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Four less than one-half of a number 72. Seven more than three times a number 91. If n represents an odd integer, what represents the next larger odd integer? 73. The quotient of a number and 8 74. The quotient of 50 and a number 92. If n represents an even integer, what represents the next larger even integer? 75. Nine less than twice a number 93. The cost of a 5-pound box of candy is c cents. What is the price per pound? 76. Six more than one-third of a number 77. Ten times the difference of a number and 6 78.

11. 7(4) ϩ 9(4) ϭ (7 ϩ 9)4 35. 7(2)3 ϩ 4(Ϫ2)3 12. (x ϩ 3) ϩ (Ϫ3) ϭ x ϩ [3 ϩ (Ϫ3)] 36. Ϫ4(Ϫ1)2 Ϫ 3(2)3 13. [(Ϫ14)(8)](25) ϭ (Ϫ14)[8(25)] 3 4 14. a ba b ϭ 1 4 3 For Problems 15–26, simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. (Objective 2) 15. 16. 17. 18. 36 ϩ (Ϫ14) ϩ (Ϫ12) ϩ 21 ϩ (Ϫ9) Ϫ 4 Ϫ37 ϩ 42 ϩ 18 ϩ 37 ϩ (Ϫ42) Ϫ 6 [83 ϩ (Ϫ99)] ϩ 18 [63 ϩ (Ϫ87)] ϩ (Ϫ64) 19. (25)(Ϫ13)(4) 3(Ϫ1)3 Ϫ 4(3)2 32. (Ϫ3)3 ϩ 32 34.

2. The product (or quotient) of one positive and one negative number is the opposite of the product (or quotient) of their absolute values. Evaluate exponential expressions. 3/Objective 3) Exponents are used to indicate repeated multiplications. The expression bn can be read “b to the nth power”. We refer to b as the base and n as the exponent. Solution The integers are Ϫ4 and 0. Solution The statement, “If x ϭ y and y ϭ 7, then x ϭ 7,” is justified by the transitive property of equality. Find the absolute value of the following: 15 ` (a) 0 Ϫ20 (b) ` (c) 0Ϫ23 0 4 Solution (a) 0 Ϫ2 0 ϭ Ϫ(Ϫ2) ϭ 2 15 15 ` ϭ (b) ` 4 4 (c) 0Ϫ 23 0 ϭ ϪAϪ 23B ϭ 23 Simplify: (a) Ϫ20 ϩ 15 ϩ (Ϫ4) (b) 40 Ϫ (Ϫ8) (c) Ϫ3(Ϫ4)(Ϫ5) Solution (a) Ϫ20 ϩ 15 ϩ (Ϫ4) ϭ Ϫ5 ϩ (Ϫ4) ϭ Ϫ9 (b) 40 Ϫ (Ϫ8) ϭ 40 ϩ (ϩ8) ϭ 48 (c) Ϫ3(Ϫ4)(Ϫ5) ϭ 12(Ϫ5) ϭ Ϫ60 Simplify 2(Ϫ5) 3 ϩ 3(Ϫ2) 2.

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### Algebraic surfaces and golomorphic vector bundles by Friedman.

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