●

booboo44 Aug 23, 2025

0

9

35

1

+1348

Math

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

In rectangle , points and lie on so that and is the midpoint of . Also, intersects at and at . The area of rectangle is 70. Find the area of triangle .
read more ..

AnswerscorrectIy Aug 23, 2025

0

14

1

+67

Geometry Please answer with steps

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.

bqimath Aug 23, 2025

0

8

36

3

+1348

Math

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 $DE$?

AnswerscorrectIy Aug 23, 2025

-1

7

32

1

+1348

Math

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 $BD$?

AnswerscorrectIy Aug 22, 2025

0

7

10

2

+1348

Math

Regular hexagon ABCDEF is inscribed in rectangle PQRS. If [AFP] = 20 and [ABC] = 25, then find [ABCDEF].

AnswerscorrectIy Aug 22, 2025

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Math

Point P lies in regular hexagon ABCDEF such that [ABP ] = 3, [CDP] = 3, and [EFP] = 3. Compute [BCP].

gnistory Aug 21, 2025

0

9

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Math

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

gnistory Aug 21, 2025

0

8

1

+490

Math

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 $k?$

MeIdHunter Aug 20, 2025

0

8

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Math

The juniors at East HS drink a total of cartons of milk per -day week. If the average senior drinks milk at the same rate as the average junior, what is the average number of total cartons of milk the seniors drink read more ..

MeIdHunter Aug 20, 2025

0

9

5

4

+123

Alcumus

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[PBC] = 15$ and $CD = 3 \cdot AD,$ what is $[ABCD]$?

nerdboy Aug 19, 2025

-1

8

1

+275

Help me help

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[ABD]=8$ and $[PBC]=8$, then what is $[PAB]$?

CInsbstnkng Aug 19, 2025

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Need help

Let p(x) be defined on such that
where y is the greatest prime factor of . Express the range of p in interval notation.
Thanks and also please show the steps too!

CInsbstnkng Aug 19, 2025

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Algebra

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bqimath Aug 19, 2025

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Math

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 ..

Given 5 colors to choose from, how many ways can we color the four unit squares of a 2\times 2 board, given that two colorings are considered the same if one is a rotation or reflection of the other? (Note that we can use the same color for more than one read more ..

MeIdHunter Aug 19, 2025

0

7

39

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how to solve

An equilateral triangle, a regular heptagon, a square, a 20-gon, a regular pentagon, a regular hexagon, and a regular n-gon, all with the same side length also completely surround a point. Find n.

AUnVerifedTaxPayer Aug 19, 2025

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41

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help me help me

Let ABCDE be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 90^{\circ},$ then what is the degree measure of $\angle E$?

CInsbstnkng Aug 18, 2025

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41

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help me

Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

CInsbstnkng Aug 18, 2025

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41

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Help help

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 $n$.

CInsbstnkng Aug 17, 2025

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32

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Help me help

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $15$ positive divisors, and $mn$ has exactly $14$ positive divisors, then how many divisors does $m^2 n^2$ have?

CInsbstnkng Aug 17, 2025

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35

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CPhill answer me

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

cooIcooIcooI17 Aug 16, 2025

0

50

2

+226

Help me CPhill Now

Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?

HumanBemg Aug 16, 2025

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51

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Help me

For integers $a$ and $T$, $T \neq 0,$ a parabola whose general equation is $y = ax^2 + bx + c$ passes through the points $A = (0,0),$, $B = (2T,0)$, $C = (2T + 1,28).$ and $N$ Let be the sum read more ..

bIueb3rry Aug 16, 2025

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38

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NEED HELP CPhill ASAP

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.

Dragononweb2.0calc Aug 16, 2025

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45

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Geometry

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 ..

nathanl6656 Aug 15, 2025

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39

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Math

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

gnistory Aug 15, 2025

0

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41

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I need answer

In the diagram below, is a square. Find x[asy]
unitsize(1.5 cm);
pair A, B, C, D, P;
A = (0,3);
B = (0,0);<#> C = (3,0);<#> D = (3,3);<#> P = (0.8,1.8);<#> draw(A--B--C--D--cycle);<#> draw(A--P);<#> draw(B--P);<#> read more ..

booboo44 Aug 15, 2025

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48

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+5

help me plz

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askdjlkadjwl123 Aug 14, 2025

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34

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help me now

Shown below is rectangle EFGH. Its diagonals meet at Y. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If EX = 24 and $GY = 30$, find the perimeter of rectangle $EFGH$.

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

CInsbstnkng Aug 13, 2025

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Help help help

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.

CInsbstnkng Aug 11, 2025

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35

1

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Help me

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

CInsbstnkng Aug 11, 2025

-1

38

1

+275

Help me!

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

CInsbstnkng Aug 11, 2025

-1

38

1

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Help

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

CInsbstnkng Aug 11, 2025

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39

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help 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 ..

CInsbstnkng Aug 10, 2025

-1

34

1

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HELP!!!

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 $AB$?

CInsbstnkng Aug 9, 2025

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52

0

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help me now

CInsbstnkng Aug 8, 2025

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47

0

+275

help!!!

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 ..

CInsbstnkng Aug 8, 2025

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31

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help me plz

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.

For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

CInsbstnkng Aug 8, 2025

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39

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help me!

For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does $n$ leave when divided by $23$?

CInsbstnkng Aug 7, 2025

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help help help

Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.

CInsbstnkng Aug 7, 2025

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I need help

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.

CInsbstnkng Aug 5, 2025

-1

16

1

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Help me

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 $XZ = 5$ and $YZ = 2,$ find $WX.$

CInsbstnkng Aug 5, 2025

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44

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Help help

CInsbstnkng Aug 3, 2025

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Need help

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 $AB = 2$, then find $AC.$

CInsbstnkng Aug 3, 2025

-1

11

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Help me help

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.

CInsbstnkng Aug 3, 2025

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Algebra

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

bqimath Aug 2, 2025

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Plz help

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.

CInsbstnkng Aug 2, 2025

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Help

There is a group of five children, where two of the children are twins. In how many ways can I distribute $12$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

CInsbstnkng Aug 2, 2025

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25

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Need help (it's really me!!!)

How many solutions are there to the equation
u + v + w + x + y + z = 6
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $8$ and $y$ is even?

CInsbstnkng Aug 2, 2025

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29

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Help!!! (really me)

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Aug 2, 2025

+1

11

5

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HELP!!! (From the real Clnsbstnkng)

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 ..

Clnsbstnkng Aug 2, 2025

-1

36

0

+275

HELP!!!

CInsbstnkng Aug 1, 2025

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34

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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

CInsbstnkng Aug 1, 2025

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22

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Help me

If z is a complex number such that z + 1/z = 3, what is the value of z^2 + 1/z^2?

Let z1 and z2 be two complex numbers such that |z1| = 5 and (z1/z2)+(z2/z1)=0.
Find z1+z2.

CInsbstnkng Aug 1, 2025

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HELP HELP

George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for , and wants each husband to be seated opposite his wife. How many seating arrangements can he make, read more ..

CInsbstnkng Aug 1, 2025

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14

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Counting & Probability

An ellipse has its foci at (-1, -1) and (-1, -3).
Given that it passes through the point (0, 2), its equation can be written in the form ((x-h)2/a2)/((y-k)2/b2)=1 where a, b, h, k are constants, and a and b are positive. Find a+k.

bqimath Aug 1, 2025

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38

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HELP ME

CInsbstnkng Jul 31, 2025

-1

7

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HELP

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $BY = 2$ and $AZ = 4$, then what is the area of rectangle $WXYZ$?

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 2$, $BY = 16$, $\angle ACB = 90^\circ$, and $CY = 2 \cdot CX$, then find $AB$.

CInsbstnkng Jul 31, 2025

-1

27

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+275

help help

CInsbstnkng Jul 31, 2025

-1

27

1

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help me!

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

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 ..

CInsbstnkng Jul 31, 2025

-1

25

1

+275

HELP!!!

Suppose a does not equal 0. Compute log base 8a (4^b) in terms of a and b.

CInsbstnkng Jul 31, 2025

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23

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Help!

The ellipse shown below is defined by the equation PF1+PF2=d.
Find d.

CInsbstnkng Jul 31, 2025

+1

21

5

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HELP!!!

Rectangle ADEH is divided into rectangles ABGH, BCFG, and CDEF. If $AC = 15,$ $GE = 15,$ $[ABGH] = 8,$ and $[CDEF] = 8,$ find $[BCFG].$

Clnsbstnkng Jul 30, 2025

-1

35

0

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help help

CInsbstnkng Jul 30, 2025

-1

46

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help me

In the diagram, XY = 2\cdot AX = 2\cdot YB and $\dfrac{AZ}{BX} = \dfrac{2}{5}$. Find $\dfrac{[YBC]}{[ZYC]}$.

CInsbstnkng Jul 30, 2025

-1

17

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plz help

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 \le 1
in nonnegative integers.

In how many ways can you distribute $8$ indistinguishable balls among $6$ distinguishable boxes, if at least three of the boxes must be empty?

CInsbstnkng Jul 29, 2025

-1

30

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Help help!

Point X is on side \overline{AC} of triangle $ABC$ such that $\angle AXB =\angle ABX + 20^\circ$, and $\angle ABC - \angle BAC = 36^\circ$. Find $\angle XBC$ in degrees.

CInsbstnkng Jul 29, 2025

-1

34

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Help me

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_8,$ $a_9,$ $a_{10}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 = 5$ and $a_2 + a_4 + a_6 + a_8 + a_{10} = -2$, then find $a_1$.

CInsbstnkng Jul 29, 2025

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16

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Help!! real

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

CInsbstnkng Jul 29, 2025

+1

12

7

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Geometry from alcumus

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bqimath Jul 29, 2025

-1

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Help me plz

Triangle DEF is the medial triangle of triangle ABC, and triangle $XYZ$ is the medial triangle of triangle $DEF.$ If the area of triangle $XYZ$ is $8$, what is the area of triangle $ABC?$

In triangle ABC, \angle A = 90^\circ. Altitude $\overline{AP},$ angle bisector $\overline{AQ},$ and median $\overline{AR}$ are drawn. If $PQ = 3$ and $QC = 4,$ find $AR.$

CInsbstnkng Jul 29, 2025

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29

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Need help now

An ellipse has its foci at (-1, -1) and (-1, -3).
Given that it passes through the point (4, -2), its equation can be written in the form ((x-h)2/a2)/((y-k)2/b2)=1 where a, b, h, k are constants, and a and b are positive. Find a+k.

CInsbstnkng Jul 29, 2025

+1

16

7

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HELP!!! (From the real Clnsbstnkng)

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Clnsbstnkng Jul 29, 2025

-1

46

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Help!

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

CInsbstnkng Jul 28, 2025

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Help help

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

CInsbstnkng Jul 28, 2025

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Help

Four cubes of volumes $1 \text{ cm}^3$, $2 \text{ cm}^3$, $3 \text{ cm}^3$, and $4 \text{ cm}^3$ are glued together at their faces. What is the number of square centimeters in the smallest possible surface area of the resulting solid figure?

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 ..

CInsbstnkng Jul 28, 2025

-1

26

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Help!!

Triangle ABC is congruent to triangle DEF, but triangle ABC is not congruent to triangle XYZ. Which of the following relationships cannot hold?
ABC and DEF have the same area
ABC and DEF have the same perimeter
ABC read more ..

CInsbstnkng Jul 28, 2025

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Help with geo

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

CInsbstnkng Jul 28, 2025

-1

23

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Need help

Compute the smallest positive integer n such that n+i, (n+i)*2, and (n+i)*3 are the vertices of a triangle in the complex plane whose area is greater than 2015.

CInsbstnkng Jul 28, 2025

-1

31

1

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Plz help!!!

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Jul 28, 2025

+1

17

2

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HELP!!! (From the OG Clnsbstnkng)

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

Clnsbstnkng Jul 28, 2025

+1

9

3

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HELP!!!

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

Clnsbstnkng Jul 28, 2025

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Plz help

Two points, A and B, are on the pavement 6 inches apart. Cassidy the caterpillar traces out a path walking along all the points that are equidistant to as from . Cassidy has red paint on her feet, so she literally traces out the whole path! read more ..

CInsbstnkng Jul 27, 2025

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Help me

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

CInsbstnkng Jul 27, 2025

-1

19

3

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Plz help

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

CInsbstnkng Jul 27, 2025

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Help help help

Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter. For example, there are five partitions of 4:
4
3 + 1
2 + 2 read more ..

CInsbstnkng Jul 27, 2025

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Help me

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

CInsbstnkng Jul 27, 2025

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Need help

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Jul 27, 2025

+1

9

4

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HELP!!!

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

Clnsbstnkng Jul 26, 2025

-1

19

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Help CPHILL!!!

Compute the smallest positive integer n such that n+i, (n+i)2, and (n+i)3 are the vertices of a triangle in the complex plane whose area is greater than 2015.

CInsbstnkng Jul 26, 2025

+1

10

6

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HELP!!!

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Clnsbstnkng Jul 25, 2025

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19

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Help!

In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

CInsbstnkng Jul 25, 2025

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Help

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

CInsbstnkng Jul 25, 2025

0

13

1

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Help

Karlanna places 600 marbles into m total boxes such that each box contains an equal number of marbles. There is more than one box, and each box contains more than one marble. For how many values of m can this be done?

CInsbstnkng Jul 25, 2025

+1

17

4

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Number Theory

Right triangles ABC, ADE, EFG, and GHC are all similar. Also, $[ADE] = 1,$ $[EFG] = 1,$ and $[GHC] = 1.$ Find the area of the red region.

bqimath Jul 25, 2025

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Help help

CInsbstnkng Jul 25, 2025

-1

41

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Help me

Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

CInsbstnkng Jul 24, 2025

-1

41

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Help!

The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

CInsbstnkng Jul 24, 2025

+1

12

4

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HELP!!!

Let z be a complex number such that |z|=1.
Find the maximum value of |1+z|+|1-z+z2|.

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Clnsbstnkng Jul 24, 2025

-1

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CInsbstnkng Jul 24, 2025

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A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

CInsbstnkng Jul 24, 2025

-1

35

1

+275

Help help