bIueb3rry

119 Questions
13 Answers

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Geometry

In the diagram, AB is parallel to CD. Select the two products of lengths that must be equal.
AO \cdot BO
BO \cdot CE
CO \cdot AB read more ..

bIueb3rry Dec 12, 2025

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Geometry

Find length BC
AB = 13, AP = 12, BAC = 2*BPC, AC \perp BD

bIueb3rry Dec 12, 2025

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1

1

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Geometry

If ST = 2, QS = 4, and PT = 5, find PQ.

bIueb3rry Dec 12, 2025

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1

1

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Geometry

In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.

bIueb3rry Dec 12, 2025

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31

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Help me

Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?

bIueb3rry Aug 16, 2025

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2

7

2

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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

+1

5

2

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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

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2

6

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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

0

3

28

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Geometry

Two runners start at vertices A and B simultaneously and run clockwise around the perimeter of square ABCD at the same speed. A drone flies so that it is always at the midpoint of the two runners. What is the minimum distance between the two runners? read more ..

bIueb3rry May 27, 2025

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12

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Counting

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.

bIueb3rry May 19, 2025

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1

5

1

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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

0

5

1

+499

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

0

2

12

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Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is less than 20. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry Apr 19, 2025

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1

15

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Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry Apr 19, 2025

0

3

11

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Counting

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 ..

bIueb3rry Apr 17, 2025

0

1

18

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Counting

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.

bIueb3rry Apr 17, 2025

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1

17

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Counting

How many ordered pairs of positive integers (m,n) satisfy \text{lcm}[m,n] = 360 and \gcd(m,n) = 360?

bIueb3rry Apr 17, 2025

0

3

15

0

+499

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 Apr 17, 2025

0

1

12

0

+499

Geometry

Find sin B.
BD = 15, CD = 10, AC = 6

bIueb3rry Apr 4, 2025