By Karakhanyan M.I., Khor'kova T.A.
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Extra info for A Characteristic Property of the Algebra C(Q)B
49. Bottled Water. A driver left a production plant with 300 fivegallon bottles of drinking water on his truck. His delivery route consisted of office buildings, each of which was to receive 6 bottles of water. Describe the relationship between the number of bottles of water left on his truck and the number of stops that he has made. 50. Collectibles. A woman inherited 9 antique dolls. She decided to add to her collection by purchasing two more dolls each month. Describe the relationship between the number of antique dolls in her collection and the number of months since she began to purchase them.
10 ϭ 5, because 2(5) ϭ 10 2 Ϫ10 ϭ 5, because Ϫ2(5) ϭ Ϫ10 Ϫ2 Ϫ10 ϭ Ϫ5, because 2(Ϫ5) ϭ Ϫ10 2 10 ϭ Ϫ5, because Ϫ2(Ϫ5) ϭ 10 Ϫ2 These results suggest the following rules for dividing real numbers. Note that they are similar to those for multiplying real numbers. Dividing Two Real Numbers To divide two real numbers, divide their absolute values. 1. The quotient of two numbers with like signs is positive. 2. The quotient of two numbers with unlike signs is negative. EXAMPLE 4 Divide: a. 7 Ϫ44 b. 11 Ϫ9 Strategy We will use the rules for dividing positive and negative real numbers.
A. b. 61. a. b. 62. a. b. 5% of 6 miles more than the altitude twice the sum of the tax and 200 the sum of twice the tax and 200 the square of 14 less than a number 14 less than the square of a number double the cube of a number the cube of double a number APPLICATIONS 63. Production Planning. Suppose r towel racks like that shown below are to be manufactured. Complete the two equations that could be used to order the necessary number of bar holders b and wood screws s . bϭ sϭ r Bar holder Use the given equation to complete each table.
A Characteristic Property of the Algebra C(Q)B by Karakhanyan M.I., Khor'kova T.A.