All Questions ⁺⁰235674 Questions

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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?

cooIcooIcooI17 Nov 20, 2024

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Counting

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

cooIcooIcooI17 Nov 20, 2024

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Counting

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

cooIcooIcooI17 Nov 20, 2024

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Algebra

The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + 4x^2 - 5x + 7. What is A+B?

crimefightingvigiI Nov 20, 2024

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Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.

crimefightingvigiI Nov 20, 2024

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Algebra

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

crimefightingvigiI Nov 20, 2024

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Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

crimefightingvigiI Nov 20, 2024

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Algebra

Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.

crimefightingvigiI Nov 20, 2024

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Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from read more ..

crimefightingvigiI Nov 20, 2024

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Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

crimefightingvigiI Nov 20, 2024

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Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the largest number of primes that could divide a terrific positive integer?

crimefightingvigiI Nov 20, 2024

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Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

crimefightingvigiI Nov 20, 2024

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+243

Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. How many prime numbers are divisors of $n?$

bIueb3rry Nov 20, 2024

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Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. What is the smallest possible value of $n?$

bIueb3rry Nov 20, 2024

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Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.
Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, read more ..

bIueb3rry Nov 20, 2024

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really help me

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

crimefightingvigiI Nov 20, 2024

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plz help

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

crimefightingvigiI Nov 20, 2024

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help help help

Write the equation of the line below in the form Ax+By=C, where A, B, and C are integers with greatest common divisor 1 and A is positive.
The line passes through (-2,5) and (9,1).

crimefightingvigiI Nov 20, 2024

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help with algebra

The system of equations
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 2
has exactly one solution. What is $z$ in this solution?

crimefightingvigiI Nov 20, 2024

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Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 99% water, by weight. After two days in the sun, the water content of the berries was only 75%, by weight. What was the total weight of read more ..

MeIdHunter Nov 20, 2024

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