All Questions ⁺⁰232717 Questions

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Algebra

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

RedDragonl May 25, 2024

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4

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+404

Algebra

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

RedDragonl May 25, 2024

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+404

Algebra

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

RedDragonl May 25, 2024

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+121

Find the remainder when is divided by 9.

Find the remainder when is divided by 9.

Hi69420 May 25, 2024

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+121

Help

If an integer ends in the digit $0$ and the sum of its digits is divisible by $3$, then how many of the numbers $2, 3, 4, 5, 6, 8, 9$ necessarily divide it?

Hi69420 May 25, 2024

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+591

Counting

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

Hi6942O May 25, 2024

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+591

Counting

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

Hi6942O May 25, 2024

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+660

Need some help, havent posted in a while :)

1. Let f(x) and g(x) be functions. Find if
for all x, where f(x)= 3x-4 and g(x)= 8x+c
2. The function f(x,y) gives ordered pairs as its output. It is defined according to the following rules:
If x>4, read more ..

Keihaku May 25, 2024

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+1367

Algebra

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

parmen May 25, 2024

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+1367

Algebra

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

parmen May 25, 2024

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+1367

Geometry

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

parmen May 25, 2024

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+121

help

Compute and express your answer as a decimal.

Hi69420 May 25, 2024

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+177

Geometry

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

Stanry May 25, 2024

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+177

Geometry

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

Stanry May 25, 2024

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+177

Geometry

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

Stanry May 25, 2024

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+24

Counting

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

jaekg May 25, 2024

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+24

Counting

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

jaekg May 25, 2024

May 24, 2024

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+24

Counting

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

jaekg May 24, 2024

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+24

Hard algebra

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

jaekg May 24, 2024

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+24

Need help

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

jaekg May 24, 2024

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+24

Help me plz

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

jaekg May 24, 2024

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+12

Geometry help plzz

Let G be the center of equilateral triangle XYZ A dilation centered at G with scale factor-7/5 is applied to triangle XYZ to obtain triangle X'Y'Z' Let A be the area of the region that is contained inside both triangles XYZ and X'Y'Z' Find read more ..

jackg May 24, 2024

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+177

Geometry

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

Stanry May 24, 2024

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+22

Rational Function

Howdy, been spending a lot of time trying to figure this one out.
The equation of an asymptote can be a constant, which makes it a horizontal asymptote. An asymptote can also be linear, which makes it an oblique asymptote. But asymptotes read more ..

Chadly May 24, 2024

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