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.

Accepted Answer

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.

Accepted Answer

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 $$5b - a = 3b + ax.$$

Accepted Answer

Question 17

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

Accepted Answer

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.

Accepted Answer

College Algebra: Core Concepts, Equations, and Applications

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