All Questions ⁺⁰237293 Questions

-1

45

0

+1855

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.

ABJeIIy May 30, 2024

+2

24

4

+280

Geometry

In the figure, angles ABC and AST are right angles. If AC=35 then what is AS?

ABJelly May 30, 2024

+1

24

0

+613

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

Pythagorearn May 30, 2024

0

22

1

+613

Algebra

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

Pythagorearn May 30, 2024

0

44

1

+613

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

Pythagorearn May 30, 2024

0

32

1

+613

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

Pythagorearn May 30, 2024

-5

39

1

+216

Frustum

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

BRAlNBOLT May 30, 2024

-5

53

1

+216

Geometry

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.

BRAlNBOLT May 30, 2024

-5

28

1

+216

Trig

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

BRAlNBOLT May 30, 2024

-4

42

1

+216

Trig

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

BRAlNBOLT May 30, 2024

0

37

1

+864

Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

RedDragonl May 30, 2024

0

30

1

+864

Counting

In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable boxes, if at least three of the boxes must be empty?

RedDragonl May 30, 2024

0

30

0

+864

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

RedDragonl May 30, 2024

0

48

1

+864

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

RedDragonl May 30, 2024

0

42

0

+864

Geometry

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction.

RedDragonl May 30, 2024

0

30

1

+864

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.</ read more ..

RedDragonl May 30, 2024

0

27

1

+864

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

RedDragonl May 30, 2024

0

45

0

+864

Probability

Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 3 orange balls and 2 purple read more ..

RedDragonl May 30, 2024

May 29, 2024

-6

38

0

+216

Geometry

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

BRAlNBOLT May 29, 2024

-7

23

1

+216

Geometry

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.

BRAlNBOLT May 29, 2024

-7

26

1

+216

Pyramid

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

BRAlNBOLT May 29, 2024

-1

25

1

+216

Algebra

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.

NotThatSmart ●

BRAlNBOLT May 29, 2024

0

24

1

+972

Geometry

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 ..

Rangcr897 May 29, 2024

0

27

1

+972

Geometry

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 ..

Rangcr897 May 29, 2024

0

24

1

+972

Geometry

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 $a + b$.

Rangcr897 May 29, 2024

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