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4)(- 2)(- 1) 54. - 23 # 0 57. 2(- 3)(-1)(- 2)(- 4) 58. 3(- 2)(- 1)(-5)(-3) 2(-2) - 4(-3) 5 - 8 59. (-10)2 60. (- 8)2 61. -102 62. -82 63. (-2)3 64. (- 3)3 (5 - 6)2 - 2 3 - 7 89 - 3 # 52 12 , 3 # 5 22 + 32 94. 6(- 4) - 5(- 3) 9 - 10 7 + 3 - 62 97. 15 - 23 - (- 1) + 12 , 2 # 3 98. 17 - 5 - (-2) + 12 , 2 # 3 99. 20 + 1 - 2102 - (5 + 1)2(- 2) 100. 24 , 23 # (5 - 2) , [- 1 - (- 3)]2 In Exercises 101–104, write an algebraic expression equivalent to the given expression using each of the commutative properties.
We used a right triangle with two legs of length 1. The remaining side has a length measuring 12. 4 The real number line Real numbers are graphed on a number line by placing a dot at the correct location for each number. The integers are easiest to locate. 5, we’ve graphed six rational numbers and three irrational numbers on a real number line. 5 Graphing numbers on a real number line We’ll have lots more to say about right triangles later in the book. Every real number corresponds to a point on the number line and every point on the number line corresponds to a real number.
Solution a. Because 100 is an integer, the statement 100 {x x is an integer} is true. The number 100 is an element of the set of integers. b. Because 20 is not an element of {5, 10, 15}, the statement 20 {5, 10, 15} is true. ✓ Check Point 5 Determine whether each statement is true or false: a. 13 {x x is an integer} b. 6 {7, 8, 9, 10}. Another common set is the set of rational numbers. Each of these numbers can be expressed as an integer divided by a nonzero integer. Rational Numbers The set of rational numbers is the set of all numbers that can be expressed as a quotient of two integers, with the denominator not 0.
