Rational Function Operations Short Answer Simplify the given expression. 1. 2. 3. 4. 5. 6. 7. + 8. 19 + 9. – 10. – Find the LCM of the set of polynomials. 11. 12. , , , 13. If y varies directly as x and y = 9 when x = –3, find y when x = 18. 14. If y varies directly as x and y = 42 when x = 6, find y when x = 28. 15. Suppose y varies jointly as x and z. Find y when x = 5 and z = 6, if y = 144 when x = 6 and z = 10. 16. Suppose y varies jointly as x and z. Find y when x = 2 and z = 25, if y = 205 when x = 7 and z = 10. 17. If y varies inversely as x and y = 107 when x = –12, find y when x = 2. 18. If y varies inversely as x and y = 196 when x = 19, find y when x = 20. 19. Carl drove from his house to work at an average speed of 35 miles per hour. The drive took him 25 minutes. If the drive home took him 30 minutes and he used the same route in reverse, what was his average speed going home? In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day. 20. Write an equation to represent the amount of meat needed (m) to sustain x Siberian tigers for d days. 21. How much meat would seven Siberian tigers need for the month of April? It has been found that the average number of daily phone calls C between two cities is directly proportional to the product of the populations and between the cities. That is, C = of the two cities and inversely proportional to the square of the distance d . 22. The distance between Albany, New York, and Cleveland, Ohio, is about 480 miles. If the average number of daily phone calls between the cities is 250,000, find the value of k and write the equation of variation. Round to the nearest thousandth. The population of New York and Ohio is 95,000 and 2,900,000 respectively. 23. Can you use this formula to find the average number of phone calls between two adjoining cities? According to the website www.bottledwaterweb.com, the average American drinks about eight servings of hydrated beverages everyday. 24. Write an equation to represent the total servings of hydrated beverages consumed (w) by m household members during a period of d days. 25. A household of four members drinks the same amount of hydrated beverages each day as the average American. How many servings of hydrated beverages (w) would the members of the household consume in a week? 26. Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs the same distance at a speed of 8 miles per hour, what is the average time taken? 27. Many areas of Northern California depend on the snowpack of the Sierra Nevada Mountains for their water supply. If 300 cubic centimeters of snow will melt to 33 cubic centimeters of water, how much water does 600 cubic centimeters of snow produce? 28. Megan drove from her house to work at an average speed of 45 miles per hour. The drive took her 20 minutes. If the drive home took her 30 minutes and she used the same route in reverse, what was her average speed going home? Solve the given equation. 29. 30. 30 = + 13 Rational Function Operations Answer Section SHORT ANSWER 1. ANS: OBJ: 9-1.1 Multiply rational expressions. STA: NC 1.03 TOP: Multiply rational expressions. KEY: Rational Expressions | Multiply Rational Expressions 2. ANS: NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 OBJ: 9-1.1 Multiply rational expressions. STA: NC 1.03 TOP: Multiply rational expressions. KEY: Rational Expressions | Multiply Rational Expressions 3. ANS: NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 OBJ: 9-1.2 Divide rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Divide rational expressions. KEY: Rational Expressions | Divide Rational Expressions 4. ANS: OBJ: 9-1.2 Divide rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Divide rational expressions. KEY: Rational Expressions | Divide Rational Expressions 5. ANS: OBJ: 9-1.3 Simplify complex fractions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Simplify complex fractions. KEY: Complex Fractions 6. ANS: OBJ: 9-1.3 Simplify complex fractions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Simplify complex fractions. KEY: Complex Fractions 7. ANS: OBJ: 9-2.2 Add rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Add rational expressions. KEY: Rational Expressions | Add Rational Expressions 8. ANS: OBJ: 9-2.2 Add rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Add rational expressions. KEY: Rational Expressions | Add Rational Expressions 9. ANS: OBJ: 9-2.3 Subtract rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Subtract rational expressions. KEY: Rational Expressions | Subtract Rational Expressions 10. ANS: OBJ: 9-2.3 Subtract rational expressions. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Subtract rational expressions. KEY: Rational Expressions | Subtract Rational Expressions 11. ANS: OBJ: 9-2.1 Determine the LCM of polynomials. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Determine the LCM of polynomials. KEY: Polynomials | LCM 12. ANS: OBJ: 9-2.1 Determine the LCM of polynomials. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 TOP: Determine the LCM of polynomials. KEY: Polynomials | LCM 13. ANS: –54 OBJ: 9-4.1 Recognize and solve direct variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve direct variation problems. KEY: Direct Variation 14. ANS: 196 OBJ: 9-4.1 Recognize and solve direct variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve direct variation problems. KEY: Direct Variation 15. ANS: 72 OBJ: 9-4.2 Recognize and solve joint variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve joint variation problems. KEY: Joint Variation 16. ANS: 146 OBJ: 9-4.2 Recognize and solve joint variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve joint variation problems. KEY: Joint Variation 17. ANS: –642 OBJ: 9-4.3 Recognize and solve inverse variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve inverse variation problems. KEY: Inverse Variation 18. ANS: –186.2 OBJ: 9-4.3 Recognize and solve inverse variation problems. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Recognize and solve inverse variation problems. KEY: Inverse Variation 19. ANS: 29.17 miles per hour OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 20. ANS: m = 25xd OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 21. ANS: 5,250 pounds OBJ: NAT: TOP: KEY: 22. ANS: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a Solve real-world problems involving direct, inverse, and joint variation. Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 0.209 OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 23. ANS: No, as the distance between two adjoining cities is zero. OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 24. ANS: w = 8md OBJ: NAT: TOP: KEY: 25. ANS: 224 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a Solve real-world problems involving direct, inverse, and joint variation. Direct Variation | Joint Variation | Inverse Variation | Real-World Problems OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 26. ANS: 14.06 minutes OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 27. ANS: 66 cubic centimeters OBJ: 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a TOP: Solve real-world problems involving direct, inverse, and joint variation. KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems 28. ANS: 30 miles per hour OBJ: NAT: TOP: KEY: 29. ANS: 0.56 9-4.4 Solve real-world problems involving direct, inverse, and joint variation. NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NC 1.03 | NC 1.05 | NC 2.05a Solve real-world problems involving direct, inverse, and joint variation. Direct Variation | Joint Variation | Inverse Variation | Real-World Problems OBJ: 9-6.1 Solve rational equations. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Solve rational equations. KEY: Rational Equations | Solve Rational Equations 30. ANS: 0.12 OBJ: 9-6.1 Solve rational equations. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: NC 1.03 | NC 2.05a TOP: Solve rational equations. KEY: Rational Equations | Solve Rational Equations

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