Q: Which of the following is the correct simplification of $$c)\ |3x - |2y||$$ when $$x = 3$$ and $$y = -2$$?

$$|3 \times 3 - |2 \times -2|| = |9 - | -4|| = |9 - 4| = |5| = 5$$

Question 1

Which of the following statements correctly describes the meaning of the inequality $$x \geq 0$$?

Accepted Answer

x is a nonnegative number

Question 2

What is the absolute value $$| -4 |$$?

Accepted Answer

$$4$$

Question 3

Evaluate the expression $$-2|x + 5y| - \frac{|y|}{y}$$ when $$x = 3$$ and $$y = -2.$$

Accepted Answer

$$-16$$

Question 4

Which of the following best describes the domain of the expression $$\frac{x^2$ - 9}{x + 5}$$?

Accepted Answer

All real numbers except $$x = -5$$

Question 5

Simplify $$(x^3$$ $$y^4)^5$ using the laws of exponents.

Accepted Answer

$$x^{15}$$ $$y^{20}$$

Question 6

What is the result of $$a^{-n}$$ for $$a 
eq 0$$?

Accepted Answer

$$\frac{1}{a^n}$$

Question 7

Simplify $$\frac{x^5$}{x^3$}$$ using the laws of exponents.

Accepted Answer

$$x^2$$

Question 8

Which of the following is the correct domain for the expression $$\frac{x^3$ - 1}{8(x + 3)(x - 7)}$$?

Accepted Answer

All real numbers except $$x = -3$$ and $$x = 7$$

Question 9

Simplify $$(-3)^2.$$

Accepted Answer

$$9$$

Question 10

What is the value of $$x^0$$ for $$x 
eq 0$$?

Accepted Answer

$$1$$

Question 11

Simplify $$-3^2.$$

Accepted Answer

$$-9$$

Question 12

Which of the following expressions is equivalent to $$(\frac{x^3$}{y^5$})^4$?

Accepted Answer

$$\frac{x$$^{12}$$}{y$$^{20}$$}$$

Question 13

Simplify $$(2u w$$^{-4}$$ x^3$ y$$^{-5}$$ z^8$ / 3 w^2$ x$$^{-5}$$ y^5$ z^8$)^{-2}$ so that all exponents are positive.

Accepted Answer

$$\frac{9 w$$^{12}$$ x$$^{16}$$ y$$^{40}$$}{4 u$$^{2}$$}$$

Question 14

Which of the following is the correct domain for the expression $$\frac{x}{x^2$ + 9}$$?

Accepted Answer

All real numbers

Question 15

Simplify $$\frac{a$$^{-n}$$}{b$$^{-m}$$}$$ for $$a 
eq 0$$, $$b 
eq 0.$$

Accepted Answer

$$\frac{b$$^{m}$$}{a$$^{n}$$}$$

Question 16

A chemical reaction produces a compound whose concentration is modeled by $$C(t) = 2^t. If $$the concentration doubles every hour, what will $$C(3) be$$?

Accepted Answer

$$8$$

Question 17

Which of the following is a strict inequality?

Accepted Answer

$$x \u003c 0$$

Question 18

Simplify $$(x^3)^2$ using the laws of exponents.

Accepted Answer

$$x^6$$

Question 19

A medical dosage is calculated as $$D = \frac{m^2$}{h}$$, where $$m is $$mass and $$h is $$hours since last dose. What is the domain of $$h$$?

Accepted Answer

All real numbers except $$h = 0$$

Question 20

Which of the following is the correct simplification of $$c)\ |3x - |2y||$$ when $$x = 3$$ and $$y = -2$$?

Accepted Answer

$$|3 	imes 3 - |2 	imes -2|| = |9 - | -4|| = |9 - 4| = |5| = 5$$

Algebra Essentials: Inequalities, Absolute Value, Domains, and Exponents

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