All Questions

+1056

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 ..

Hi6942O 6 hours ago

May 14, 2026

+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 6 hours ago

+1056

help

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

Hi6942O 7 hours ago

+982

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 ..

booboo44 May 14, 2026

May 13, 2026

+982

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 13, 2026

+982

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

+982

help

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

booboo44 May 13, 2026

May 12, 2026

+1313

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 ..

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AnswerscorrectIy May 12, 2026

May 11, 2026

May 9, 2026

May 8, 2026

+982

help

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

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booboo44 May 8, 2026

May 7, 2026

+234

help

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

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Boseo May 7, 2026

May 6, 2026

+234

help

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

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Boseo May 6, 2026

May 5, 2026

May 4, 2026

May 3, 2026

May 2, 2026

+1536

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)?

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learnmgcat May 2, 2026

+1536

help

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

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learnmgcat May 2, 2026

May 1, 2026

+1536

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,___).

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learnmgcat May 1, 2026

Apr 30, 2026

+228

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,___).

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BlackoutMiIkshake Apr 30, 2026

Apr 29, 2026

Apr 28, 2026

+105

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 ..

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Jyrgernry Apr 28, 2026

Apr 27, 2026

+105

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).

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Jyrgernry Apr 27, 2026

+105

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)

Ichbineule ●

Jyrgernry Apr 27, 2026

+105

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)

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Jyrgernry Apr 27, 2026

+105

help

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)

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Jyrgernry Apr 27, 2026

+105

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)

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Jyrgernry Apr 27, 2026

+105

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)

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Jyrgernry Apr 27, 2026

+105

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)

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Jyrgernry Apr 27, 2026

Apr 25, 2026

Apr 24, 2026

+105

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 = ___.

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Jyrgernry Apr 24, 2026

Apr 23, 2026

+1844

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 = ___.

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blackpanther Apr 23, 2026

+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 ___ %.

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blackpanther Apr 23, 2026

+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

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blackpanther Apr 23, 2026

+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 ..

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blackpanther Apr 23, 2026

+1056

help

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Hi6942O Apr 23, 2026

+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 ..

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Hi6942O Apr 23, 2026

+105

help

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Jyrgernry Apr 23, 2026

Apr 22, 2026

+105

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)).

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Jyrgernry Apr 22, 2026

+105

help

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

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Jyrgernry Apr 22, 2026

+105

help

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

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Jyrgernry Apr 22, 2026

+21

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 ..

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Jyrgerhry Apr 22, 2026

+1944

help

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

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tomtom Apr 22, 2026

+105

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 ..

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Jyrgernry Apr 22, 2026

+105

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?

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Jyrgernry Apr 22, 2026

+105

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 ..

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Jyrgernry Apr 22, 2026

+105

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.

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Jyrgernry Apr 22, 2026

+105

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).

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Jyrgernry Apr 22, 2026

+2741

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.

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LiIIiam0216 Apr 22, 2026

+2741

help

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

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LiIIiam0216 Apr 22, 2026

+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 ..

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LiIIiam0216 Apr 22, 2026

+1313

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

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AnswerscorrectIy Apr 22, 2026

+1863

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?

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ABJeIIy Apr 22, 2026

+1863

help

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

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ABJeIIy Apr 22, 2026

need help learning please

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 ..

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huntsigh Apr 22, 2026

+105

Algebra

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

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Jyrgernry Apr 22, 2026

+105

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)).

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Jyrgernry Apr 22, 2026

+105

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.

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Jyrgernry Apr 22, 2026

+105

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 $a-b$?

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Jyrgernry Apr 22, 2026

+21

The Custom Trophy Base

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 ..

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Jyrgerhry Apr 22, 2026

+1313

help

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.

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AnswerscorrectIy Apr 22, 2026

+1313

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 ..

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AnswerscorrectIy Apr 22, 2026

+665

help

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

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Pythagorearn Apr 22, 2026

+665

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.

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Pythagorearn Apr 22, 2026

+665

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.

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Pythagorearn Apr 22, 2026

+665

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.

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Pythagorearn Apr 22, 2026

Apr 21, 2026

+1014

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)?

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gnistory Apr 21, 2026

+1014

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)?

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gnistory Apr 21, 2026

+1014

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 ..

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gnistory Apr 21, 2026

+1014

help

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

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gnistory Apr 21, 2026

+665

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.

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Pythagorearn Apr 21, 2026

+665

help

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

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Pythagorearn Apr 21, 2026

+665

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 $f(f(f(x)))=-3$ ?

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Pythagorearn Apr 21, 2026

+665

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?

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Pythagorearn Apr 21, 2026

+1661

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 ..

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kittykat Apr 21, 2026

+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 ..

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kittykat Apr 21, 2026

+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.

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kittykat Apr 21, 2026

+234

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)).

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Boseo Apr 21, 2026

+234

help

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

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Boseo Apr 21, 2026

+234

help

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

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Boseo Apr 21, 2026

+890

help

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

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cooIcooIcooI17 Apr 21, 2026

+890

help

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

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cooIcooIcooI17 Apr 21, 2026

+890

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?

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cooIcooIcooI17 Apr 21, 2026

+228

help

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

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BlackoutMiIkshake Apr 21, 2026

+228

help

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

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BlackoutMiIkshake Apr 21, 2026

+228

help

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

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BlackoutMiIkshake Apr 21, 2026

+1844

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.

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blackpanther Apr 21, 2026

+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 $a-b$?

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blackpanther Apr 21, 2026

+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.

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blackpanther Apr 21, 2026

+1014

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)).

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gnistory Apr 21, 2026

+1014

help

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

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gnistory Apr 21, 2026

+1014

help

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

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gnistory Apr 21, 2026

+1056

help

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

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Hi6942O Apr 21, 2026

+1056

help

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

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Hi6942O Apr 21, 2026

+1056

help

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

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Hi6942O Apr 21, 2026

+1757

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 $m-n$?

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parmen Apr 21, 2026

+1757

help

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

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parmen Apr 21, 2026

+1757

help

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

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parmen Apr 21, 2026

+1661

help

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

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kittykat Apr 21, 2026

+1661

help

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

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kittykat Apr 21, 2026

+1661

help

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

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kittykat Apr 21, 2026

+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?

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kittykat Apr 21, 2026

+1661

help

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kittykat Apr 21, 2026

+1661

help

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

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kittykat Apr 21, 2026

-1

+407

help

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

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ikleyn Apr 21, 2026

+1661

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.

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kittykat Apr 21, 2026

+1661

help

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

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kittykat Apr 21, 2026

+1014

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 ..

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gnistory Apr 21, 2026

+1014

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

+226

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 ..

HumanBemg Apr 21, 2026

+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

+105

help

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

Jyrgernry Apr 21, 2026

+105

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

+890

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?

cooIcooIcooI17 Apr 21, 2026

+890

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

+105

helpme

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?

Jyrgernry Apr 21, 2026

+105

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.

Jyrgernry Apr 21, 2026

Apr 20, 2026

+890

help

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

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cooIcooIcooI17 Apr 20, 2026

+890

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

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cooIcooIcooI17 Apr 20, 2026

+665

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 ..

Pythagorearn Apr 20, 2026

+665

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

+275

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.

CInsbstnkng Apr 20, 2026

+275

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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

+226

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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.

HumanBemg Apr 20, 2026

-1

+226

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

HumanBemg Apr 20, 2026

+665

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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

+665

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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

+228

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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

+228

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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

+228

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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

+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

+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

+1014

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

+1014

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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

+1313

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

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AnswerscorrectIy Apr 20, 2026

+1313

help

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

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AnswerscorrectIy Apr 20, 2026

+64

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

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NotThatSmartTwo Apr 20, 2026

+64

help me

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

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NotThatSmartTwo Apr 20, 2026

+1056

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?

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Hi6942O Apr 20, 2026

+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 ..

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Hi6942O Apr 20, 2026

+890

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.

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cooIcooIcooI17 Apr 20, 2026

+890

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.

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cooIcooIcooI17 Apr 20, 2026

+21

Help

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 ..

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Jyrgerhry Apr 20, 2026

+21

Math

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 ..

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Jyrgerhry Apr 20, 2026

Apr 18, 2026

+312

Algebra

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

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AUnVerifedTaxPayer Apr 18, 2026

+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

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AUnVerifedTaxPayer Apr 18, 2026

Apr 17, 2026

+312

Algebra

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

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AUnVerifedTaxPayer Apr 17, 2026

+312

Geometry

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.)

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AUnVerifedTaxPayer Apr 17, 2026

Apr 16, 2026

+1056

Algebra

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

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Hi6942O Apr 16, 2026

+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

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Hi6942O Apr 16, 2026

+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

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Hi6942O Apr 16, 2026

Apr 15, 2026

Apr 14, 2026

Apr 13, 2026

+665

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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Pythagorearn Apr 13, 2026

+12

number theory

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?

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BatchOfQuestions Apr 13, 2026

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