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All Textbook Solutions for Elementary Algebra

In the following exercises, solve. 387. A veterinarian prescribed Sunny, a 65 pound dog, an antibacterial medicine in case an infection emerges after her teeth were cleaned. If the dosage is 5 mg for every pound, how much medicine was Sunny given?In the following exercises, solve.388. Belle, a 13 pound cat, is suffering from joint pain. How much medicine should the veterinarian prescribe if the dosage is 1.8 mg per pound?In the following exercises, solve. 389. A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink?In the following exercises, solve. 390. One 12 ounce can of soda has 150 calories. If Josiah drinks the big 32 ounce size from the local mini-mart, how many calories does he get?In the following exercises, solve. 391. A new 7 ounce lemon ice drink is advertised for having only 140 calories. How many ounces could Sally drink if she wanted to drink Just 100 calories?In the following exercises, solve. 392. Reese loves to drink healthy green smoothies. A 16 ounce serving of smoothie has 170 calories. Reese drinks 24 ounces of these smoothies in one day. How many calories of smoothie is he consuming in one day?In the following exercises, solve. 393. Janice is traveling to Canada and will change $250 US dollars into Canadian dollars. At the current exchange rate, $1 US is equal to $1.01 Canadian. How many Canadian dollars will she get for her trip?In the following exercises, solve. 394. Todd is traveling to Mexico and needs to exchange $450 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip?In the following exercises, solve. 395. Steve changed $600 into 480 Euros. How many Euros did he receive for each US dollar?In the following exercises, solve. 396. Martha changed $350 US into 385 Australian dollars. How many Australian dollars did she receive for each US dollar?In the following exercises, solve. 397. When traveling to Great Britain, Bethany exchanged her $900 into 570 British pounds. How many pounds did she receive for each American dollar?In the following exercises, solve. 398. A missionary commissioned to South Africa had to exchange his $500 for the South African Rand which is worth 12.63 for every dollar. How many Rand did he have after the exchange?In the following exercises, solve. 399. Ronald needs a morning breakfast drink that will give him at least 390 calories. Orange Juice has 130 calories in one cup. How many cups does he need to drink to reach his calorie goal?In the following exercises, solve. 400. Sarah drinks a 32-ounce energy drink containing 80 calories per 12 ounce. How many calories did she drink?In the following exercises, solve. 401. Elizabeth is returning to the United States from Canada. She changes the remaining 300 Canadian dollars she has to $230.05 in American dollars. What was $1 worth in Canadian dollars?In the following exercises, solve. 402. Ben needs to convert $1000 to the Japanese Yen. One American dollar is worth 123.3Yen. How much Yen will he have?In the following exercises, solve. 403. A golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds. How much medicine should he be given?In the following exercises, solve. 404. Five-year-old Lacy was stung by a bee. The dosage for the anti-itch liquid is 150 mg for her weight of 40 pounds. What is the dosage per pound?In the following exercises, solve. 405. Karen eats 12 cup of oatmeal that counts for 2 points on her weight loss program. Her husband, Joe, can have 3 points of oatmeal for breakfast. How much oatmeal can he have?In the following exercises, solve. 406. An oatmeal cookie recipe calls for 12 cup of butter to make 4 dozen cookies. Hilda needs to make 10 dozen cookies for the bake sale. How many cups of butter will she need?In the following exercises, ABC is similar to XYZ . Find the length of the indicated side. 407. side b In the following exercises, ABC is similar to XYZ . Find the length of the indicated side. 408. side x In the following exercises, DEF is similar to NPQ . 409. Find the length of side d.In the following exercises, DEF is similar to NPQ . 410. Find the length of side q.In the following two exercises, use the map shown. On the map, New York City, Chicago, and Memphis form a triangle whose sides are shown in the figure below. The actual distance from New York to Chicago is 800 miles. 411. Find the actual distance from New York to Memphis.In the following two exercises, use the map shown. On the map, New York City, Chicago, and Memphis form a triangle whose sides are shown in the figure below. The actual distance from New York to Chicago is 800 miles. 412. Find the actual distance from Chicago to Memphis.In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 413. Find the actual distance from New Orleans to Miami.In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 414. Find the actual distance from Atlanta to Miami.In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 415. A 2 foot tall dog casts a 3 foot shadow at the same time a cat casts a one foot shadow. How tall is the cat?In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 416. Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 417. The tower portion of a windmill is 212 feet tall. A six foot tall person standing next to the tower casts a seven foot shadow. How long is the windmill’s shadow?In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles. 418. The height of the Statue of Liberty is 305 feet. Nicole, who is standing next to the statue, casts a 6 foot shadow and she is 5 feet tall. How long should the shadow of the statue be?Heart Rate At the gym, Carol takes her pulse for 10 seconds and counts 19 beats. a. How many beats per minute is this? b. Has Carol met her target heart rate of 140 beats per minute?Heart Rate Kevin wants to keep his heart rate at 160 beats per minute while training. During his workout he counts 27 beats in 10 seconds. a. How many beats per minute is this? b. Has Kevin met his target heart rate?Cost of a Road Trip Jesse’s car gets 30 miles per gallon of gas. a. If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home? b. If gas is $3.09 per gallon, what is the total cost of the gas for the trip?Cost of a Road Trip Danny wants to drive to Phoenix to see his grandfather. Phoenix is 370 miles from Danny’s home and his car gets 18.5 miles per gallon. a. How many gallons of gas will Danny need to get to and from Phoenix? b. If gas is $3.19 per gallon, what is the total cost for the gas to drive to see his grandfather?Lawn Fertilizer Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 square feet. How many bags of fertilizer will he have to buy?House Paint April wants to paint the exterior of her house. One gallon of paint covers about 350 square feet, and the exterior of the house measures approximately 2000 square feet. How many gallons of paint will she have to buy?Cooking Natalia’s pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?Heating Oil A 275 gallon oil tank costs $400 to fill. How much would it cost to fill a 180 gallon oil tank?Marisol solves the proportion 144a=94 by ‘cross multiplying’, so her first step looks like 4144=9a. Explain how this differs from the method of solution shown in Example 8.72.Find a printed map and then write and solve an application problem similar to Example 8.79.Link can ride his bike 20 miles into a 3 mph headwind in the same amount of time he can ride 30 miles with a 3 mph tailwind. What is Link’s biking speed?Judy can sail her boat 5 miles into a 7 mph headwind in the same amount of time she can sail 12 miles with a 7 mph tailwind. What is the speed of Judy’s boat without a wind?Dennis went cross-country skiing for 6 hours on Saturday. He skied 20 mile uphill and then 20 miles back downhill, returning to his starting point. His uphill speed was 5 mph slower than his downhill speed. What was Dennis’ speed going uphill and his speed going downhill?Tony drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on country roads. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads?Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed. Find Kayla’s biking speed.Victoria jogs 12 miles to the park along a flat trail and then returns by jogging on an 18 mile hilly trail. She jogs 1 mile per hour slower on the hilly trail than on the flat trail, and her return trip takes her two hours longer. Find her rate of jogging on the flat trail.One gardener can mow a golf course in 4 hours, while another gardener can mow the same golf course in 6 hours. How long would it take if the two gardeners worked together to mow the golf course?Carrie can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them working together?Two hoses can fill a swimming pool in 10 hours. It would take one hose 26 hours to fill the pool by itself. How long would it take for the other hose, working alone, to fill the pool?Cara and Cindy, working together, can rake the yard in 4 hours. Working alone, it takes Cindy 6 hours to rake the yard. How long would it take Cara to rake the yard alone?In the following exercises, solve uniform motion applications 429. Mary takes a sightseeing tour on a helicopter that can fly 450 miles against a 35 mph headwind in the same amount of time it can travel 702 miles with a 35 mph tailwind. Find the speed of the helicopter.In the following exercises, solve uniform motion applications 430. A private jet can fly 1210 miles against a 25 mph headwind in the same amount of time it can fly 1694 miles with a 25 mph tailwind. Find the speed of the jet.In the following exercises, solve uniform motion applications 431. A boat travels 140 miles downstream in the same time as it travels 92 miles upstream. The speed of the current is 6mph. What is the speed of the boat?In the following exercises, solve uniform motion applications 432. Darrin can skateboard 2 miles against a 4 mph wind in the same amount of time he skateboards 6 miles with a 4 mph wind. Find the speed Darrin skateboards with no wind.In the following exercises, solve uniform motion applications 433. Jane spent 2 hours exploring a mountain with a dirt bike. When she rode the 40 miles uphill, she went 5 mph slower than when she reached the peak and rode for 12 miles along the summit. What was her rate along the summit?In the following exercises, solve uniform motion applications 434. Jill wanted to lose some weight so she planned a day of exercising. She spent a total of 2 hours riding her bike and jogging. She biked for 12 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than biking rate. What was her rate when jogging?In the following exercises, solve uniform motion applications 435. Bill wanted to try out different water craft. He went 62 miles downstream in a motor boat and 27 miles downstream on a jet ski. His speed on the jet ski was 10 mph faster than in the motor boat. Bill spent a total of 4 hours on the water. What was his rate of speed in the motor boat?In the following exercises, solve uniform motion applications 436. Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?In the following exercises, solve uniform motion applications 437. Chester rode his bike uphill 24 miles and then back downhill at 2 mph faster than his uphill. If it took him 2 hours longer to ride uphill than downhill, I, what was his uphill rate?In the following exercises, solve uniform motion applications 438. Matthew jogged to his friend’s house 12 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 25 mph slower than the rate when he was riding. What was his jogging rate?In the following exercises, solve uniform motion applications 439. Hudson travels 1080 miles in a jet and then 240 miles by car to get to a business meeting. The jet goes 300 mph faster than the rate of the car, and the car ride takes 1 hour longer than the jet. What is the speed of the car?In the following exercises, solve uniform motion applications 440. Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?In the following exercises, solve uniform motion applications 441. John can fly his airplane 2800 miles with a wind speed of 50 mph in the same time he can travel 2400 miles against the wind. If the speed of the wind is 50 mph, find the speed of his airplane.In the following exercises, solve uniform motion applications 442. Jim’s speedboat can travel 20 miles upstream against a 3 mph current in the same amount of time it travels 22 miles downstream with a 3 mph current speed. Find the speed of the Jim’s boat.In the following exercises, solve uniform motion applications 443. Hazel needs to get to her granddaughter’s house by taking an airplane and a rental car. She travels 900 miles by plane and 250 miles by car. The plane travels 250 mph faster than the car. If she drives the rental car for 2 hours more than she rode the plane, find the speed of the car.In the following exercises, solve uniform motion applications 444. Stu trained for 3 hours yesterday. He ran 14 miles and then biked 40 miles. His biking speed is 6 mph faster than his running speed. What is his running speed?In the following exercises, solve uniform motion applications 445. When driving the 9 hour trip home, Sharon drove 390 miles on the interstate and 150 miles on country roads. Her speed on the interstate was 15 more than on country roads. What was her speed on country roads?In the following exercises, solve uniform motion applications 446. Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?In the following exercises, solve work applications. 447. Mike, an experienced bricklayer, can build a wall in 3 hours, while his son, who is learning, can do the job in 6 hours. How long does it take for them to build a wall together?In the following exercises, solve work applications. 448. It takes Sam 4 hours to rake the front lawn while his brother, Dave, can rake the lawn in 2 hours. How long will it take them to rake the lawn working together?In the following exercises, solve work applications. 449. Mary can clean her apartment in 6 hours while her roommate can clean the apartment in 5 hours. If they work together, how long would it take them to clean the apartment?In the following exercises, solve work applications. 450. Brian can lay a slab of concrete in 6 hours, while Greg can do it in 4 hours. If Brian and Greg work together, how long will it take?In the following exercises, solve work applications. 451. Leeson can proofread a newspaper copy in 4 hours. If Ryan helps, they can do the job in 3 hours. How long would it take for Ryan to do his job alone?In the following exercises, solve work applications. 452. Paul can clean a classroom floor in 3 hours. When his assistant helps him, the job takes 2 hours. How long would it take the assistant to do it alone?In the following exercises, solve work applications. 453. Josephine can correct her students’ test papers in 5 hours, but if her teacher’s assistant helps, it would take them 3 hours. How long would it take the assistant to do it alone?In the following exercises, solve work applications. 454. Washing his dad’s car alone, eight year old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?In the following exercises, solve work applications. 455. Jackson can remove the shingles off of a house in 7 hours, while Martin can remove the shingles in 5 hours. How long will it take them to remove the shingles if they work together?In the following exercises, solve work applications. 456. At the end of the day Dodie can clean her hair salon in 15 minutes. Ann, who works with her, can clean the salon in 30 minutes. How long would it take them to clean the shop if they work together?In the following exercises, solve work applications. 457. Ronald can shovel the driveway in 4 hours, but if his brother Donald helps it would take 2 hours. How long would it take Donald to shovel the driveway alone?In the following exercises, solve work applications. 458. It takes Tina 3 hours to frost her holiday cookies, but if Candy helps her it takes 2 hours. How long would it take Candy to frost the holiday cookies by herself?Dana enjoys taking her dog for a walk, but sometimes her dog gets away and she has to run after him. Dana walked her dog for 7 miles but then had to run for 1 mile, spending a total time of 2.5 hours with her dog. Her running speed was 3 mph faster than her walking speed. Find her walking speed.Ken and Joe leave their apartment to go to a football game 45 miles away. Ken drives his car 30 mph faster Joe can ride his bike. If it takes Joe 2 hours longer than Ken to get to the game, what is Joe’s speed?In Example 8.83, the solution h=4 is crossed out. Explain why.Paula and Yuki are roommates. It takes Paula 3 hours to clean their apartment. It takes Yuki 4 hours to clean the apartment. The equation 13+14=1t can be used to find t, the number of hours it would take both of them, working together, to clean their apartment. Explain how this equation models the situation.If y varies directly as x and y=3 , when x=10 , find the equation that relates x and y.If y varies directly as x and y=12 when x=4 find the equation that relates x and y.The number of calories, c, burned varies directly with the amount of time, t, spent exercising. Arnold burned 312 calories in 65 minutes exercising. a. Write the equation that relates c and t. b. How many calories would he burn if he exercises for 90 minutes?The distance a moving body travels, d, varies directly with time, t, it moves. A train travels 100 miles in 2 hours a. Write the equation that relates d and t. b. How many miles would it travel in 5 hours?The distance that Brad travels varies directly with the time spent traveling. Brad travelled 660 miles in 12 hours, a. Write the equation that relates the number of miles travelled to the time. b. How many miles could Brad travel in 4 hours?The weight of a liquid varies directly as its volume. A liquid that weighs 24 pounds has a volume of 4 gallons. a. Write the equation that relates the weight to the volume. b. If a liquid has volume 13 gallons, what is its weight?The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds. a. Write the equation that relates the distance to the time. b. How far will an object fall in 4 seconds?The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square Inches. a. Write the equation that relates the area to the radius. b. What is the area of a pizza with a radius of 9 Inches?If p varies inversely with q and p=30 when q=12 find the equation that relates p and q.If y varies inversely with x and y=8 when x=2 find the equation that relates x and y.A car’s value varies inversely with its age. Elena bought a two-year-old car for $20,000. a. Write the equation of variation. b. What will be the value of Elena’s car when it is 5 years old?The time required to empty a pool varies inversely as the rate of pumping. It took Lucy 2.5 hours to empty her pool using a pump that was rated at 400 gpm (gallons per minute). a. Write the equation of variation. b. How long will it take her to empty the pool using a pump rated at 500 gpm?The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees. a. Write the equation of variation. b. How many hours would it take for the same block of ice to melt if the temperature was 78 degrees?The force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot long board. a. Write the equation of variation. b. How many pounds of pressure is needed to break a 5-foot long board?In the following exercises, solve. 463. If y varies directly as x and y=14 , when x=3 , find the equation that relates x and y.In the following exercises, solve. 464. If p varies directly as q and p=5 , when q=2 , find the equation that relates p and q.In the following exercises, solve. 465. If v varies directly as w and v = 24, when w = 8, find the equation that relates v and w.In the following exercises, solve. 466. If a varies directly as b and a=16 , when b=4 , find the equation that relates a and b.In the following exercises, solve. 467. If p varies directly as q and p=9.6 , when q=3 , find the equation that relates p and q.In the following exercises, solve. 468. If y varies directly as x and y=12.4 , when x=4 , find the equation that relates x and y In the following exercises, solve. 469. If a varies directly as b and a=6 , when b=13 , find the equation that relates a and b.In the following exercises, solve. 470. If V varies directly as w and v=8 , when w=12 , find the equation that relates v and w.In the following exercises, solve. 471. The amount of money Sally earns, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces she earns $150. a. Write the equation that relates P and n. b. How much money would she earn if she sold 4 necklaces?In the following exercises, solve. 472. The price, P, that Eric pays for gas varies directly with the number of gallons, g, he buys. It costs him $50 to buy 20 gallons of gas. a. Write the equation that relates P and g. b. How much would 33 gallons cost Eric?In the following exercises, solve. 473. Terri needs to make some pies for a fundraiser. The number of apples, a, varies directly with number of pies, p. It takes nine apples to make two pies. a. Write the equation that relates a and p. b. How many apples would Tern need for six pies?In the following exercises, solve. 474. Joseph is traveling on a road trip. The distance, d, he travels before stopping for lunch varies directly with the speed, v, he travels. He can travel 120 miles at a speed of 60 mph. a. Write the equation that relates d and v. b. How far would he travel before stopping for lunch at a rate of 65 mph?In the following exercises, solve. 475. The price of gas that Jesse purchased varies directly to how many gallons he purchased. He purchased 10 gallons of gas for $39.80. a. Write the equation that relates the price to the number of gallons. b. How much will it cost Jesse for 15 gallons of gas?In the following exercises, solve. 476. The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8 hours. a. Write the equation that relates the distance to the number of hours. b. How far can Sally travel in 6 hours?In the following exercises, solve. 477. The mass of a liquid varies directly with its volume. A liquid with mass 16 kilograms has a volume of 2 liters. a. Write the equation that relates the mass to the volume. b. What is the volume of this liquid if its mass is 128 kilograms?In the following exercises, solve. 478. The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10 pound watermelon on a hanging scale, the spring stretched 5 inches. a. Write the equation that relates the length of the spring to the weight. b. What weight of watermelon would stretch the spring 6 inches?In the following exercises, solve. 479. The distance an object falls varies directly to the square of the time it falls. A ball falls 45 feet in 3 seconds. a. Write the equation that relates the distance to the time. b. How far will the ball fall in 7 seconds?In the following exercises, solve. 480. The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds. a. Write the equation that relates the load to the diagonal of the cross-section. b. What load will a beam with a 10 inch diagonal support?In the following exercises, solve. 481. The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square inches. a. Write the equation that relates the area to the radius. b. What is the area of a personal pizza with a radius 4 inches?In the following exercises, solve. 482. The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds, a. Write the equation that relates the distance to the time. b. How far will the ball have fallen in 8 seconds?In the following exercises, solve. 483. If v varies inversely with x and y=5when x=4 find the equation that relates x and y.In the following exercises, solve. 484. If p varies inversely with q and p=2 when q=1 find the equation that relates p and q.In the following exercises, solve. 485. If v varies inversely with w and v=6 when w=12 find the equation that relates v and w.In the following exercises, solve. 486. If a varies inversely with b and a=12 when b=13 find the equation that relates a and b.Write an inverse variation equation to solve the following problems. 487. The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds and gets 33 mpg on the highway. a. Write the equation that relates the mpg to the car’s weight. b. What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?Write an inverse variation equation to solve the following problems. 488. A car’s value varies inversely with its age. Jackie bought a 10 year old car for $2,400. a. Write the equation that relates the car’s value to its age. b. What will be the value of Jackie’s car when it is 15 years old?Write an inverse variation equation to solve the following problems. 489. The time required to empty a tank varies inversely as the rate of pumping. It took Janet 5 hours to pump her flooded basement using a pump that was rated at 200 gpm (gallons per minute), a. Write the equation that relates the number of hours to the pump rate. b. How long would it take Janet to pump her basement if she used a pump rated at 400 gpm?Write an inverse variation equation to solve the following problems. 490. The volume of a gas in a container varies inversely as pressure on the gas. A container of helium has a volume of 370 cubic inches under a pressure of 15 psi. a. Write the equation that relates the volume to the pressure. b. What would be the volume of this gas if the pressure was increased to 20 psi?Write an inverse variation equation to solve the following problems. 491. On a string instrument, the length of a string varies inversely as the frequency of its vibrations. An 11-inch string on a violin has a frequency of 400 cycles per second. a. Write the equation that relates the string length to its frequency. b. What is the frequency of a 10-inch string?Write an inverse variation equation to solve the following problems. 492. Paul, a dentist, determined that the number of cavities that develops in his patient’s mouth each year varies inversely to the number of minutes spent brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds (0.5 minutes) each night. a. Write the equation that relates the number of cavities to the time spent brushing. b. How many cavities would Paul expect Lon to have if she had brushed her teeth for 2 minutes each night?Write an inverse variation equation to solve the following problems. 493. The number of tickets for a sports fundraiser varies inversely to the price of each ticket. Brianna can buy 25 tickets at $5each. a. Write the equation that relates the number of tickets to the price of each ticket. b. How many tickets could Brianna buy if the price of each ticket was $2.50?Write an inverse variation equation to solve the following problems. 494. Boyle’s Law states that if the temperature of a gas stays constant, then the pressure varies inversely to the volume of the gas. Braydon, a scuba diver, has a tank that holds 6 liters of air under a pressure of 220 psi. a. Write the equation that relates pressure to volume. b. If the pressure increases to 330 psi, how much air can Braydon’s tank hold?If y varies directly as x and y=5, when x=3 ., find the equation that relates x and y.If v varies directly as w and v=21 , when w=8 . find the equation that relates v and w.If p vanes inversely with q and p=5when q=6 , find the equation that relates p and q.If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.If p varies directly as q and p=10 , when q=2 . find the equation that relates p and q.If v varies inversely with w and v=18 when w=13 find the equation that relates v and w.The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1 .5-foot long board, how many pounds of pressure would he need to use to break a 6 foot long board?The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours when the temperature is 54 degrees. How long would it take for the same block of Ice to melt if the temperature was 45 degrees?The length a spring stretches varies directly with a weight placed at the end of the spring. When Meredith placed a 6-pound cantaloupe on a hanging scale, the spring stretched 2 inches. How far would the spring stretch if the cantaloupe weighed 9 pounds?The amount that June gets paid varies directly the number of hours she works. When she worked 15 hours, she got paid $111. How much will she be paid for working 18 hours?The fuel consumption (mpg) of a car varies inversely with its weight. A Ford Focus weighs 3000 pounds and gets 28.7 mpg on the highway. What would the fuel consumption be for a Ford Expedition that weighs 5,500 pounds? Round to the nearest tenth.The volume of a gas in a container varies inversely as the pressure on the gas. If a container of argon has a volume of 336 cubic inches under a pressure of 2,500 psi, what will be its volume if the pressure is decreased to 2,000 psi?The distance an object falls varies directly to the square of the time it falls. If an object falls 52.8 feet in 4 seconds, how far will it fall in 9 seconds?The area of the face of a Ferris wheel varies directly with the square of its radius. If the area of one face of a Ferris wheel with diameter 150 feet is 70,650 square feet, what is the area of one face of a Ferris wheel with diameter of 16 feet?Ride Service It costs $35 for a ride from the city center to the airport, 14 miles away. a. Write the equation that relates the cost, c, with the number of miles, m. b. What would it cost to travel 22 miles with this service?Road Trip The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his average driving speed. When he drives at an average speed of 40 miles per hour, it takes him 6 hours for the trip. a. Write the equation that relates the number of hours, h, with the speed, s. b. How long would the trip take if his average speed was 75 miles per hour?In your own words, explain the difference between direct variation and inverse variation.Make up an example from your life experience of inverse variation.In the following exercises, determine the values for which the rational expression is undefined. 513. 2a+13a2 In the following exercises, determine the values for which the rational expression is undefined. 514. b3b216 In the following exercises, determine the values for which the rational expression is undefined. 515. 3xy25y In the following exercises, determine the values for which the rational expression is undefined. 516. u3y2u30 In the following exercises, evaluate the rational expressions for the given values. 517. 4p1p2+5 when p=1 In the following exercises, evaluate the rational expressions for the given values. 518. q25q+3 when q=7 In the following exercises, evaluate the rational expressions for the given values. 519. y28y2y2 when y=1 In the following exercises, evaluate the rational expressions for the given values. 520. z2+z4zz2 when z=3 In the following exercises, simplify. 521. 1024 In the following exercises, simplify. 522. 8m416mn3 In the following exercises, simplify. 523. 14a14a1 In the following exercises, simplify. 524. b2+7b+12b2+8b+16 In the following exercises, simplify. 525. c2c24c2 In the following exercises, simplify. 526. d1616d In the following exercises, simplify. 527. 7v3525v2 In the following exercises, simplify. 528. w23w2849w2 In the following exercises, multiply. 529. 38215 In the following exercises, multiply. 530. 2xy28y316y24x In the following exercises, multiply. 531. 3a2+21aa2+6a7a1ab In the following exercises, multiply. 532. 5z25z2+40z+35z213z In the following exercises, divide. 533. t24t+12t2+8t+12t2366t In the following exercises, divide. 534. r2164r3642r28r+32 In the following exercises, divide. 535. 11+ww9121w29w In the following exercises, divide. 536. 3y212y634y+3(6y242y)In the following exercises, divide. 537. c2643c2+26c+16c24c3215c+10 In the following exercises, divide. 538. 8m28mm4m2+2m24m2+7m+102m26mm+5 In the following exercises, add. 539. 35+25 In the following exercises, add. 540. 4a22a112a1 In the following exercises, add. 541. p2+10pp+5+25p+5 In the following exercises, add. 542. 3xx1+2x1 In the following exercises, subtract. 543. d2d+43d+28d+4 In the following exercises, subtract. 544. z2z+10100z+10 In the following exercises, subtract. 545. 4q2q+3q2+6q+53q2q6q2+6q+5 In the following exercises, subtract. 546. 5t+4t+3t2254t28t32t225 In the following exercises, add and subtract. 547. 18w6w1+3w216w In the following exercises, add and subtract. 548. a2+3aa243a84a2 In the following exercises, add and subtract. 549. 2b2+3b15b249b2+16b149b2 In the following exercises, add and subtract. 550. 8y210y+72y5+2y2+7y+252y In the following exercises, find the LCD. 551. 4m23m10,2mm2m20 In the following exercises, find the LCD. 552. 6n24,2nn24n+4 In the following exercises, find the LCD. 553. 53p2+17p6,2m3p223p8 In the following exercises, rewrite as equivalent rational expressions with the given denominator. 554. Rewrite as equivalent rational expressions with denominator (m+2)(m5)(m+4) : 4m23m10,2mm2m20.In the following exercises, rewrite as equivalent rational expressions with the given denominator. 555. Rewrite as equivalent rational expressions with denominator (n2)(n2)(n+2) : 6n24n+4,2nn24.In the following exercises, rewrite as equivalent rational expressions with the given denominator. 556. Rewrite as equivalent rational expressions with denominator (3p+1)(p+6)(p+8) : 53p2+19p+6,7p3p2+25p+8.In the following exercises, add. 557. 23+35 In the following exercises, add. 558. 75a+32b In the following exercises, add. 559. 2c2+9c+3 In the following exercises, add. 560. 3dd29+5d2+6d+9 In the following exercises, add. 561. 2xx2+10x+24+3xx2+8x+16 In the following exercises, add. 562. 5qp2qp2+4qq21 In the following exercises, subtract and add. 563. 3vv+2v+2v+8 In the following exercises, subtract and add. 564. 3w15w2+w20w+24w In the following exercises, subtract and add. 565. 7m+3m+25 In the following exercises, subtract and add. 566. nn+3+2n3n9n29 In the following exercises, subtract and add. 567. 8dd2644d+8 In the following exercises, subtract and add. 568. 512x2y+720xy3 In the following exercises, simplify. 569. 5a+210a2a24 In the following exercises, simplify. 570. 25+5613+14 In the following exercises, simplify. 571. x3xx+51x+5+1x5 In the following exercises, simplify. 572. 2m+mnnm1n In the following exercises, simplify. 573. 6+2q45q+4 In the following exercises, simplify. 574. 3a21b1a+1b2 In the following exercises, simplify. 575. 2z249+1z+79z+7+12z7 In the following exercises, simplify. 576. 3y24y322y8+1y+4 In the following exercises, solve. 577. 12+23=1x In the following exercises, solve. 578. 12m=8m2 In the following exercises, solve. 579. 1b2+1b+2=3b24 In the following exercises, solve. 580. 3q+82q2=1 In the following exercises, solve. 581. v15v29v+18=4v3+2v6 In the following exercises, solve. 582. z12+z+33z=1z In the following exercises, solve for the indicated variable. 583. vl=hw for l In the following exercises, solve for the indicated variable. 584. 1x2y=5 for y In the following exercises, solve for the indicated variable. 585. x=y+5z7 for z In the following exercises, solve for the indicated variable. 586. P=kV for V In the following exercises, solve. 587. x4=35 In the following exercises, solve. 588. 3y=95 In the following exercises, solve. 589. ss+20=37 In the following exercises, solve. 590. t35=t+29 In the following exercises, solve using proportions. 591. Rachael had a 21 ounce strawberry shake that has 739 calories. How many calories are there in a 32 ounce shake?In the following exercises, solve using proportions. 592. Leo went to Mexico over Christmas break and changed $525 dollars into Mexican pesos. At that time, the exchange rate had $1 US is equal to 16.25 Mexican pesos. How many Mexican pesos did he get for his trip?In the following exercises, solve. 593. ABC is similar to XYZ. The lengths of two sides of each triangle are given in the figure. Find the lengths of the third sides.In the following exercises, solve. 594. On a map of Europe, Paris, Rome, and Vienna form a triangle whose sides are shown in the figure below. If the actual distance from Rome to Vienna is 700 miles, find the distance from (a) Paris to Rome (b) Paris to Vienna In the following exercises, solve. 595. Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 feet long. Find the height of the tree.In the following exercises, solve. 596. The height of a lighthouse in Pensacola, Florida is 150 feet. Standing next to the statue, 5.5 foot tall Natalie cast a 1.1 foot shadow How long would the shadow of the lighthouse be?In the following exercises, solve. 597. When making the 5-hour drive home from visiting her parents, Lisa ran into bad weather. She was able to drive 176 miles while the weather was good, but then driving 10 mph slower, went 81 miles in the bad weather. How fast did she drive when the weather was bad?In the following exercises, solve. 598. Mark is riding on a plane that can fly 490 miles with a tailwind of 20 mph in the same time that it can fly 350 miles against a tailwind of 20 mph. What is the speed of the plane?In the following exercises, solve. 599. John can ride his bicycle 8 mph faster than Luke can ride his bike. It takes Luke 3 hours longer than John to ride 48 miles. How fast can John ride his bike?In the following exercises, solve. 600. Mark was training for a triathlon. He ran 8 kilometers and biked 32 kilometers in a total of 3 hours. His running speed was 8 kilometers per hour less than his biking speed. What was his running speed?In the following exercises, solve. 601. Jerry can frame a room in 1 hour, while Jake takes 4 hours. How long could they frame a room working together?In the following exercises, solve. 602. Lisa takes 3 hours to mow the lawn while her cousin, Barb, takes 2 hours. How long will it take them working together?In the following exercises, solve. 603. Jeffrey can paint a house in 6 days, but if he gets a helper he can do it in 4 days. How long would it take the helper to paint the house alone?In the following exercises, solve. 604. Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone it would take her 120 days. How long would it take Deb to write the book alone?In the following exercises, solve. 605. If y varies directly as x, when y=9 and x=3 , find x when y=21 .In the following exercises, solve. 606. If y varies inversely as x, when y=20 and x=2 find y when x=4 .In the following exercises, solve. 607. If m varies inversely with the square of n , when m=4 and n=6 find m when n=2 .In the following exercises, solve. 608. Vanessa is traveling to see her fiancé. The distance, d, varies directly with the speed, v, she drives. If she travels 258 miles driving 60 mph, how far would she travel going 70 mph?In the following exercises, solve. 609. If the cost of a pizza varies directly with its diameter, and if an 8” diameter pizza costs $12, how much would a 6” diameter pizza cost?In the following exercises, solve. 610. The distance to stop a car varies directly with the square of its speed. It takes 200 feet to stop a car going 50 mph. How many feet would it take to stop a car going 60 mph?In the following exercises, solve. 611. The number of tickets for a music fundraiser varies inversely with the price of the tickets. If Madelyn has just enough money to purchase 12 tickets for $6, how many tickets can Madelyn afford to buy if the price increased to $8?In the following exercises, solve. 612. On a string instrument, the length of a string varies inversely with the frequency of its vibrations. If an 11-inch string on a violin has a frequency of 360 cycles per second, what frequency does a 12 inch string have?In the following exercises, simplify. 613. 3a2b6ab2 In the following exercises, simplify. 614. 5b25b225 In the following exercises, perform the indicated operation and simplify. 615. 4xx+2x2+5x+612x2 In the following exercises, perform the indicated operation and simplify. 616. 5y4y8y2410 In the following exercises, perform the indicated operation and simplify. 617. 4pq+5p In the following exercises, perform the indicated operation and simplify. 618. 1z93z+9 In the following exercises, perform the indicated operation and simplify. 619. 23+3525 In the following exercises, perform the indicated operation and simplify. 620. 1m1n1n+1m In the following exercises, solve each equation. 621. 12+27=1x In the following exercises, solve each equation. 622. 5y6=3y+6 In the following exercises, solve each equation. 623. 1z5+1z+5=1z225 In the following exercises, solve each equation. 624. t4=35 In the following exercises, solve each equation. 625. 2r2=3r1 In the following exercises, solve. 626. If y varies directly with x, and x=5 when y=30 , find x when y=42 .In the following exercises, solve. 627. If y varies inversely with x and x=6 when y=20 , find y when x=2 .In the following exercises, solve. 628. If y varies inversely with the square of x and x=3 when y=9 , find y when x=4 .In the following exercises, solve. 629. The recommended erythromycin dosage for dogs, is 5 mg for every pound the dog weighs. If Daisy weighs 25 pounds, how many milligrams of erythromycin should her veterinarian prescribe?In the following exercises, solve each equation. 630. Julia spent 4 hours Sunday afternoon exercising at the gym. She ran on the treadmill for 10 miles and then biked for 20 miles. Her biking speed was 5 mph faster than her running speed on the treadmill. What was her running speed?In the following exercises, solve. 631. Kurt can ride his bike for 30 miles with the wind in the same amount of time that he can go 21 miles against the wind. If the wind’s speed is 6 mph, what is Kurt’s speed on his bike?In the following exercises, solve. 632. Amanda jogs to the park 8 miles using one route and then returns via a 14-mile route. The return trip takes her 1 hour longer than her jog to the park. Find her jogging rate.In the following exercises, solve. 633. An experienced window washer can wash all the windows in Mike’s house in 2 hours, while a new trainee can wash all the windows in 7 hours. How long would it take them working together?In the following exercises, solve. 634. Josh can split a truckload of logs in 8 hours, but working with his dad they can get it done in 3 hours. How long would it take Josh’s dad working alone to split the logs?In the following exercises, solve. 635. The price that Tyler pays for gas varies directly with the number of gallons he buys. If 24 gallons cost him $59.76, what would 30 gallons cost?In the following exercises, solve. 636. The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number.In the following exercises, solve. 637. The cities of Dayton, Columbus, and Cincinnati form a triangle in southern Ohio, as shown on the figure below, that gives the map distances between these cities in inches. The actual distance from Dayton to Cincinnati is 48 miles. What is the actual distance between Dayton and Columbus?Simplify: (a) 149 (b) 225 .Simplify: (a) 64 (b) 121 .Simplify: (a) 196 (b) 81 .Simplify: (a) 49 (b) 121 .Simplify: (a) 9+16 (b) 9+16 .Simplify: (a) 64+225 (b) 64+225 .Estimate the square root 38 between two consecutive whole numbers.Estimate the square root 84 between two consecutive whole numbers.Round 11 to two decimal places.Round 13 to two decimal places.Simplify: (a) y8 (b) z12 .Simplify: (a) m4 (b) b10 .Simplify: 64x2 .Simplify: 169y2 .Simplify: 121y2 .Simplify: 100p2 .Simplify: 100a2b2 .Simplify: 225m2n2 .Simplify: 49x30 .Simplify: 81w36 .Simplify: 169x10y14 .Simplify: 144p12q20 .In the following exercises, simplify. 1. 36 In the following exercises, simplify. 2. 4 In the following exercises, simplify. 3. 64

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