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EXAMPLE Solve for a Variable GEOMETRY The formula for the surface area S of a cone is S = πr + πr2, where is the slant height of the cone and r is the radius of the base. Solve the formula for . S = πr + πr2 Surface area formula R S - πr2 = πr + πr2 - πr2 Subtract πr2 from each side. S - πr2 = πr Simplify. S - πr2 πr _ =_ Divide each side by πr. S - πr2 _ = Simplify. πr πr πr 6. The formula for the surface area S of a cylinder is S = 2πr2 + 2πrh, where r is the radius of the base, and h is the height of the cylinder.

REVIEW How many cubes that are 3 inches on each edge can be placed completely inside a box that is 9 inches long, 6 inches wide, and 27 inches tall? 4 ft by 50 ft G 36 J 72 PREREQUISITE SKILL Evaluate each expression. 42. √9 43. √16 44. √100 46. - √4 47. - √25 48. 10 Chapter 1 Equations and Inequalities √_49 45. √169 49. 36 √_ 49 1-2 Properties of Real Numbers Main Ideas • Classify real numbers. • Use the properties of real numbers to evaluate expressions. 0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

49. If mn = m and m ≠ 0, what is the value of n? MATH HISTORY For Exercises 50–52, use the following information. The Greek mathematician Pythagoras believed that all things could be described by numbers. By number he meant a positive integer. 50. To what set of numbers was Pythagoras referring when he spoke of numbers? c 51. Use the formula c = √2s2 to calculate the length of the hypotenuse c, or longest side, of this right triangle using 1 unit s, the length of one leg. 52. Explain why Pythagoras could not find a “number” for the value of c.