208 Chapter 2 Linear Equations and Inequalities 17. Graph the inequalities and write the sets in interval notation. a. 5x 0 x 6 06 1, 02 b. 5x 02 x 6 56 ( 0 For Exercises 18–21, solve the inequality. Graph the solution and write the solution set in set-builder notation and interval notation. 18. 19. 20. 21. ) 5x 14 7 2x 2 4 213 x2 14 312y 42 1 7 212y 32 8 13 3p 2 5 a 3 2 , b 22. The total bill for a pair of basketball shoes (including sales tax) is $87.74. If the tax rate is 7%, find the cost of the shoes before tax. The cost was $82.00. 23. Clarita borrowed money at a 6% simple interest rate. If she paid back a total of $8000 at the end of 10 yr, how much did she originally borrow? Clarita originally borrowed $5000. 24. One number is four plus one-half of another. The sum of the numbers is 31. Find the numbers. The numbers are 18 and 13. 25. Two families leave their homes at the same time to meet for lunch.The families live 210 mi apart, and one family drives 5 mph slower than the other. If it takes them 2 hr to meet at a point between their homes, how fast does each family travel? 50 mph. One family travels 55 mph and the other travels 26. The average winter snowfall for Syracuse, New York, for December, January, and February is 27.5 in. per month. If Syracuse receives 24 in. of snow in December and 32 in. in January, how much snow is required in February to exceed the 3-month average? More than 26.5 in. is required. 27. The perimeter of a pentagon (a five-sided polygon) is 315 in.The five sides are represented by consecutive integers. Find the measures of the sides. The sides are 61 in., 62 in., 63 in., 64 in., and 65 in. 28. Paula mixes macadamia nuts that cost $9.00 per pound with 50 lb of peanuts that cost $5.00 per pound. How many pounds of macadamia nuts should she mix to make a nut mixture that costs $6.50 per pound? Paula needs 30 lb of macadamia nuts. 29. A couple purchased two hockey tickets and two basketball tickets for $153.92. A hockey ticket cost $4.32 more than a basketball ticket.What were the prices of the individual tickets? Each basketball ticket was $36.32, and each hockey ticket was $40.64. 30. Two angles are complementary. One angle is 26° more than the other angle.What are the measures of the angles? The measures of the angles are 32° 58° and . 31. The length of a soccer field for international matches is 40 m less than twice its width. If the perimeter is 370 m, what are the dimensions of the field? The field is 110 m long and 75 m wide. 32. Given the triangle, find the measures of each angle by first solving for y. y 30; The measures of the angles are 30°, 39°, and 111°. ey 0 y 7 3 2 f; 5x 0 x 7 26; 12, 2 5x 0 x 46; 1, 44 5p 0 5 p 16; 35, 1 4 ( 32 5 1 ( 32, 52 2 5 Chapters 1–2 Cumulative Review Exercises For Exercises 1–5, perform the indicated operations. 1 5 7 10 ` 2 ` 5 233 14 724 1 1. 2. 32 1522 5 12 2 3 2b2 a1 3. 4. 16 5. 25 1202 32 4 For Exercises 6 and 7, translate the mathematical expressions and simplify the results. 6. The square root of the difference of five squared and nine 252 9; 4 7. The sum of and 12 14 14 12; 2 8. List the terms of the expression: 7x 7x2y, 4xy, 6 2y 4xy 6 9. Simplify: 432x 31x 424 51x 72 9x 13 For Exercises 10–15, solve the equations. 10. 8t 8 24 4 11. 2.5x 5.2 12.8 7.2 7 (y 9) (4y 9) y° Writing Translating Expression Geometry Scientific Calculator Video
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