All Questions ⁺⁰230999 Questions

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5

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+916

need help

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Mar 26, 2024

0

8

4

+916

counting question

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

LiIIiam0216 Mar 26, 2024

0

5

1

+916

help counting

Help I need Venn Diagram
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 $100$ dogs in the school.
$62$ read more ..

LiIIiam0216 Mar 26, 2024

-1

7

0

+916

Counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters if exactly read more ..

LiIIiam0216 Mar 26, 2024

0

4

1

+971

Chords

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX. read more ..

Akhain1 Mar 26, 2024

0

7

1

+971

Semicircle

A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ, and is tangent to the other two sides. If XY = 10, XZ = 10, and YZ = 10*sqrt(2), then find the area of the semicircle.

Akhain1 Mar 26, 2024

0

7

1

+971

Tangent circles

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

Akhain1 Mar 26, 2024

+1

9

1

+971

need help

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 $a + b$.

Akhain1 Mar 26, 2024

0

4

1

+971

help coordinates

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 ..

Akhain1 Mar 26, 2024

0

2

1

+971

Coordinates

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
\[PA^2 + PB^2 + PC^2 = 3PQ^2 + k.\]
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

Akhain1 Mar 26, 2024

0

4

2

+85

More Geometry

3D Geometry problems
1.

2.
<#> 3.<#> read more ..

Akhaim1 Mar 26, 2024

Mar 25, 2024

0

4

3

+85

Geometry

Can you solve these?
1.

2.
<#> 3.<#> read more ..

Akhaim1 Mar 25, 2024

0

8

1

+1602

Circle

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
\[x^2 + y^2 = 4x - 8y + 17x - 5y + 25,\]
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

bader Mar 25, 2024

0

6

0

+357

Pyramid

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid.

falafronk Mar 25, 2024

0

5

1

+357

Prism

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

falafronk Mar 25, 2024

0

9

0

+357

Prism

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

falafronk Mar 25, 2024

0

7

3

+1602

help with trig

Let \theta be an acute angle. If $\cos \theta = \frac{1}{4},$ then what is $\sin \theta?$

bader Mar 25, 2024

0

6

1

+1602

Trig

Let x be an acute angle such that \tan x + \sec x = 0. Find $\cos x$.

bader Mar 25, 2024

-1

5

0

+359

Cone

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

ChiIIBill Mar 25, 2024

0

9

0

+4

Circles

What is the length of PC?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.
https://static.k12.com/nextgen_media/assets/8093696-NG_GMT_SemB_10_UT_04.png

Sugarplum Mar 25, 2024

-1

5

0

+359

Solid geo

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

ChiIIBill Mar 25, 2024

-1

6

0

+359

3d geo

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.

ChiIIBill Mar 25, 2024

+1

3

1

+359

3d geo

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

ChiIIBill Mar 25, 2024

0

5

0

+971

Polygon

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 Mar 25, 2024

0

6

0

+971

Square

In the diagram, ABCD is a square. Find PR.

L, M, N, O, are midpoints of sides.
Side AB = 12

Akhain1 Mar 25, 2024

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