All Questions ⁺⁰236046 Questions

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+1678

Algebra

Expand (a + 2)(3a^2 - 2a - 12)(a^2 - 2a + 1).

wiseowl Dec 13, 2023

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26

1

+1678

Quadratic

Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

wiseowl Dec 13, 2023

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27

0

+1678

Quadratic

Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = x^2 - 6x + 8$ Find $1/u + 1/v$.

wiseowl Dec 13, 2023

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30

0

+1678

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 2x^2 - 3x + 1. Compute (a - 4) + (b - 4).

wiseowl Dec 13, 2023

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57

0

+1678

quadratic

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are $a^2$ and $b^2.$

wiseowl Dec 13, 2023

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39

0

+1678

Algebra

Let c be a real number, and consider the system of quadratic equations
y = 6x^2 - 9x + c - 3x^2 + 17x
y = 5x^2 - 3x - 2x^2 + 10x - 18

For which values of c does this system have:
(a) Exactly one real read more ..

wiseowl Dec 13, 2023

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35

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+1678

system

The real numbers $a$ and $b$ satisfy $a - b = 1$ and $a^3 - b^3 = 1.$
(a) Find all possible values of $ab.$
(b) Find all possible values of $a + b.$
(c) Find all possible values of $a$ and $b.$

wiseowl Dec 13, 2023

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35

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+1678

complex numbers

Compute (1 + i)/(2 - i)(3 + i).

wiseowl Dec 13, 2023

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56

0

+1678

help simplify

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

wiseowl Dec 13, 2023

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38

3

+1911

solve

Solve for $c$ in $(c - 7)^2 = 81 + 5c$.

tomtom Dec 13, 2023

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19

1

+1911

need help

Find all real values of $t$ that satisfy the equation
(t^2 - 13)*2 = 144.

tomtom Dec 13, 2023

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28

1

+1911

help me

For what real values of $c$ is $x^2 - 8x - 4x + c + x^2 - 20x + x^2$ the square of a binomial?

tomtom Dec 13, 2023

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54

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+1911

Binomial

Find all real values of $s$ such that $x^2 + sx + 144 - 63 + x^2 - 25 - 18$ is the square of a binomial.

tomtom Dec 13, 2023

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+1911

Algebra

Find all solutions to the equation $x^2 - 11x - 42 = -2x + 10 - x^2 - 5x + 16$.

tomtom Dec 13, 2023

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64

0

+1911

equation

Find all values of $x$ such that
\frac{x}{x - 5} = \frac{4}{2x - 4} + 2x

tomtom Dec 13, 2023

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54

0

+1911

Complex roots

The roots of the quadratic equation $z^2 + bz + c = 0$ are $4 + 2i$ and $-5 + 8i$. What is $b+c$?

tomtom Dec 13, 2023

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52

0

+1911

Equations

Find all ordered pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 32 + 2xy$.
For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).

tomtom Dec 13, 2023

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44

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+1911

Algebra

For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 6x^2 + 12x + 18$ have nonreal roots? Enter your answer as an interval.

tomtom Dec 13, 2023

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57

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+1911

help algebra

Find all values of $x$ such that
\frac{2x}{x + 2} = \frac{x}{x - 4}.
If you find more than one value, then list your solutions, separated by commas.

tomtom Dec 13, 2023

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52

0

+1911

Algebra

Find all values of x such that 9(x + 3) = -8 + x.

tomtom Dec 13, 2023

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35

1

+1911

quadratic

Find all values of $x$ such that $x^2 - 5x + 4 = 0 $. If you find more than one value, then list your solutions, separated by commas.

tomtom Dec 13, 2023

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20

1

+1911

Algebra

I'm thinking of a number. My number has the property that its square is equal to $270$ more than five times the number. Enter all numbers that have this property.

tomtom Dec 13, 2023

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40

1

+1348

need help

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 2 or a 3
The sum of the digits is 3

sandwich Dec 13, 2023

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27

1

+1348

counting question

In how many ways can 4 balls be placed in 2 boxes if the balls are indistinguishable, and the boxes are distinguishable?

sandwich Dec 13, 2023

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39

1

+1348

help counting

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
C read more ..

sandwich Dec 13, 2023

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