All Questions ⁺⁰237641 Questions

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

CInsbstnkng Jul 29, 2025

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Help help!

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

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Help me

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

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Help!! real

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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Geometry from alcumus

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 ..

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bqimath Jul 29, 2025

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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 $ABC?$

CInsbstnkng Jul 29, 2025

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Need help now

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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HELP!!! (From the real Clnsbstnkng)

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.

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Clnsbstnkng Jul 29, 2025

Jul 28, 2025

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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?

CInsbstnkng Jul 28, 2025

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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 Jul 28, 2025

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Help with geo

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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Need help

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

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Plz 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

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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

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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.

Clnsbstnkng Jul 28, 2025

Jul 27, 2025

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Plz 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.

CInsbstnkng Jul 27, 2025

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Help me

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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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

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