All Questions ⁺⁰235702 Questions

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44

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+1439

Line segment

Segment $AB$ is $2808$ units long. Point $X$ is the midpoint of segment $AB.$ Point $R$ is $\frac{3}{5}$ of the way from $X$ to $B.$ Point $S$ is $\frac{2}{17}$ of the way from $X$ to $R.$ How many units long is segment $RS \, ?$

kittykat Feb 11, 2024

0

3

0

+1768

Angles

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.

bader Feb 11, 2024

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3

0

+1768

Hexagon

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 $IJKLMN$.

bader Feb 11, 2024

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20

3

+1768

Square

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

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

bader Feb 11, 2024

0

41

0

+1768

Polygon Angles

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.

bader Feb 11, 2024

0

18

3

+0

Hellp Lol

At a meeting, $4$ scientists, $3$ mathematicians, and $2$ journalists to be seated around a circular table. How many different arrangements are possible if the scientists must all sit together (in $4$ consecutive seats) and the $3$ mathematicians must sit read more ..

ChocolateFudge Feb 11, 2024

0

3

1

+688

Equation of line

Line $\ell_1$ represents the graph of $3x + 2y = -14 - 8x + 5y$. Line $\ell_2$ passes through the point $(5,-6)$, and is perpendicular to line $\ell_1$. Write the equation of line $\ell_2$ in the form $y=mx +b$.

booboo44 Feb 11, 2024

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23

2

+0

Help plz

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

ChocolateFudge Feb 11, 2024

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56

0

+1533

Frustum

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

parmen Feb 11, 2024

0

31

1

+1533

Plane and Sphere

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.

parmen Feb 11, 2024

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27

0

+1533

3D Geometry

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

parmen Feb 11, 2024

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4

0

+1533

Cone

The cone below has a lateral surface area of $16 \sqrt{11} \cdot \pi$. Find the volume of the cone.

Also, the radius read more ..

parmen Feb 11, 2024

-1

36

1

+1911

Trig Equation

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

tomtom Feb 11, 2024

-1

51

0

+1911

Trig question

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

tomtom Feb 11, 2024

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26

0

+0

Prism

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

Vxrtate Feb 11, 2024

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43

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+0

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.

Vxrtate Feb 11, 2024

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39

0

+0

Pyramid

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

Vxrtate Feb 11, 2024

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35

0

+0

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.

Vxrtate Feb 11, 2024

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36

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+0

Bisecting angle

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.

Vxrtate Feb 11, 2024

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23

0

+0

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 read more ..

Vxrtate Feb 11, 2024

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43

0

+0

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 ..

Vxrtate Feb 11, 2024

-1

29

1

+1443

Complex Numbers

Let $x$ and $y$ be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

blackpanther Feb 11, 2024

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48

0

+0

Coordinates

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 $a + b$.

Vxrtate Feb 11, 2024

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