belongs to the set of irrational numbers.
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1 State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. The absolute value of a number is always negative. The absolute value of a number is always nonnegative. So, the sentence is false. 2. belongs to the set of rational numbers. The sentence is false because belongs to the set of irrational numbers. 3. An equation is a statement that two expressions have the same value. The sentence is true. 4. A solution of an equation is a value that makes the equation false. A solution of an equation is a value that makes the equation true. So, the sentence is false. 5. The empty set contains no elements. The sentence is true. 6. A mathematical sentence containing one or more variables is called an open sentence. The sentence is true. 7. The graph of a compound inequality containing and is the union of the solution sets of the two inequalities. The graph of a compound inequality containing or is the union of the solution sets of the two inequalities. So, the sentence is false. 8. Variables are used to represent unknown quantities. The sentence is true. 9. The set of rational numbers includes terminating and repeating decimals. The sentence is true. 10. Expressions that contain at least one variable are called algebraic expressions. The sentence is true. esolutions Manual - Powered by Cognero Page 1
2 Evaluate each expression Evaluate each expression if and 14. esolutions Manual - Powered by Cognero Page 2
3 GEOMETRY The formula for the volume of a cylinder is, where V is volume, r is radius, and h is the height. What is the volume of a cylinder that is 6 inches high and has a radius of 3 inches? 18. The volume of the cylinder is about cubic inches. Name the sets of numbers to which each value belongs. The number is a real number. Since can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is not a part of the set { 2, 1, 0, 1, 2, } so it is not an integer. Since it is not a part of the set { 0, 1, 2, 3, } it is not a whole number or a natural number. Q, R esolutions Manual - Powered by Cognero Page 3
4 19. The number = 2 which is a real number. Since 2 can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is part of the set { 2, 1, 0, 1, 2, } so it is an integer. It is part of the set { 0, 1, 2, 3, } so it is a whole number and since it is not 0 it is also a natural number. N, W, Z, Q, R 20. The number is a real number. Since can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is not a part of the set { 2, 1, 0, 1, 2, } so it is not an integer. Since it is not a part of the set { 0, 1, 2, 3, } it is not a whole number or a natural number. Q, R Simplify each expression esolutions Manual - Powered by Cognero Page 4
5 24. MONEY At Fun City Amusement Park, hot dogs sell for $3.50 and sodas sell for $2.50. Dion bought 3 hot dogs and 3 sodas during one day at the park. a. Illustrate the Distributive Property by writing two expressions to represent the cost of the hot dogs and the sodas. b. Use the Distributive Property to find how much money Dion spent on food and drinks. a. Since Dion bought 3 of each, you can write the expression in two ways. Either add the costs of 1 hot dog and 1 soda together and multiply by 3 or multiply the cost of each item by 3 and then add. The expressions are: 3( ) or 3(3.50) + 3(2.50). b. Dion spent $18 on food and drinks. Solve each equation. Check your solution. 25. So, the solution of the equation is r = 7. esolutions Manual - Powered by Cognero Page 5
6 26. So, the solution of the equation is. esolutions Manual - Powered by Cognero Page 6
7 27. So, the solution of the equation is. esolutions Manual - Powered by Cognero Page 7
8 28. So, the solution of the equation is. 29. MONEY It cost Lori $14 to go to the movies. She bought popcorn for $3.50 and a soda for $2.50. How much was her ticket? The cost of the ticket was $8. esolutions Manual - Powered by Cognero Page 8
9 Solve each equation or formula for the specified variable. 30. for k 31. for m 32. for h esolutions Manual - Powered by Cognero Page 9
10 33. GEOMETRY Yu-Jun wants to fill the water container at the right. He knows that the radius is 2 inches and the volume is cubic inches. What is the height of the water bottle? Use the formula for the volume of a cylinder,, to find the height of the bottle. Substitute r = 2, and V = in the formula V = πr 2 h. The height of the bottle is about 8 inches. Solve each equation. Check your solution. 34. There appear to be two solutions, 7 and 17. Check: Substitute each value in the original equation. The solution set is. esolutions Manual - Powered by Cognero Page 10
11 35. There appear to be two solutions, 2 and 10. Check: Substitute each value in the original equation. The solution set is. esolutions Manual - Powered by Cognero Page 11
12 36. There appear to be two solutions,. Check: Substitute each value in the original equation. Because 15 15, the solution set is. esolutions Manual - Powered by Cognero Page 12
13 37. There appear to be two solutions,. Check: Substitute each value in the original equation. Because, is an extraneous solution. So, the solution set is. esolutions Manual - Powered by Cognero Page 13
14 38. MEASUREMENT Marcos is cutting ribbons for a craft project. Each ribbon needs to be yard long. If each piece is always within plus or minus yard, how long are the shortest and longest pieces of ribbon? Let x be the length of the shortest and longest pieces of ribbon. Solve the equation. Solve each inequality. Then graph the solution set on a number line. 39. To graph this inequality, draw a solid circle at 6 and draw an arrow extending to the right. esolutions Manual - Powered by Cognero Page 14
15 40. To graph this inequality, draw an open circle at 55 and draw an arrow extending to the right. 41. To graph this inequality, draw a solid circle at and draw an arrow extending to the left. esolutions Manual - Powered by Cognero Page 15
16 42. To graph this inequality, draw an open circle at 2 and draw an arrow extending to the right. 43. MONEY Ms. Hawkins is taking her science class on a field trip to a museum. She has $572 to spend on the trip. There are 52 students that will go to the museum. The museum charges $5 per student, and Ms. Hawkins gets in for free. If the students will have slices of pizza for lunch that cost $2 each, how many slices can each student have? Let x be the number of slices can each student have. Therefore, each student can have 3 or fewer slices. esolutions Manual - Powered by Cognero Page 16
17 Solve each inequality. Graph the solution set on a number line. 44. or or The solution set is. To graph, draw an open circle at extending to the right. and an arrow extending to the left and an open circle at 3 and an arrow 45. The solution set is. To graph, draw an open circle at 2 and an open circle at 4 and draw a line to connect the circles. esolutions Manual - Powered by Cognero Page 17
18 46. or or The solution set is. To graph, draw a solid circle at extending to the right. and an arrow extending to the left and an open circle at 3 and an arrow 47. The solution set is. To graph, draw a solid circle at and an open circle at and draw a line to connect the circles. esolutions Manual - Powered by Cognero Page 18
19 48. The solution set is. To graph, draw an open circle at 13 and an open circle at 13 and draw a line to connect the circles. 49. The solution set is. To graph, draw a solid circle at 5 and a solid circle at 33 and draw a line to connect the circles. esolutions Manual - Powered by Cognero Page 19
20 50. The solution set is. To graph, draw an open circle at and an open circle at and draw a line to connect the circles. 51. Since the absolute value of a number is always positive, the solution set of the inequality is. Since there are no solutions, leave the graph blank. esolutions Manual - Powered by Cognero Page 20
21 52. The solution set is. To graph, draw a solid circle at extending to the right. and an arrow extending to the left and a solid circle at 2 and an arrow esolutions Manual - Powered by Cognero Page 21
22 53. MONEY Cara is making a beaded necklace for a gift. She wants to spend between $20 and $30 on the necklace. The bead store charges $2.50 for large beads and $1.25 for small beads. If she buys 3 large beads, how many small beads can she buy to stay within her budget? Write and solve a compound inequality to describe the range of possible beads. Let b represent the number of small beads she can buy to stay within the budget. Solve the compound inequality. The range of number of possible beads is 10 b 18. esolutions Manual - Powered by Cognero Page 22
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