Q: Which of the following is the correct definition of the absolute value $$|x|$$?

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

Question 1

Evaluate the algebraic expression $$5 + 4(x^2$ - 2x)$$ for $$x = -3.$$

Accepted Answer

$$5 + 4((-3)^2$ - 2(-3)) = 5 + 4(9 + 6) = 5 + 4(15) = 5 + 60 = 65$$

Question 2

A formula for the cost $$C (in $$dollars) to rent a car is $$C = 40d + 25$$, where $$d is $$the number of days rented. What is the cost to rent the car for 5 days?

Accepted Answer

$$C = 40(5) + 25 = 200 + 25 = 225$$

Question 3

Which of the following sets is the intersection of $$A = \{2, 4, 6, 8\}$$ and $$B = \{4, 5, 6, 7\}$$?

Accepted Answer

$$\{4, 6\}$$

Question 4

Which of the following sets is the union of $$A = \{1, 3, 5\}$$ and $$B = \{2, 3, 4\}$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Question 5

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 6

Which property of real numbers justifies the equation $$7 + (2 + 5) = (7 + 2) + 5$$?

Accepted Answer

Associative Property of Addition

Question 7

Simplify the expression $$3x + 4 - 2x + 7.$$

Accepted Answer

$$x + 11$$

Question 8

Which of the following correctly expresses the distance between the points $$a = -7$$ and $$b = 2 on $$the real number line?

Accepted Answer

$$|a - b| = |-7 - 2| = |-9| = 9$$

Question 9

Which of the following is the correct definition of the absolute value $$|x|$$?

Accepted Answer

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

Question 10

If $$A = \{x | x 	ext{ is an even integer less than 10}\}$$, which of the following is $$A$$?

Accepted Answer

$$\{ -8, -6, -4, -2, 0, 2, 4, 6, 8\}$$

Question 11

Which of the following is an example of the distributive property?

Accepted Answer

$$a(b + c) = ab + ac$$

Question 12

Which of the following numbers is an irrational number?

Accepted Answer

$$\pi$$

Question 13

Given the formula $$T = -x^2$ + 361x + 3193$$ for the average cost of tuition and fees, what is the value of $$T$$ when $$x = 10$$?

Accepted Answer

$$T = -(10)^2$ + 361(10) + 3193 = -100 + 3610 + 3193 = 6703$$

Question 14

Which of the following is the empty set?

Accepted Answer

$$\emptyset$$

Question 15

Which of the following is a subset of the set of integers?

Accepted Answer

The set of whole numbers

Question 16

Which inequality symbol correctly completes the statement: $$-5\ \_\ -2$$?

Accepted Answer

$$\u003c$$

Question 17

Which of the following is the correct simplification of $$2(x + 3) - 4x$$?

Accepted Answer

$$-2x + 6$$

Question 18

If $$x = -4$$, what is the value of $$|x| + x$$?

Accepted Answer

$$|-4| + (-4) = 4 - 4 = 0$$

Question 19

Which of the following is a correct example of a mathematical model?

Accepted Answer

The formula $$A = \pi r^2$ for the area of a circle

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

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