All Questions ⁺⁰237749 Questions

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If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 4 \times 4 rectangle, then how many squares will it read more ..

CInsbstnkng Jul 24, 2025

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+295

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In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

CInsbstnkng Jul 24, 2025

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+295

Help plz

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

CInsbstnkng Jul 24, 2025

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+295

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Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $11,$ and the slope of line segment $\overline{OQ}$ is $13.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

CInsbstnkng Jul 24, 2025

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+295

Help meee

How many 7-digit sequences have a digit that appears at least 6 times?
(For example, 3339333 and 0200000 are two such sequences. A sequence is allowed to begin with 0.)

CInsbstnkng Jul 24, 2025

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+295

Need help

Triangle ABC has side lengths AB = 8, BC = 10, and AC = 12. Find \dfrac{\cos A}{\cos B}.

CInsbstnkng Jul 24, 2025

-1

10

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+295

Help me

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with read more ..

CInsbstnkng Jul 24, 2025

Jul 23, 2025

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6

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+73

HELP!!!

Let z be a complex number such that |z|=1.
Find the maximum value of |1+z|+|1-z+z2|.

Clnsbstnkng Jul 23, 2025

Jul 22, 2025

+1

5

4

+858

Help math

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{12}.

cooIcooIcooI17 Jul 22, 2025

0

3

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+1761

Help algebra

The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?

parmen Jul 22, 2025

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12

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+1004

help me

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-1$ 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 $XYZ$ and $X'Y'Z'.$ Find read more ..

Hi6942O Jul 22, 2025

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+1524

Need help

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.

learnmgcat Jul 22, 2025

0

13

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+190

help math

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

HumanBemg Jul 22, 2025

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+73

HELP!!!

If z is a complex number such that z+z-1=√3,
what is the value of z2010+z-2010?

Clnsbstnkng Jul 22, 2025

Jul 21, 2025

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+190

help me

Let \omega be a nonreal root of x^3 = 1. Compute
(1 - \omega + \omega^2)^6 + (1 + \omega - \omega^2)^6.

HumanBemg Jul 21, 2025

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10

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+1301

Math

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3)$ is a permutation of (1,2,3,4,5).
Let \pi = (x_1,x_2,x_3,\dots,x_n) be a permutation read more ..

AnswerscorrectIy Jul 21, 2025

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+1301

Math

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

AnswerscorrectIy Jul 21, 2025

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+73

HELP!!!

Let z1 and z2 be two complex numbers such that |z1| = 5 and (z1/z2)+(z2/z1)=1.
Find |z1-z2|2.
Note: The answer is not 75.

Clnsbstnkng Jul 21, 2025

Jul 20, 2025

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+483

Math

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?

bIueb3rry Jul 20, 2025

Jul 12, 2025

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5

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+483

Algebra

Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}

bIueb3rry Jul 12, 2025

Jul 11, 2025

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+483

Algebra

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

bIueb3rry Jul 11, 2025

Jul 8, 2025

Jul 7, 2025

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+1301

Math

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

AnswerscorrectIy Jul 7, 2025

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