Review Exercises 313 d. Sketch the inequalities in parts (a)–(c) to find the feasible region for the farmer’s distribution of orange and grapefruit trees. 100 90 80 60 50 40 30 20 Section 3.6 For Exercises 44–47, solve the system. If a system does not have a unique solution, state whether the system is inconsistent or the equations are dependent. 44. 5x 5y 5z 30 45. 5x 3y z 5 x y z 2 x 2y z 6 10x 6y 2z 4 x 2y z 8 46. 47. x y z 4 3x 4z 5 x 2y 3z 6 2y 3z 2 2x 4y 6z 12 2x 5y 8 48. The perimeter of a right triangle is 30 ft. One leg is 2 ft longer than twice the shortest leg. The hypotenuse is 2 ft less than 3 times the shortest leg. Find the lengths of the sides of this triangle. 49. Three pumps are working to drain a construction site.Working together, the pumps can drain 950 gal/hr of water. The slowest pump drains 150 gal/hr less than the fastest pump. The fastest pump drains 150 gal/hr less than the sum of the other two pumps. How many gallons can each pump drain per hour? 50. The smallest angle in a triangle measures 9° less than the middle angle. The largest angle is 26° more than 3 times the measure of the smallest angle. Find the measure of the three angles. Section 3.7 For Exercises 51–54, determine the order of each matrix. 2 4 1 5 0 3 1 6 10 £ § § 51. 52. £ 5 6 9 2 0 3 § 30 13 4 16 4 53. 54. £ 7 12 4 For Exercises 55–56, set up the augmented matrix. 55. 56. x y 3 x y 1 x y z 4 2x y 3z 8 2x 2y z 9 For Exercises 57–58, write a corresponding system of equations from the augmented matrix. c 1 0 ` 9 d § 0 1 3 57. 58. 59. Given the matrix C £ 1 0 0 0 1 0 0 0 1 C c1 3 4 1 ` 1 6 d † 5 2 8 a. What is the element in the second row and first column? b. Write the matrix obtained by multiplying the first row by 4 and adding the result to row 2. 60. Given the matrix D D £ 1 2 0 4 1 1 3 2 2 † 3 0 5 § a. Write the matrix obtained by multiplying the first row by 4 and adding the result to row 2. b. Using the matrix obtained in part (a), write the matrix obtained by multiplying the first row by 3 and adding the result to row 3. 70 10 20 30 40 50 60 70 80 90 100 10 y x
miller_intermediate_algebra_4e_ch1_3
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