All Questions ⁺⁰235570 Questions

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I need help

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.

Rangcr897 May 2, 2024

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12

2

+527

Counting

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

Pythagorearn May 2, 2024

+1

12

1

+1908

Trigonometry Problem

I've been working on this question for a while, but I can't come up with a defininitive solution. Can you guys help with it a bit? Thanks!
So let's such that
Find all such values read more ..

NotThatSmart May 2, 2024

-1

21

1

+527

Algebra

The graph of the exponential function f(x) is shown below. Find f(x).
f(0) = 1 and f(1) = 2.

Pythagorearn May 2, 2024

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30

1

+527

Algebra

Find the domain and range of the function f(x) = 2(2 - 3x).

NotThatSmart ●

Pythagorearn May 2, 2024

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25

1

+527

Algebra

Let x be a real number such that 625x = 9. Then 125x = ____

Pythagorearn May 2, 2024

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32

1

+527

Algebra

Let a1, a2, a3, ... be an arithmetic series. Let Sn denote the sum of the first n terms. If S1 = 5 and S2 = 15, then find S15.

Pythagorearn May 2, 2024

0

17

2

+527

Algebra

Laverne starts counting out loud by 5's. She starts with 1. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 40, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming read more ..

Pythagorearn May 2, 2024

0

15

1

+527

Algebra

Let a1, a2, a3, ..., a9, a10 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.

Pythagorearn May 2, 2024

-1

15

1

+330

Geometry

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

Stanry May 2, 2024

-2

20

1

+330

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Stanry May 2, 2024

-2

28

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+330

Geometry

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

Stanry May 2, 2024

-2

31

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+330

Geometry

Let $X$, $Y$, and $Z$ be points on a circle. Let line $XY$ and the tangent to the circle at $Z$ intersect at $W$. If $\overline{WY} \perp \overline{WZ}$, then find $YZ$.

Stanry May 2, 2024

-2

29

0

+330

Geometry

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

Stanry May 2, 2024

-2

20

0

+330

Geometry

Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. Find $SW$.

Stanry May 2, 2024

-2

20

0

+330

Geometry

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the area of the circle.

Stanry May 2, 2024

-2

20

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+330

Geometry

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

Stanry May 2, 2024

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27

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+330

Geometry

The cone below has a lateral surface area of $16 \sqrt{5} \cdot \pi$. Find the volume of the cone.

Stanry May 2, 2024

-1

29

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+330

Geometry

Let $A$ be the lateral surface area of the cone below, and let $B$ be the lateral surface area of the cylinder below. Find $\frac{A}{B}.$

Stanry May 2, 2024

-1

14

1

+330

Geometry

The circular sector below is rolled to form a cone. Find the volume of the cone.

Stanry May 2, 2024

-1

28

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+330

Geometry

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle. The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$ read more ..

Stanry May 2, 2024

-1

30

0

+330

Geometry

In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $\frac{AP}{2} = \frac{PQ}{5} = \frac{QB}{11}$ and $\frac{AR}{8} = \frac{RC}{13},$ then find $\frac{[QBC]}{[CRQ]}.$

Stanry May 2, 2024

May 1, 2024

0

32

1

+330

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $4,$ and $AB = 10$, then find the area of triangle $ABC read more ..

Stanry May 1, 2024

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19

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+330

Geometry

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?

NotThatSmart ●

Stanry May 1, 2024

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