All Questions ⁺⁰237360 Questions

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Algebra

A mathematician works for t hours per day and solves p problems per hour, where and are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 4p+5 problems per hour. In fact, he only works read more ..

MeIdHunter Nov 20, 2024

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31

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+478

Algebra

Real numbers A and B satisfy: a + ab^2 = 250 + a^3, a - ab^2 = -240 + a^3 enter all values of a, separated by commas.

MeIdHunter Nov 20, 2024

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+478

Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

MeIdHunter Nov 20, 2024

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27

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+806

Help me now

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

crimefightingvigiI Nov 20, 2024

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+806

Need help quick

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

crimefightingvigiI Nov 20, 2024

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+806

Help me plz

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

crimefightingvigiI Nov 20, 2024

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26

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+806

Help I need help

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

crimefightingvigiI Nov 20, 2024

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+36

Plz help

Hi, I need help solving:
If satisfies the simultaneous equations
where x and y may be complex numbers, determine all possible values of y^2.

crimefightingvigil Nov 20, 2024

Nov 19, 2024

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+36

Help ASAP!!

Hi I need help solving:
(a) In this multi-part problem, we will consider this system of simultaneous equations:

Let ,, and
Determine the monic cubic polynomial in terms of a variable t whose roots are t=a, t=b, and read more ..

crimefightingvigil Nov 19, 2024

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27

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+750

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 15 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

siIviajendeukie Nov 19, 2024

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+450

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(191)$?

bIueb3rry Nov 19, 2024

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23

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+450

Number Theory

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

bIueb3rry Nov 19, 2024

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26

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+450

Number Theory

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

bIueb3rry Nov 19, 2024

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23

1

+806

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?

crimefightingvigiI Nov 19, 2024

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24

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+806

Counting

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?

crimefightingvigiI Nov 19, 2024

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30

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+806

Counting

Each square below 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 squares?

crimefightingvigiI Nov 19, 2024

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27

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+921

Algebra

Solve for the variable x in terms of y and z, assuming y \neq \frac{1}{2}: xy + xz + x^2 = \frac{3x + 2y + z}{2}.

booboo44 Nov 19, 2024

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+921

Algebra

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

booboo44 Nov 19, 2024

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28

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+921

Algebra

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

booboo44 Nov 19, 2024

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27

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+921

Algebra

The sum
6\left( 1\cdot1 + 2\cdot2 + \dots + n(n) \right)
is equal to a polynomial f(n) for all n \ge 1.
Write f(n) as a polynomial with terms in descending order of n.

booboo44 Nov 19, 2024

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29

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+806

Algebra

Let
f(x) = \sqrt[3]{x - \sqrt[3]{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

crimefightingvigiI Nov 19, 2024

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