$$\{x | x \text{ is a counting number less than } 6\}$$

$$A \cap B = \{x | x \text{ is an element of } A \text{ and } x \text{ is an element of } B\}$$

$$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x \u003c 0 \end{cases}$$

Question 1

Evaluate the algebraic expression $$8 + 6(x - 3)^2$ for x = 13$.

Accepted Answer

$$8 + 6(13 - 3)^2$ = 8 + 6(10)^2$ = 8 + 600 = 608$$

Question 2

Which of the following is the correct definition of a rational number?

Accepted Answer

A number that can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b 
eq 0$$

Question 3

Given the sets $$A = \{3, 4, 5, 6, 7\}$$ and $$B = \{3, 7, 8, 9\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 7\}$$

Question 4

Which property of real numbers is illustrated by $$a + b = b + a$$?

Accepted Answer

Commutative Property of Addition

Question 5

Simplify the expression $$7(4x^2 + 3x$$) + $$2(5x^2 + x$$)$$.

Accepted Answer

$$38x^2 + 23x$

Question 6

Which of the following numbers is irrational?

Accepted Answer

$$\sqrt{5}$$

Question 7

What is the distance between the points $$-4$$ and $$5 on $$the real number line?

Accepted Answer

$$| -4 - 5 | = | -9 | = 9$$

Question 8

Rewrite $$|2 - \pi|$$ without absolute value bars, assuming $$\pi \u003e 2.$$

Accepted Answer

$$\pi - 2$$

Question 9

Which of the following is the union of the sets $$\{7, 8, 9, 10, 11\}$$ and $$\{6, 8, 10, 12\}$$?

Accepted Answer

$$\{6, 7, 8, 9, 10, 11, 12\}$$

Question 10

Which subset of real numbers does $$0$$ belong to?

Accepted Answer

Whole numbers

Question 11

If $$a = 3$$ and $$b = -5$$, what is the distance between $$a$$ and $$b on $$the real number line?

Accepted Answer

$$|3 - (-5)| = |8| = 8$$

Question 12

Which property of real numbers is illustrated by $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 13

Which of the following is the correct set-builder notation for the set $$\{1, 2, 3, 4, 5\}$$?

Accepted Answer

$$\{x | x 	ext{ is a counting number less than } 6\}$$

Question 14

Which of the following is NOT a property of real numbers?

Accepted Answer

The Distributive Property of Addition over Multiplication

Question 15

Evaluate $$2 + 3(x - 1)^2$ - 4$$ for $$x = 3.$$

Accepted Answer

$$2 + 3(3 - 1)^2$ - 4 = 2 + 3(2)^2$ - 4 = 2 + 12 - 4 = 10$$

Question 16

Which of the following is the correct definition of the intersection of two sets $$A$$ and $$B$$?

Accepted Answer

$$A \cap B = \{x | x 	ext{ is an element of } A 	ext{ and } x 	ext{ is an element of } B\}$$

Question 17

Which of the following is the correct definition of absolute value?

Accepted Answer

$$|x| = \begin{cases} x & 	ext{if } x \geq 0 \ -x & 	ext{if } x \u003c 0 \end{cases}$$

Question 18

Which of the following is a subset of the set of real numbers?

Accepted Answer

The set of integers

Fundamental Concepts of Algebra: Algebraic Expressions, Mathematical Models, and Real Numbers

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