All Questions ⁺⁰234655 Questions

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Algebra

My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team read more ..

MEMEG0D Aug 25, 2024

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+116

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

MEMEG0D Aug 25, 2024

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+116

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

MEMEG0D Aug 25, 2024

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+2651

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

LiIIiam0216 Aug 25, 2024

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+2651

Geometry

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

LiIIiam0216 Aug 25, 2024

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+484

Geometry

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

gnistory Aug 25, 2024

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+484

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

gnistory Aug 25, 2024

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+96

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 $a + b$.

bIueb3rry Aug 25, 2024

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+96

Geometry

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

bIueb3rry Aug 25, 2024

Aug 24, 2024

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+162

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

MeIdHunter Aug 24, 2024

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+162

Geometry

Triangle $ABC$ below is rotated completely around side $\overline{BC}$, sweeping out a solid in space. Find the volume of the solid.

MeIdHunter Aug 24, 2024

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+92

Geometry

A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

jaekg Aug 24, 2024

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+673

Geometry

A rectangular prism has a length of $3$, a width of $5$, and a height of $11$. What is the distance between two opposite corners of the prism?

magenta Aug 24, 2024

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+779

Geometry

Jessica has one cube with a side length of $1,$ and another cube with a side length of $1.$ She then glues the two cubes together, to form one single solid. What is the smallest possible surface area of the single solid?

eramsby1O1O Aug 24, 2024

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+1694

Geometry

Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

ABJeIIy Aug 24, 2024

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+1341

Geometry

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 $\overline{QN}\perp\overline{PR}$, $QN = 15$, and $PR = 20$, read more ..

kittykat Aug 24, 2024

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+1341

Geometry

The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the perimeter of the trapezoid.

kittykat Aug 24, 2024

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+38

I need some help understanding this

Could someone explain the steps to do these problems please? Thanks!
Let z be a complex number, and let n be a positive integer such that z^n=(z+1)^n=1
a) Prove that |z|=|z+1|=1.
b) Find the possible values read more ..

JRFPLSHelp Aug 24, 2024

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+2651

Geometry

In parallelogram EFGH, let M be the point on EF such that FM : ME = 1 : 7, and let N be the point on EH such that HN : NE = 4 : 5. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ / FH.

LiIIiam0216 Aug 24, 2024

Aug 23, 2024

+1

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+5

Calculus I The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation

The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation
s = 2 sin(𝜋t) + 2 cos(𝜋t), where t is measured in seconds. (Round your answers read more ..

CIven0l Aug 23, 2024

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+625

Algebra

Let $x$, $y$, and $z$ be nonzero real numbers. Find all possible values of
\frac{x}{|x|} + \frac{y}{|y|} + \frac{z}{|z|} + \frac{x + y + z}{|x + y + z|}

AnswerscorrectIy Aug 23, 2024

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+625

Algebra

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

AnswerscorrectIy Aug 23, 2024

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+820

Algebra

Find x if \log_2 (\log_3 x) = \log_3 (\log_2 x).

Hi6942O Aug 23, 2024

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