All Questions ⁺⁰237740 Questions

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+882

Math

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 $A$?

cooIcooIcooI17 Aug 31, 2025

Aug 30, 2025

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+805

help me plz!!!

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

bingboy Aug 30, 2025

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+805

i need help with this

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

bingboy Aug 30, 2025

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1

+774

Math

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

siIviajendeukie Aug 30, 2025

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+774

Math

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

siIviajendeukie Aug 30, 2025

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+997

Math

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

magenta Aug 30, 2025

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+997

Math

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

magenta Aug 30, 2025

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+997

Math

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

magenta Aug 30, 2025

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+1006

Math

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, read more ..

gnistory Aug 30, 2025

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+1006

Math

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$,
<read more ..

gnistory Aug 30, 2025

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+495

Math

When the polynomial f(x) is divided by x^3 + x + 1, the remainder is 3. When the polynomial f(x) is divided by x^2 + 1, the remainder is x + 1. Find the remainder when f(x) is divided by x.

bIueb3rry Aug 30, 2025

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+495

Math

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

bIueb3rry Aug 30, 2025

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+495

Math

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $47?$

bIueb3rry Aug 30, 2025

+1

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1

+823

Math

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

crimefightingvigiI Aug 30, 2025

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+823

Math

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

crimefightingvigiI Aug 30, 2025

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+823

Math

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

crimefightingvigiI Aug 30, 2025

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+4

I need help proving this problem.

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D,$ such that $AD = AB$.
Line segment $\overline{AD}$ is extended to $E,$ such that $\angle DBE = \angle BAD$.
Show that triangle $ACE$ read more ..

linxfrink Aug 30, 2025

Aug 29, 2025

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+312

Help me help

In the diagram below, ABCD is a square, DE = EF = FG = 2, GH = 1, HB = 5, and \angle DEF = \angle EFG = \angle FGH = \angle GHB = 60^\circ. Find the area of the shaded region.

CInsbstnkng Aug 29, 2025

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+312

Help!

Franklin the Fly lives at one corner of a cube of side length 1. He doesn't like to wander too far from home; in fact, Franklin is only willing to travel to a point on the cube if he can reach it by crawling a distance of at most \sqrt{5} along the read more ..

CInsbstnkng Aug 29, 2025

Aug 28, 2025

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3

+312

Plz help

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

Bosco ●●●

CInsbstnkng Aug 28, 2025

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+312

Help me

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

CInsbstnkng Aug 28, 2025

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+882

Math

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region.

cooIcooIcooI17 Aug 28, 2025

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+882

Math

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

cooIcooIcooI17 Aug 28, 2025

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+980

Math

For 0 \leq x \leq 1, the function f(x) satisfies the relations f\left(\dfrac x{x+1}\right) = f(x) and f(-x) = - f(x). What is the value of the expression
f\left(\dfrac23\right) + f\left(\dfrac25\right) + f\left(\dfrac27\right) + \dots + f\left(\dfrac2{2n+1}\right) read more ..

booboo44 Aug 28, 2025

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