Question 1

Evaluate $\sqrt[4]{10^2 \cdot 21}$ and round your answer to one decimal place.

Accepted Answer

$7.2$

Question 2

Solve for $y$ in the equation $3y + 6 = 6$.

Accepted Answer

$y = 0$

Question 3

Simplify $\dfrac{\sqrt{50} - \sqrt{200} + 2\sqrt{8}}{\sqrt{2}}$ as much as possible.

Accepted Answer

$-39\sqrt{2}$

Question 4

Simplify the expression $\dfrac{9}{3p \cdot 8p^2}$ and write your answer using only positive exponents.

Accepted Answer

$\dfrac{9}{24p^3}$

Question 5

Factor the polynomial $12x^3 - 216x^2$ completely.

Question 6

The average annual revenue for a retail company (in billions of dollars) can be approximated by $R = -0.086x^2 - 2.172x + 5.382$, where $x$ is the number of years since 2000. What is the first full year that annual revenue hits $8.3$ billion?

Accepted Answer

$2012$

Question 7

Factor $3x^2 - 2x - 21$ completely.

Accepted Answer

$(x - 3)(3x + 7)$

Question 8

Solve for $Y$ in the equation $x = \dfrac{8Y}{y + y^2}$, assuming all variables are positive real numbers.

Question 9

Simplify the complex fraction $\dfrac{z}{\dfrac{1}{z} + 1}$.

Accepted Answer

$\dfrac{z^2}{z + 1}$

Question 10

Solve the equation $5x = \dfrac{19}{24}x^2 + 8x + \dfrac{5}{8}(3x - 4)$ for $x$.

Accepted Answer

$x = 155$

Question 11

Evaluate $\left(\dfrac{3}{11}\right)^{-3}$ and give your answer without exponents.

Accepted Answer

$27$

Question 12

Solve using the quadratic formula: $x^2 + 5x + 6 = 0$.

Accepted Answer

$x = -2, -3$

Question 13

Select the correct solution for the quadratic equation $x^2 + 5x + 6 = 0$.

Accepted Answer

The solution(s) do(es) not involve(s) square roots. The solution(s) is/are $x = -2, -3$

Question 14

Simplify $(10y^3 - 3y^2 - 4y) - (-3y^3 + 6y + 10)$.

Accepted Answer

$13y^3 - 3y^2 - 10y - 6$

Question 15

The total health care expenditures $E$ (in trillions of dollars) in a certain country can be approximated by $E = 0.138x + 1.507$, where $x$ is the number of years after 2000. In which year will health care expenditures reach $2.197$ trillion?

Accepted Answer

$2012$

Question 16

Solve for $x$ in the equation $5b - a = 3b + ax$.

Question 17

Multiply $(6x + 6)(2x^2 + 5x + 3)$ and simplify.

Question 18

Add $\dfrac{3}{x^2 + 14x + 49}$ and $\dfrac{4}{x^2 + 3x - 28}$ and simplify your answer.

Accepted Answer

$\dfrac{3(x^2 + 3x - 28) + 4(x^2 + 14x + 49)}{(x^2 + 14x + 49)(x^2 + 3x - 28)}$

Question 19

Solve the equation $7x = 16$ for $x$.

Accepted Answer

$x = \dfrac{16}{7}$

Question 20

Solve $5x^2 = 3$ using the square root property.

College Algebra: Core Concepts, Equations, and Applications

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