All Questions ⁺⁰235719 Questions

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Help with counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all the sophomores are standing together?

tomtom Dec 29, 2023

Dec 28, 2023

+1

41

3

+44

Please Help

Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are dogs in the school.
62 have blue ribbons, 68 read more ..

omgitsme Dec 28, 2023

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35

1

+1439

Angle

In the diagram below, P is a point inside square ABCD. Find x.

kittykat Dec 28, 2023

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18

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+1439

dilation

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{1}{5}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles read more ..

kittykat Dec 28, 2023

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38

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+1439

Angles

Two lines $p$ and $q$ intersect at $X$. The angle between lines $p$ and $q$ is $45^\circ$. Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$. Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection read more ..

kittykat Dec 28, 2023

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26

1

+1439

help me plz

Let $ABCD$ be a square with side length $1.$ A laser is located at vertex $A,$ which fires a laser beam at point $X$ on side $\overline{BC},$ such that $BX = \frac{1}{2}.$ The beam reflects off the sides of the square, until it ends up at another read more ..

kittykat Dec 28, 2023

0

32

1

+1439

rotation

Let $A_1 A_2 A_3 \dotsb A_{15}$ be a regular polygon. A rotation centered at $A_4$ with an angle of $\alpha$ takes $A_7$ to $A_{12}$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees.

kittykat Dec 28, 2023

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25

1

+1439

Dilation

A dilation with scale factor $k$ takes figure A to figure B. Find the sum of all possible values of $k$.

kittykat Dec 28, 2023

+2

26

1

+20

Geometry Question

in triangle ABC, D is a point on the side BC such that DC = 2BD, and the areas of the triangles ABF and DEF are 6 and 2, respectively. What's the area of triangle AEF? Not for a homework question. read more ..

ethanyessir Dec 28, 2023

0

43

0

+1439

polygon

In how many ways can the polygon be placed back into the hole, if the polygon can be rotated and/or reflected?

kittykat Dec 28, 2023

+2

24

0

+1439

polygon

The regular polygon below is cut out of a flat piece of cardboard. The polygon is then placed back into the hole.
In how many ways can the polygon be placed back into the hole, if the polygon can be rotated, but not reflected?

kittykat Dec 28, 2023

+1

19

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+1439

dilation

Point $B$ is the image of point $A$ under a dilation with center $O$. If $OB = 30$, and the scale factor of the dilation is $5$, then what is $OA$?

kittykat Dec 28, 2023

+1

32

1

+83

help

In the diagram below, triangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?
<read more ..

Atlas Dec 28, 2023

Dec 27, 2023

0

34

1

+1533

frustum

Find the total surface area and the volume of the conical frustum below.

parmen Dec 27, 2023

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16

1

+1533

Cone

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

parmen Dec 27, 2023

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32

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+1533

3d geo

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

parmen Dec 27, 2023

+1

41

1

+1533

cone

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

parmen Dec 27, 2023

-1

22

1

+1533

solid

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

parmen Dec 27, 2023

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39

1

+1533

sphere

A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar. The volume of the cylinder is $\pi/174$. What is the volume of the sphere?

parmen Dec 27, 2023

-1

51

1

+1533

sphere

A plane and a sphere intersect in a circle that has an area of $14 \pi$. The distance between the plane and the center of the sphere is units. Find the surface area of the sphere.

parmen Dec 27, 2023

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