All Questions ⁺⁰237417 Questions

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Geometry

A rectangle in the coordinate plane is shown below. A line with slope 2 splits this rectangle into two regions with equal area. What is the y-intercept of this line?
The rectangle has coordinates (-1,-1), (-1,1), (1,1), read more ..

Ibrahin097YT 6 hours ago

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+56

Geometry

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 ..

Ibrahin097YT 6 hours ago

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+56

Geometry

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.

Ibrahin097YT May 13, 2025

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+56

Geometry

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.

Ibrahin097YT May 13, 2025

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+56

Geometry

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 $DE$?

Ibrahin097YT May 13, 2025

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+56

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

Ibrahin097YT May 13, 2025

May 12, 2025

May 10, 2025

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2

+456

Counting

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

Jasmo May 10, 2025

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+458

Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds read more ..

bIueb3rry May 10, 2025

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+458

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that read more ..

bIueb3rry May 10, 2025

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+56

i need answer now

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.

Ibrahin097YT May 10, 2025

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+56

plz help now

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 ..

Ibrahin097YT May 10, 2025

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+56

help me help help

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 15 \times 16 rectangle, then how many squares will read more ..

Ibrahin097YT May 10, 2025

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+56

help really need help

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

Ibrahin097YT May 10, 2025

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+9

HELP PLEASE ASAP!!!!

What is the value of the expression. Express your asnwer as a common fraction.

Ibrahim097YT May 10, 2025

May 9, 2025

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+1800

Geometry

Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. What is the area of the triangle with side lengths \tan A, \tan B, and \tan C?

blackpanther May 9, 2025

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+1800

Geometry

Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C?

blackpanther May 9, 2025

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+1800

Geometry

Find the area of the triangle with side lengths 4, 5, and 8.

blackpanther May 9, 2025

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+1800

Geometry

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

blackpanther May 9, 2025

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+608

Counting

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of read more ..

onyuIee May 9, 2025

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+608

Counting

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

onyuIee May 9, 2025

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+608

Counting

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).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

onyuIee May 9, 2025

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+56

How many subsets of \{0, 1, \dots, 9\} have the property

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

Ibrahin097YT May 9, 2025

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+56

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen).

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

Ibrahin097YT May 9, 2025

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+56

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Ibrahin097YT May 9, 2025

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+4

Trigonometric Laws and Identities

Two students are calculating the exact value of tan(7pi/12)? Choose one of the following to methods to solve.
-Student A says 7pi/12 is half of 7pi/6, and they will use the half-angle identity and the unit of circle to solve.
-Student B says read more ..

blueberiii May 9, 2025

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+56

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BC = 12, AC = 18 and BF = 3 \cdot AF. Find AB.

Ibrahin097YT May 9, 2025

+1

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+9

What is the value of the expression shown? Express your answer as a common fraction.

What is the value of the expression shown? Express your answer as a common fraction.

Ibrahim097YT May 9, 2025

May 8, 2025

+1

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+1271

Counting

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.)

Akhain1 May 1, 2025

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+829

Counting

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

cooIcooIcooI17 May 1, 2025

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+829

Counting

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

cooIcooIcooI17 May 1, 2025

Apr 27, 2025

Apr 26, 2025

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+56

Geometry

In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

PikaPika989 Apr 26, 2025

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+56

Geometry

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

PikaPika989 Apr 26, 2025

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