11-4 Multiplying and Dividing Rational Expressions. Find each product. ANSWER: 4x ANSWER: ANSWER: ANSWER: 4(r 1)

Transcription

1 1. 2. Find each product. 4x c 2 d (x + 3) Find each product (r 1) 5. CCSS PRECISION The slowest land mammal is the three-toed sloth. It travels 0.07 mile per hour on the ground. What is this speed in feet per minute? 12. 5n 6.16 ft/min 6. EXERCISE One hour of moderate inline skating burns approximately 330 Calories. If Nelia plans to do inline skating for 3 hours a week, how many Calories will she burn in a year from the skating? 7. 51,480 Calories Find each quotient x 4 z 14. esolutions Manual - Powered by Cognero Page 1

2 (t + 2) k FINANCIAL LITERACY A scarf bought in Italy cost 18 Euros. The exchange rate at the time was 1 U.S. dollar = 0.73 Euro. a. How much did the scarf cost in U.S. dollars? b. If the exchange rate at the time was 1 Canadian dollar = 0.69 Euro, how much did the scarf cost in Canadian dollars? a. about $24.66 b. about $ ROLLER COASTERS A roller coaster has 6 trains. Each train has 3 cars, and each car seats 4 people. Write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time. 23. Find each quotient. ; 72 people 19. x 4 y 4n esolutions Manual - Powered by Cognero Page 2

3 SEWING The fabric that Megan wants to buy for a costume she is making costs $7.50 per yard. To the nearest tenth, how many meters can she buy with $24? (Hint: 1 inch 2.54 centimeters) 2.9 m 35. TRAVEL A plane flies 1250 kilometers at an average speed of 540 miles per hour. a. Write a product to find the number of hours it took for the plane to make the trip. Include the units. (Hint: 1 mile km) b. Find the number of hours to the nearest tenth. a. b. 1.4 h 36. VOLUNTEERING Tyree is passing out cups of orange drink from a 3.5-gallon cooler. If each cup of orange drink is 4.25 ounces, about how many cups can he hand out? (Hint: There are 128 ounces in a gallon.) about cups 37. LAND Louisiana loses about 30 square miles of land each year to coastal erosion, hurricanes, and other natural and human causes. Approximately how many square yards of land are lost per month? (Hint: Use 1 square mile = 3,097,600 square yards.) 7,744,000 yd 2 /mo GEOMETRY Write an expression to represent the length of the rectangle. 33. BEARS A grizzly bear runs 110 feet in 5 seconds. What is the average speed of the bear in miles per hour? 15 mi/h (x + 6)(x 3) Convert each rate. Round to the nearest tenth feet per second to miles per hour about 31.4 mi/h esolutions Manual - Powered by Cognero Page 3

4 meters per second to kilometers per hour km/h milliliters per second to cups per minute. (Hint: 1 liter quarts) 6.1 c/min meters per second to miles per hour. (Hint: 1 mile kilometers) 72.5 mi/h 43. LIFE SCIENCE A human heart pumps about a cup of blood each time it beats. On average, a person s heart beats about 70 times a minute. Write and simplify an expression to find how many gallons of blood are pumped per hour. 44. GEOMETRY Refer to the prism shown. a. Find the volume in cubic inches. b. Use the ratio to write a = gal/h multiplication expression to convert the volume to cubic feet. Then convert the volume. a in 3 b. ; ft CCSS PRECISION Find each product. Describe what the final answer represents. $7644/yr; Sample answer: earnings per year about $4.28/day; the average cost of gasoline per day about 71.6 mi/h; converting 32 meters per second to miles per hour about $15.38; converting yearly salary to hourly wage 49. SPACE The highest speed at which any spacecraft has ever escaped from Earth is 35,800 miles per hour by the New Horizons probe, which was launched in Convert this speed to feet per second. Round to the nearest tenth. about 52,506.7 ft/s 50. ELECTRICITY Simplify the expression below to find the cost of running a 3500-watt air conditioner for one week. $58.80 esolutions Manual - Powered by Cognero Page 4

5 51. AMUSEMENT PARKS In an amusement park ride, riders stand along the wall of a circular room with a radius of 3.1 meters. The room completes 27 rotations per minute. a. Write an expression for the number of meters the room moves per second. (Hint: The circumference of a circle is 2πr.) b. Simplify the expression you wrote in Part a and describe what it means. a. b. about 8.8 m/s; The room spins at a rate of 8.8 m/s. 52. AQUARIUMS An aquarium is a rectangular prism 30 inches long, 15 inches wide, and 18 inches high. a. Sketch and label a diagram of the aquarium. Then find the volume of the tank in cubic inches. b. Describe how to use the ratio to find the volume of the tank in cubic feet. Then find the volume. Round to the nearest tenth. c. Pure water weighs 62 pounds per cubic foot. How much would the water in the tank weigh if the tank were filled? d. A saltwater aquarium requires 2 pounds of minerals for each cubic foot of water. Find the percent concentration by weight of the saltwater by dividing the weight of the minerals by the sum of the weights of the minerals and the water. e. Kim accidentally added twice the required minerals. Find the percent concentration by weight. Is it twice the recommended concentration? Explain. a in 3 b. Sample answer: Multiply the volume in cubic inches by the ratio. about 4.7 ft 3 c. about lbs d % e. 6.06%; No, the numerator is doubled and the denominator is changed. 53. ERROR ANALYSIS Mei and Tamika are finding. Is either of them correct? Explain. Neither; Tamika did not multiply by the reciprocal, and Mei incorrectly factored out the 2 in 2x + 6. esolutions Manual - Powered by Cognero Page 5

6 54. REASONING Find the missing term. Justify your answer. 58. WRITE A QUESTION A classmate found that the product of two rational expressions is. She wants to find the excluded 55. CCSS PERSEVERANCE Find. Write in simplest form. 56. WRITING IN MATH Give an example and describe how you could use dimensional analysis to solve a real-world problem involving rational expressions. Sample answer: You can use dimensional analysis in situations that involve units of measure when dividing rational expressions. For example, to change 30 miles/hour to feet/second, multiply 57. OPEN ENDED Give an example of a real-world situation that could be modeled by the quotient of two rational expressions. Provide an example of this quotient. Sample answer: The height of a cylinder when you know an expression for the volume and radius; ; V = π(x 3 6x 2 + 9x), r = (x 3). values. Write a question to help her solve the problem. Sample answer: What values of x make the denominators that were multiplied equal to 0? 59. WRITING IN MATH Describe how to use dimensional analysis to find the number of hours in one year. Sample answer: Write ratios comparing the number of days in one year and the number of hours in one day. Then multiply the ratios: = 8760 hours. 60. GEOMETRY The perimeter of a rectangle is 30 inches. Its area is 54 square inches. Find the length of the longest side. A 6 inches B 9 inches C 12 inches D 30 inches B 61. Find. F G H J F esolutions Manual - Powered by Cognero Page 6

7 62. EXTENDED RESPONSE The weekly salaries of six employees at a fast food restaurant are $140, $220, $90, $180, $140, $200. a. What is the mean of the six salaries? b. What is the median of the six salaries? c. What is the mode of the six salaries? a. $ b. $160 c. $ Tito has three times as many CDs as Dasan. Dasan has two thirds as many CDs as Brant. Brant has 27 CDs. How many CDs does Tito have? A 54 B 32 C 27 D A Simplify each expression. State the excluded values of the variables. x 0, y 0 ; g 0, h 0 ; q 0, t y + 8; ; 3, ; 2, 1 Identify the asymptotes of each function. 70. x = 0, y = x = 0, y = x = 5, y = x = 3, y = 0 esolutions Manual - Powered by Cognero Page 7

8 x = 6, y = 7 x = 8, y = FORESTRY The number of board feet B that a log will yield can be estimated by using the formula (D 2 8D + 16), where D is the diameter in inches and L is the log length in feet. For logs that are 16 feet long, what diameter will yield approximately 256 board feet? 20 in. Find the degree of each polynomial a x 2 + 3x d 4 6c x 3 4z + 8xz 82. 3d 4 + 5d 3 4c DRIVING Tires should be kept within 2 pounds per square inch (psi) of the manufacturer s recommended tire pressure. If the recommendation for a tire is 30 psi, what is the range of acceptable pressures? {p 28 p 32} Factor each polynomial. 84. x 2 18x 40 (x + 2)(x 20) 85. x 2 5x + 6 (x 2)(x 3) 86. x 2 2x 24 (x + 4)(x 6) 87. 3x 2 + 7x 20 (x + 4)(3x 5) 88. 2x 2 + x 15 (x + 3)(2x 5) 89. 8x 2 4x 40 4(x + 2)(2x 5) 3 esolutions Manual - Powered by Cognero Page 8