If you place one vertical and cross at the 0 point, then the intersection forms a coordinate system. So, the statement is true.

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1 State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 2. A coordinate system is formed by the intersection of two number lines. A coordinate system is formed by the intersection of two number lines, the horizontal axis and the vertical axis. Consider the number line. If you place one vertical and cross at the 0 point, then the intersection forms a coordinate system. So, the statement is true. 4. In an expression involving multiplication, the quantities being multiplied are called factors. In an expression involving multiplication, the quantities being multiplied are called factors. For example, in the expression (3x + 5)2x, (3x + 5) and 2x are factors. So, the statement is true. 6. Order of operations tells us to always perform multiplication before subtraction. The rule that lets you know which operation to perform first is called the order of operations. Consider the expression 3(2) 4. If you preform the subtraction before the multiplication you get 3(2) 4 = 3( 2) or 6. If you preform the multiplication first, you get 3(2) 4 = 6 4 or 2. The correct answer is 2. So, the statement is true. Write a verbal expression for each algebraic expression. 8. h 7 The expression shows h minus seven. So, the verbal expression the difference between h and 7 can be used to describe the algebraic expression h 7. esolutions Manual - Powered by Cognero Page 1

2 m 3 The expression shows the sum of 5 and 6m 3. The term 6m 3 represents the product of the factors 6 and m 3. The factor m 3 represents a number raised to the third power or cubed. So, the verbal expression five more than the product of six and m cubed can be used to describe the algebraic expression 5 + 6m 3. Write an algebraic expression for each verbal expression. 12. two thirds of a number d to the third power The words two-thirds of suggest multiplication. So, the verbal expression two-thirds of a number d to the third power can be written as the algebraic expression. Evaluate each expression Evaluate each expression (9 3) esolutions Manual - Powered by Cognero Page 2

3 22. [(2 5 5) 9]11 Evaluate each expression if a = 4, b = 3, and c = c + 3a Replace c with 9 and a with (a 2 + 2bc) 7 Replace a with 4, b with 3 and c with 9. Evaluate each expression using properties of numbers. Name the property used in each step (1 3) 18 3(1 3) = 18 (3) Substitution = 18 1 Multiplicative Inverse = 18 Multiplicative Identity esolutions Manual - Powered by Cognero Page 3

4 30. ( ) + 9 ( ) + 9 = Substitution = Additive Inverse = 9 Additive Identity = Commutative (+) = ( ) + (41 + 9) Associative (+) = Substitution = 100 Substitution = Commutative ( ) = (8 5) 0.5 Associative ( ) = Substitution = 20 Substitution 36. SCHOOL SUPPLIES Monica needs to purchase a binder, a textbook, a calculator, and a workbook for her algebra class. The binder costs $9.25, the textbook $32.50, the calculator $18.75, and the workbook $ Find the total cost for Monica s algebra supplies. To find the total cost for Monica s Algebra supplies, find the sum of the costs of the binder, the textbook, the calculator and the workbook. $ $ $ $15.00 = $75.50 So, the total cost for Monica s Algebra supplies is $ Use the Distributive Property to rewrite each expression. Then evaluate ( ) esolutions Manual - Powered by Cognero Page 4

5 40. (11 4)3 42. (8 3)4 Rewrite each expression using the Distributive Property. Then simplify. 44. (m + 8) (5 2t) 48. 6(4z + 3) Find the solution set of each equation if the replacement sets are x: {1, 3, 5, 7, 9} and y: {6, 8, 10, 12, 14} 50. y 9 = 3 y y 9 = 3 True or False? = 3 False = 3 False = 3 False = 3 True = 3 False The solution set is {12}. esolutions Manual - Powered by Cognero Page 5

6 52. 4y = y 4y = 32 True or False? 6 4(6) = 32 False 8 4(8) = 32 True 10 4(10) = 32 False 12 4(12) = 32 False 14 4(14) = 32 False The solution set is {8}. y True or False? 6 True 8 False 10 False 12 False 14 False The solution set is {6}. Solve each equation. 56. a = 24 7(3) esolutions Manual - Powered by Cognero Page 6

7 58. AGE Shandra s age is four more than three times Sherita s age. Write an equation for Shandra s age. Then solve the equation if Sherita s is 3 years old. Let K = Sherita s age. Let E = Shandra s age. The words more than suggest addition and the word times suggests multiplication. So, 3K + 4 = E. To find Shandra s age when Sherita is 3, replace the K in the equation with 3 and solve for E. So, Shandra is 13 years old. Express each relation as a table, a graph, and a mapping. Then determine the domain and range. 60. {( 1, 1), (0, 2), (3, 1), (4, 1)} Table: Place the x-coordinates into the first column of the table. Place the corresponding y-coordinates in the second column of the table. Graph: Graph each ordered pair on a coordinate plane. Mapping: List the x-values in the domain and the y-values in the range. Draw arrows from the x-values in the domain to the corresponding y-values in the range. The domain is { 1, 0, 3, 4}, and the range is { 2, 1, 1}. esolutions Manual - Powered by Cognero Page 7

8 Express the relation shown in each table, mapping, or graph as a set of ordered pairs. 62. To express the relation as a set of ordered pairs, write the x-coordinates followed by the corresponding y- coordinates. So, the ordered pairs are {(5, 3), (3, 1), (1, 2), ( 1, 0)}. 64. GARDENING On average, 7 plants grow for every 10 seeds of a certain type planted. Make a table to show the relation between seeds planted and plants growing for 50, 100, 150, and 200 seeds. Then state the domain and range and graph the relation. To find the number of plants that grow for a certain number of seeds, divid the number of seeds by 10 and then multiply by 7. Planted Growing = = = = 140 The domain is the number of seeds planted, {50, 100, 150, 200}. The range is the number of plants growing, {35, 70, 105, 140}. Graph the number of seeds planted on the x-axis and the number of plants growing on the y-axis. Then, graph the ordered pairs from the table. esolutions Manual - Powered by Cognero Page 8

9 Determine whether each relation is a function. 66. A function is a relationship between input and output. In a function, there is exactly one output for each input. So, this relation is a function. If f (x) = 2x + 4 and g(x) = x 2 3, find each value. 68. f ( 3) 70. f (0) 72. f (m + 2) esolutions Manual - Powered by Cognero Page 9

10 74. GRADES A teacher claims that the relationship between number of hours studied for a test and test score can be described by g(x) = x, where x represents the number of hours studied. Graph this function. To graph the function, first make a table of values. x g(x) = x 1 g(1) = (1) = 54 2 g(2) = (2) = 63 3 g(3) = (3) = 72 4 g(4) = (4) = 81 5 g(5) = (5) = 90 Graph the hours studied, x, on the x-axis and the test scores, g(x), on the y-axis. Then, graph the ordered pairs in the table. Draw a line through the points. esolutions Manual - Powered by Cognero Page 10