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All Textbook Solutions for Intermediate Algebra

In the following exercises, answer each question. 282. 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 exercises, answer each question. 283. 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 exercises, answer each question. 284. The height of the Statue of Liberty is 305 feet. Nikia, 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?In the following exercises, solve the application problem provided. 285. 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 the application problem provided. 286. A private jet can fly 1,210 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 the application problem provided. 287. 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 the application problem provided. 288. 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 the application problem provided. 289. Jane spent 2 hours exploring a mountain with a dirt bike. First, she rode 40 miles uphill. After she reached the peak she rode for 12 miles along the summit. While going uphill, she went 5 mph slower than when she was on the summit. What was her rate along the summit?In the following exercises, solve the application problem provided. 290. Laney 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 the application problem provided. 291. Byron 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 the application problem provided. 292. 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 the application problem provided. 293. 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, what was his uphill rate?In the following exercises, solve the application problem provided. 294. 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 the application problem provided. 295. 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 the application problem provided. 296. 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 the application problem provided. 297. 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 the application problem provided. 298. 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 the application problem provided. 299. 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 the application problem provided. 300. 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 the application problem provided. 301. 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 the application problem provided. 302. 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 the application problem provided. 303. 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.In the following exercises, solve the application problem provided. 304. 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?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?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?Mia 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?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?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?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 Levi’s dad to wash the car by himself?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?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. 313. 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. 314. 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. 315. 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. 316. 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. 317. 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. 318. 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. 319. 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. 320. 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. 321. 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. 322. 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. 323. If y varies inversely with x and y=5 when x=4 , find the equation that relates x and y.In the following exercises, solve. 324. 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. 325. 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. 326. If a varies inversely with b and a=12 when b=13 , find the equation that relates a and b.In the following exercises, write an inverse variation equation to solve the following problems. 327. The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds getting 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?In the following exercises, write an inverse variation equation to solve the following problems. 328. 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?In the following exercises, write an inverse variation equation to solve the following problems. 329. The time required to empty a tank varies inversely as the rate of pumping. It took Ada 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 Ada to pump her basement if she used a pump rated at 400 gpm?In the following exercises, write an inverse variation equation to solve the following problems. 330. 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?In the following exercises, write an inverse variation equation to solve the following problems. 331. 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 four 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 Lori to have if she had brushed her teeth for 2 minutes each night?In the following exercises, write an inverse variation equation to solve the following problems. 332. 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?In the following exercises, write an inverse variation equation to solve the following problems. 333. The cost of a ride service varies directly with the distance traveled. 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?In the following exercises, write an inverse variation equation to solve the following problems. 334. 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?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 7.44.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.In your own words, explain the difference between direct variation and inverse variation.Make up an example from your life experience of inverse variation.Solve and write the solution in interval notation: x2x+40 .Solve and write the solution in interval notation: x+2x40 .Solve and write the solution in interval notation: 3xx31 .Solve and write the solution in interval notation: 3xx42 .Solve and write the solution in interval notation: 1x2+2x80 .Solve and write the solution in interval notation: 3x2+x120 .Solve and write the solution in interval notation: 12+4x23x .Solve and write the solution in interval notation: 13+6x23x .Given the function R(x)=x2x+4 , find the values of x that make the function less than or equal to 0.Given the function R(x)=x+1x4 , find the values of x that make the function less than or equal to 0.The function C(x)=20x+6000 represents the cost to produce x, number of items. Find ? the average cost function, c(x) ? how many items should be produced so that the average cost is less than $60?The function C(x)=5x+900 represents the cost to produce x, number of items. Find ? the average cost function, c(x) ? how many items should be produced so that the average cost is less than $20?In the following exercises, solve each rational inequality and write the solution in interval notation. 339. x3x+40 In the following exercises, solve each rational inequality and write the solution in interval notation. 340. x+6x50 In the following exercises, solve each rational inequality and write the solution in interval notation. 341. x+1x30 In the following exercises, solve each rational inequality and write the solution in interval notation. 342. x4x+20 In the following exercises, solve each rational inequality and write the solution in interval notation. 343. x7x10 In the following exercises, solve each rational inequality and write the solution in interval notation. 344. x+8x+30 In the following exercises, solve each rational inequality and write the solution in interval notation. 345. x6x+50 In the following exercises, solve each rational inequality and write the solution in interval notation. 346. x+5x20 In the following exercises, solve each rational inequality and write the solution in interval notation. 347. 3xx51 In the following exercises, solve each rational inequality and write the solution in interval notation. 348. 5xx21 In the following exercises, solve each rational inequality and write the solution in interval notation. 349. 6xx62 In the following exercises, solve each rational inequality and write the solution in interval notation. 350. 3xx42 In the following exercises, solve each rational inequality and write the solution in interval notation. 351. 2x+3x61 In the following exercises, solve each rational inequality and write the solution in interval notation. 352. 4x1x41 In the following exercises, solve each rational inequality and write the solution in interval notation. 353. 3x2x42 In the following exercises, solve each rational inequality and write the solution in interval notation. 354. 4x3x32 In the following exercises, solve each rational inequality and write the solution in interval notation. 355. 1x2+7x+120 In the following exercises, solve each rational inequality and write the solution in interval notation. 356. 1x24x120 In the following exercises, solve each rational inequality and write the solution in interval notation. 357. 3x25x+40 In the following exercises, solve each rational inequality and write the solution in interval notation. 358. 4x2+7x+120 In the following exercises, solve each rational inequality and write the solution in interval notation. 359. 22x2+x150 In the following exercises, solve each rational inequality and write the solution in interval notation. 360. 63x22x50 In the following exercises, solve each rational inequality and write the solution in interval notation. 361. 26x213x+60 In the following exercises, solve each rational inequality and write the solution in interval notation. 362. 110x2+11x60 In the following exercises, solve each rational inequality and write the solution in interval notation. 363. 1 2 + 12 x 2 5 x In the following exercises, solve each rational inequality and write the solution in interval notation. 364. 13+1x243x In the following exercises, solve each rational inequality and write the solution in interval notation. 365. 124x21x In the following exercises, solve each rational inequality and write the solution in interval notation. 366. 1232x21x In the following exercises, solve each rational inequality and write the solution in interval notation. 367. 1x2160 In the following exercises, solve each rational inequality and write the solution in interval notation. 368. 4x2250 In the following exercises, solve each rational inequality and write the solution in interval notation. 369. 4x23x+1 In the following exercises, solve each rational inequality and write the solution in interval notation. 370. 5x14x+2 In the following exercises, solve each rational function inequality and write the solution in interval notation. 371. Given the function R(x)=x5x2 , find the values of x that make the function less than or equal to 0.In the following exercises, solve each rational function inequality and write the solution in interval notation. 372. Given the function R(x)=x+1x+3 , find the values of x that make the function less than or equal to 0.In the following exercises, solve each rational function inequality and write the solution in interval notation. 373. Given the function R(x)=x6x+2 , find the values of x that make the function less than or equal to 0.In the following exercises, solve each rational function inequality and write the solution in interval notation. 374. Given the function R(x)=x+1x4 , find the values of x that make the function less than or equal to 0.Write the steps you would use to explain solving rational inequalities to your little brother.Create a rational inequality whose solution is (2][4,) .In the following exercises, determine the values for which the rational expression is undefined. 377. 5a+33a2 In the following exercises, determine the values for which the rational expression is undefined. 378. b7b225 In the following exercises, determine the values for which the rational expression is undefined. 379. 5x2y28y In the following exercises, determine the values for which the rational expression is undefined. 380. x3x2x30 In the following exercises, simplify. 381. 1824 In the following exercises, simplify. 382. 9m418mn3 In the following exercises, simplify. 383. x2+7x+12x2+8x+16 In the following exercises, simplify. 384. 7v3525v2 In the following exercises, multiply. 385. 58415 In the following exercises, multiply. 386. 3xy28y316y224x In the following exercises, multiply. 387. 72x12x28x+32x2+10x+24x236 In the following exercises, multiply. 388. 6y22y109y2y26y+96y2+2920 In the following exercises, divide. 389. x24x12x2+8x+12x2363x In the following exercises, divide. 390. y2164y3642y2+8y+32 In the following exercises, divide. 391. 11+ww9121w29w In the following exercises, divide. 392. 3y212y634y+3(6y242y)In the following exercises, divide. 393. c2643c2+26c+16c24c3215c+10 In the following exercises, divide. 394. 8a2+16aa4a2+2a24a2+7a+102a26aa+5 Find R(x)=f(x)g(x) where f(x)=9x2+9xx23x4 and g(x)=x2163x2+12x .Find R(x)=f(x)g(x) where f(x)=27x23x21 and g(x)=9x2+54xx2x42 .In the following exercises, perform the indicated operations. 397. 715+815 In the following exercises, perform the indicated operations. 398. 4a22a112a1 In the following exercises, perform the indicated operations. 399. y2+10yy+5+25y+5 In the following exercises, perform the indicated operations. 400. 7x2x29+21xx29 In the following exercises, perform the indicated operations. 401. x2x73x+28x7 In the following exercises, perform the indicated operations. 402. y2y+11121y+11 In the following exercises, perform the indicated operations. 403. 4q2q+3q2+6q+53q2q6q2+6q+5 In the following exercises, perform the indicated operations. 404. 5t+4t+3t2254t28t32t225 In the following exercises, add and subtract. 405. 18w6w1+3w216w In the following exercises, add and subtract. 406. a2+3aa243a84a2 In the following exercises, add and subtract. 407. 2b2+3b15b249b2+16b149b2 In the following exercises, add and subtract. 408. 8y210y+72y5+2y2+7y+252y In the following exercises, find the LCD. 409. 7a23a10,3aa2a20 In the following exercises, find the LCD. 410. 6n24,2nn24n+4 In the following exercises, find the LCD. 411. 53p2+17p6,2m3p223p8 In the following exercises, perform the indicated operations. 412. 75a+32b In the following exercises, perform the indicated operations. 413. 2c2+9c+3 In the following exercises, perform the indicated operations. 414. 3xx29+5x2+6x+9 In the following exercises, perform the indicated operations. 415. 2xx2+10x+24+3xx2+8x+16 In the following exercises, perform the indicated operations. 416. 5qp2qp2+4pq21 In the following exercises, perform the indicated operations. 417. 3yy+2y+2y+8 In the following exercises, perform the indicated operations. 418. 3w15w2+w20w+24w In the following exercises, perform the indicated operations. 419. 7m+3m+25 In the following exercises, perform the indicated operations. 420. nn+3+2n3n9n29 In the following exercises, perform the indicated operations. 421. 8aa2644a+8 In the following exercises, perform the indicated operations. 422. 512x2y+720xy3 In the following exercises, find R(x)=f(x)+g(x)where f(x)and g(x)are given. 423. f(x)=2x2+12x11x2+3x10,g(x)=x+12x In the following exercises, find R(x)=f(x)+g(x)where f(x)and g(x)are given. 424. f(x)=4x+31x2+x30,g(x)=5x+6 In the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 425. f(x)=4xx2121,g(x)=2x11 In the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 426. f(x)=7x+6,g(x)=14xx236 In the following exercises, simplify. 427. 7xx+214x2x24 In the following exercises, simplify. 428. 25+5613+14 In the following exercises, simplify. 429. x3xx+51x+5+1x5 In the following exercises, simplify. 430. 2m+mnnm1n In the following exercises, simplify. 431. 13+1814+112 In the following exercises, simplify. 432. 3a21b1a+1b2 In the following exercises, simplify. 433. 2z249+1z+79z+7+12z7 In the following exercises, simplify. 434. 3y24y322y8+1y+4 In the following exercises, solve. 435. 12+23=1x the following exercises, solve. 436. 12m=8m2 In the following exercises, solve. 437. 1b2+1b+2=3b24 In the following exercises, solve. 438. 3q+82q2=1 In the following exercises, solve. 439. v15v29v+18=4v3+2v6 In the following exercises, solve. 440. z12+z+33z=1z For rational function, f(x)=x+2x26x+8 , (a) find the domain of the function (b) solve f(x)=1 (c) find the points on the graph at this function value.For rational function, f(x)=2xx2+7x+10 (a) find the domain of the function (b) solve f(x)=2 (c) find the points on the graph at this function value.In the following exercises, solve for the indicated variable. 443. vl=hw for l.In the following exercises, solve for the indicated variable. 444. 1x2y=5 for y.In the following exercises, solve for the indicated variable. 445. x=y+5z7 for z.In the following exercises, solve for the indicated variable. 446. P=kv for V.In the following exercises, solve. 447. x4=35 In the following exercises, solve. 448. 3y=95 In the following exercises, solve. 449. ss+20=37 In the following exercises, solve. 450. t35=t+29 In the following exercises, solve. 451. 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. 452. 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. 453. 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. 454. 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. 455. Francesca is 5.75 feet tall. Late one afternoon, her 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. 456. The height of a lighthouse in Pensacola, Florida is 150 feet. Standing next to the statue, 5.5-foot-tall Natasha cast a 1.1-foot shadow. How long would the shadow of the lighthouse be?In the following exercises, solve. 457. When making the 5-hour drive home from visiting her parents, Lolo 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 when it turned bad. How fast did she drive when the weather was bad?In the following exercises, solve. 458. 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. 459. Josue can ride his bicycle 8 mph faster than Arjun can ride his bike. It takes Luke 3 hours longer than Josue to ride 48 miles. How fast can John ride his bike?In the following exercises, solve. 460. Curtis 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. 461. Brandy 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. 462. Prem 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. 463. 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. 464. Marta 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. 465. If y varies directly as x when y=9 and x=3 , find x when y=21 .In the following exercises, solve. 466. If y varies inversely as x when y=20 and x=2 , find y when x=4 .In the following exercises, solve. 467. 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. 468. 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. 469. 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. 470. If m varies inversely with the square of n, when m=4 and n=6 find mwhen n=2 .In the following exercises, solve. 471. 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. 472. 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, solve each rational inequality and write the solution in interval notation. 473. x3x+40 In the following exercises, solve each rational inequality and write the solution in interval notation. 474. 5xx21 In the following exercises, solve each rational inequality and write the solution in interval notation. 475. 3x2x42 In the following exercises, solve each rational inequality and write the solution in interval notation. 476. 1x24x120 In the following exercises, solve each rational inequality and write the solution in interval notation. 477. 124x21x In the following exercises, solve each rational inequality and write the solution in interval notation. 478. 4x23x+1 In the following exercises, solve each rational function inequality and write the solution in interval notation 479. Given the function, R(x)=x5x2 , find the values of x that make the function greater than or equal to 0.In the following exercises, solve each rational function inequality and write the solution in interval notation 480. Given the function, R(x)=x+1x+3 , find the values of x that make the function less than or equal to 0.In the following exercises, solve each rational function inequality and write the solution in interval notation 481. The function C(x)=150x+10,000 represents the cost to produce x, number of items. Find (a) the average cost function, c(x) (b) how many items should be produced so that the average cost is less than $160.In the following exercises, solve each rational function inequality and write the solution in interval notation 482. Tillman is starting his own business by selling tacos at the beach. Accounting for the cost of his food truck and ingredients for the tacos, the function C(x)=2x+6,000 represents the cost for Tillman to produce x, tacos. Find (a) the average cost function, c(x) for Tillman’s Tacos (b) how many tacos should Tillman produce so that the average cost is less than $4.In the following exercises, simplify. 483. 4a2b12ab2 In the following exercises, simplify. 484. 6x18x29 In the following exercises, perform the indicated operation and simplify. 485. 4xx+2x2+5x+612x2 In the following exercises, perform the indicated operation and simplify. 486. 2y2y21y3y2+yy31 In the following exercises, perform the indicated operation and simplify. 487. 6x2x+20x2815x2+11x7x281 In the following exercises, perform the indicated operation and simplify. 488. 3a3a3+5aa2+3a4 In the following exercises, perform the indicated operation and simplify. 489. 2n2+8n1n21n27n11n2 In the following exercises, perform the indicated operation and simplify. 490. 10x2+16x78x3+2x2+3x138x In the following exercises, perform the indicated operation and simplify. 491. 1m1n1n+1m In the following exercises, solve each equation. 492. 1x+34=58 In the following exercises, solve each equation. 493. 1z5+1z+5=1z225 In the following exercises, solve each equation. 494. z2z+834z8=3z216z168z2+2z64 In the following exercises, solve each rational inequality and write the solution in interval notation. 495. 6xx62 In the following exercises, solve each rational inequality and write the solution in interval notation. 496. 2x+3x61 In the following exercises, solve each rational inequality and write the solution in interval notation. 497.12+12x25x In the following exercises, find R(x)given f(x)=x4x23x10and g(x)=x5x22x8. 498.R(x)=f(x)g(x)In the following exercises, find R(x)given f(x)=x4x23x10and g(x)=x5x22x8. 499. R(x)=f(x)g(x)In the following exercises, find R(x)given f(x)=x4x23x10and g(x)=x5x22x8. 500. R(x)=f(x)g(x)In the following exercises, find R(x)given f(x)=x4x23x10and g(x)=x5x22x8. 501. Given the function, R(x)=22x2+x15 , find the values of x that make the function less than or equal to 0.In the following exercises, solve. 502. If y varies directly with x, and x=5 when y=30 , find x when y=42 .In the following exercises, solve. 503. 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. 504. Matheus 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 Matheus’ speed on his bike?In the following exercises, solve. 505. Oliver 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 Oliver’s dad working alone to split the logs?In the following exercises, solve. 506. 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. 507. The cities of Dayton, Columbus, and Cincinnati form a triangle in southern Ohio. The diagram 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) 64 (b) 225 .Simplify: (a) 100 (b) 121 .Simplify: (a) 169 (b) 81 .Simplify: (a) 49 (b) 121 .Simplify: (a) 273 (b) 2564 (c) 2435 .Simplify: (a) 10003 (b) 164 (c) 2435 .Simplify: (a) 273 (b) 2564 (c) 325 .Simplify: (a) 2163 (b) 814 (c) 10245 .Estimate each root between two consecutive whole numbers: (a) 38 (b) 933 Estimate each root between two consecutive whole numbers: (a) 84 (b) 1523 Round to two decimal places: (a) 11 (b) 713 (c) 1274 .Round to two decimal places: (a) 13 (b) 843 (c) 984 .Simplify:(a) b2 (b) w33 (c) m44 (d) q55 .Simplify:(a) y2 (b) p33 (c) z44 (d) q55 .Simplify: (a) y18 (b) z12 .Simplify: (a) m4 (b) b10 .Simplify: (a) u124 (b) v153 .Simplify: (a) c205 (b) d246 Simplify: (a) 64x2 (b) 100p2 .Simplify: (a) 169y2 (b) 121y2 .Simplify: (a) 27x273 (b) 81q284 .Simplify: (a) 125q93 (b) 243q255 .Simplify: (a) 100a2b2 (b) 144p12q20 (c) 8x30y123 .Simplify: (a) 225m2n2 (b) 169x10y14 (c) 27w36z153 .In the following exercises, simplify. 1. (a) 64 (b) 81 In the following exercises, simplify. 2. (a) 169 (b) 100 In the following exercises, simplify. 3. (a) 196 (b) 1 In the following exercises, simplify. 4. (a) 144 (b) 121 In the following exercises, simplify. 5. (a) 49 (b) 0.01 In the following exercises, simplify. 6. (a) 64121 (b) 0.16 In the following exercises, simplify. 7. (a) 121 (b) 289 In the following exercises, simplify. 8. (a) 400 (b) 36 In the following exercises, simplify. 9. (a) 225 (b) 9 In the following exercises, simplify. 10. (a) 49 (b) 256 In the following exercises, simplify. 11. (a) 2163 (b) 2564 In the following exercises, simplify. 12. (a) 273 (b) 164 (c) 2435 In the following exercises, simplify. 13. (a) 5123 (b) 814 (c) 15 In the following exercises, simplify. 14. (a) 1253 (b) 12964 (c) 10245 In the following exercises, simplify. 15. (a) 83 (b) 814 (c) 325 In the following exercises, simplify. 16. (a) 643 (b) 164 (c) 2435 In the following exercises, simplify. 17. (a) 1253 (b) 12964 (c) 10245 In the following exercises, simplify. 18. (a) 5123 (b) 814 (c) 15 In the following exercises, estimate each root between two consecutive whole numbers. 19. (a) 70 (b) 713 In the following exercises, estimate each root between two consecutive whole numbers. 20. (a) 55 (b) 1193 In the following exercises, estimate each root between two consecutive whole numbers. 21. (a) 200 (b) 1373 In the following exercises, estimate each root between two consecutive whole numbers. 22. (a) 172 (b) 2003 In the following exercises, approximate each root and round to two decimal places. 23. (a) 19 (b) 893 (c) 974 In the following exercises, approximate each root and round to two decimal places. 24. (a) 21 (b) 933 (c) 1014 In the following exercises, approximate each root and round to two decimal places. 25. (a) 53 (b) 1473 (c) 4524 In the following exercises, approximate each root and round to two decimal places. 26. (a) 47 (b) 1633 (c) 5274 In the following exercises, simplify using absolute values as necessary. 27. (a) u55 (b) v88 In the following exercises, simplify using absolute values as necessary. 28. (a) a33 (b) b99 In the following exercises, simplify using absolute values as necessary. 29. (a) y44 (b) m77 In the following exercises, simplify using absolute values as necessary. 30. (a) k88 (b) p66 In the following exercises, simplify using absolute values as necessary. 31. (a) x6 (b) y16 In the following exercises, simplify using absolute values as necessary. 32. (a) a14 (b) w24 In the following exercises, simplify using absolute values as necessary. 33. (a) x24 (b) y22 In the following exercises, simplify using absolute values as necessary. 34. (a) a12 (b) b26 In the following exercises, simplify using absolute values as necessary. 35. (a) x93 (b) y124 In the following exercises, simplify using absolute values as necessary. 36. (a) a105 (b) b273 In the following exercises, simplify using absolute values as necessary. 37. (a) m84 (b) n205 In the following exercises, simplify using absolute values as necessary. 38. (a) r126 (b) s303

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