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All Questions
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235634 Questions
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+293
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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+293
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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1
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+293
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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+113
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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1
+113
Need help quick
What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?
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crimefightingvigiI
Nov 20, 2024
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1
1
+113
Help me plz
What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?
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crimefightingvigiI
Nov 20, 2024
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1
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+113
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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2
+24
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.
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crimefightingvigil
Nov 20, 2024
Nov 19, 2024
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+24
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 ..
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crimefightingvigil
Nov 19, 2024
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1
+611
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?
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siIviajendeukie
Nov 19, 2024
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+243
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 $\phi(191)$?
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bIueb3rry
Nov 19, 2024
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1
+243
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?
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bIueb3rry
Nov 19, 2024
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1
1
+243
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?
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bIueb3rry
Nov 19, 2024
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1
+113
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?
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crimefightingvigiI
Nov 19, 2024
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1
+113
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?
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crimefightingvigiI
Nov 19, 2024
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+113
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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1
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+682
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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1
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+682
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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1
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+682
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
0
1
0
+682
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
0
1
0
+113
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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