All Questions ⁺⁰237283 Questions

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Each face of a cube is painted randomly one

Each face of a cube is painted randomly one of the colors red, orange, yellow, green, blue or purple. What is the probability that the cube has at least one pair of faces that share an edge and are the same color? Express your answer as a decimal to the read more ..

UniCorns555 Feb 19, 2024

-1

74

1

+1926

Complex Numbers

Simplify $(1-3i) + (2-i) + (2+i) + (1+3i)$.

tomtom Feb 19, 2024

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32

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+1926

Complex Numbers

Express $\frac{15 - 16i}{2 - 3i - 5 + 7i}$ in standard form.

tomtom Feb 19, 2024

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45

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+1926

Complex Roots

Find the solutions to $x^2 + 64 = 4x + 16.$ Enter your answers separated by commas.

tomtom Feb 19, 2024

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72

2

+1729

System

For certain values of k and m, the system
a + 2b = 2 - 4b - 3a + 7
5a + 2b = k + 5a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

parmen Feb 19, 2024

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62

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+1729

Inequality

Find the smallest integer that satisfies the inequality: (x - 5)(x + 5)(x - 3) > 0.

parmen Feb 19, 2024

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58

2

+1729

Integer

What is the greatest integer $n$ such that $n^2 - 11n +24 \leq 17n - 8$?

parmen Feb 19, 2024

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36

1

+1729

Inequality

Find all $x$ that satisfy the inequality $(2x+10)(x+3)<(3x+1)(x+6)$. Express your answer in interval notation.

parmen Feb 19, 2024

Feb 18, 2024

-1

56

1

+1766

Simplify

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

blackpanther Feb 18, 2024

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35

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+1766

Complex Numbers

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

blackpanther Feb 18, 2024

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41

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+1766

Equation

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

blackpanther Feb 18, 2024

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64

1

+1776

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 $a^2 + b$ and $b^2 + a.$

bader Feb 18, 2024

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41

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+1776

Help 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 ..

bader Feb 18, 2024

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3

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Roots

Let $a$ and $b$ be the roots of the quadratic $2x^2 - 8x + 7 = -3x^2 + 5x + 11.$ Compute $a^3/b^2 + b^3/a^2.$

bader Feb 18, 2024

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41

3

+1776

Algebra question

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 $b.$

bader Feb 18, 2024

0

62

1

+965

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $15$ days earlier. If the job needs to be completed $40$ days earlier, how many additional workers should be hired?

magenta Feb 18, 2024

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3

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Rate problem

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

magenta Feb 18, 2024

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48

2

+965

System question

For a certain value of $k$, the system
x + y + 3z &= 10, \\
x - 2y + 8z &= 7, \\
kx + 5z &= 3
has no solutions. What is this value of $k$?

magenta Feb 18, 2024

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39

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+965

Equation

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.

magenta Feb 18, 2024

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67

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Help

Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not, it becomes Bob's turn. On Bob's turn, he flips a coin. If he gets a tails, he wins. If not, it becomes Alice's turn. What is read more ..

UniCorns555 Feb 18, 2024

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60

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+1776

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

bader Feb 18, 2024

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