All Questions ⁺⁰235636 Questions

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10

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The hardest question in the world

"What is the Riemann Hypothesis and why is it considered one of the most challenging problems in mathematics?"

Bacha Feb 13, 2024

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18

1

+0

Semicircles

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

Vxrtate Feb 13, 2024

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29

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+0

Triangles

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

Vxrtate Feb 13, 2024

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3

1

+0

Tangent

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 ..

Vxrtate Feb 13, 2024

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30

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Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side $\overline{AO}$ and arc $AB.$ Find the radius of the circle.

Vxrtate Feb 13, 2024

0

43

1

+688

Geometric sequence

In a geometric sequence, the $23$rd term is $16$ and the $26$th term is $18$. What is the $24$th term?

booboo44 Feb 13, 2024

0

25

1

+688

Polynomial

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

booboo44 Feb 13, 2024

0

26

1

+688

Polynomial

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

booboo44 Feb 13, 2024

0

4

1

+688

Coefficient

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

booboo44 Feb 13, 2024

-2

11

1

+1911

Help 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 ..

tomtom Feb 13, 2024

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4

0

+1911

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.
* $41$ have blue ribbons, $23$ have read more ..

tomtom Feb 13, 2024

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19

1

+1911

Counting

A speech class has five freshmen and four sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that at least four of the freshmen are standing next to each other?

tomtom Feb 13, 2024

-1

46

1

+1911

Counting

I have $5$ different mathematics textbooks and $4$ different psychology textbooks. In how many ways can I place the $9$ textbooks on a bookshelf, in a row, if all the psychology textbooks must be together, and all the mathematics textbooks must be toge read more ..

tomtom Feb 13, 2024

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5

1

+1911

Integers

Find the number of ordered pairs (a, b) of integers such that
\frac{a + 2}{a + 3} = \frac{b}{7}

tomtom Feb 13, 2024

-1

16

1

+1911

Counting

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

tomtom Feb 13, 2024

0

31

0

+0

Circumcircles

In triangle ABC, point X is on side BC such that AX=12, BX=12, CX=5, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Vxrtate Feb 13, 2024

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30

1

+0

Equilateral

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

Vxrtate Feb 13, 2024

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20

1

+0

Square

In the diagram, ABCD is a square. Find sin PAQ.

Vxrtate Feb 13, 2024

0

44

1

+68

Trig question help

Point is the terminal point of angle theta. Points Q, R, and S and are other terminal points.

List the points P,Q,R, and S and in read more ..

LearningCat Feb 13, 2024

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40

6

+1443

Help plz

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?

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blackpanther Feb 13, 2024

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44

2

+1443

Counting question

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

blackpanther Feb 13, 2024

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