All Questions ⁺⁰235549 Questions

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Algebra

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

ABJeIIy Apr 13, 2024

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20

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+1839

Algebra

The system of equations
\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5\]
has exactly one solution. What is $z$ in this solution?

ABJeIIy Apr 13, 2024

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33

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+1839

Algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

ABJeIIy Apr 13, 2024

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33

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+1839

Need help

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

ABJeIIy Apr 13, 2024

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+1839

Help plz

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

ABJeIIy Apr 13, 2024

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15

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+355

pls help ASAP

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly three ch read more ..

Lilliam0216 Apr 13, 2024

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36

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+1839

Counting

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

ABJeIIy Apr 13, 2024

+1

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+5

Find the speed and CW/CCW of the particle with parametric equations.

If you can't read the $LaTeX$, it is:
The position of a particle is given by the parametric equations
$x=3+2\sin(2t)$
$y=4+2\cos(2t)$
as $t$ ranges over all real numbers.
What is the speed of this particle, read more ..

myphofstahs Apr 13, 2024

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28

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+1839

Algebra

Expand (x^2 + 1/x)*(x + x^4)^3.

ABJeIIy Apr 13, 2024

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18

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+54

A translation maps A ti A' and B to B'. We know AA'=6, AB=5, and AB'=5 find BA'

A translation maps A ti A' and B to B'. We know AA'=6, AB=5, and AB'=5 find BA'

RedDragon1 Apr 13, 2024

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+54

Question

Equilateral triangle ABC is inscribed in a circle. Let P be a point on arc BC. Given that PB=18 and PC=7 find PA.

RedDragon1 Apr 13, 2024

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+54

Question

A,B,C, and D are distinct points on the plane. A rotation about point O maps A to B, B to C, and C to D. We know angle AOD is 24 Enter all three possible degree measures (between 0 and 180) of angle AOB separated read more ..

RedDragon1 Apr 13, 2024

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+54

Question

In the diagram below, Point A is sqrt(3) units above O. Whenever Tasha moves a point, she translates the point sqrt(2) units to the right. Whenever Richard moves a point, he rotates the point clockwise about point O by 90˚
In read more ..

RedDragon1 Apr 13, 2024

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16

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+1234

Geometry

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

Akhain1 Apr 13, 2024

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+1234

Geometry

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

Akhain1 Apr 13, 2024

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27

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+1234

Geometry

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 $IJKLMN$.

Akhain1 Apr 13, 2024

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29

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+1234

Geometry

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. read more ..

Akhain1 Apr 13, 2024

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+1234

Geometry

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.

Akhain1 Apr 13, 2024

+1

24

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+21

Try to solve this difficult probability question: [DUPLICATE]

Try to solve this difficult probability question:
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than $10$ times? read more ..

blueorange Apr 13, 2024

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