Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
Simplify: (26y4)(1230y) .Simplify: (a) ( 12)2 (b) ( 15)2 .Simplify: (a) ( 16)2 (b) ( 20)2 .Simplify: (a) (611)(511) (b) (58)2 .Simplify: (a) (37)(107) (b) (46)2 .Simplify: (a) 2(35) (b) 3(218) .Simplify: (a) 6(2+6) (b) 7(1+14) .Simplify: (a) 6(1+36) (b) 12(3+24) .Simplify: (a) 8(258) (b) 14(2+42) .Simplify: (1+6)(36) .Simplify: (410)(2+10) .Simplify: (637)(3+47) .Simplify: (2311)(411) .Simplify: (537)(3+27) .Simplify: (638)(26+8) .Simplify: (65m)(2+3m) .Simplify: (10+3n)(15n) .Simplify: (a) (10+2)2 (b) (1+36)2 .Simplify: (a) (65)2 (b) (92 10)2 .Simplify: (2+5m)2 .Simplify: (34n)2 .Simplify: (23)(2+3) .Simplify: (1+5)(15) .Simplify: (325)(3+25) .Simplify: (4+57)(457) .In the following exercises, simplify. 233. (a) 28 (b) (33)(218)In the following exercises, simplify. 234. (a) 66 (b) (32)(232)In the following exercises, simplify. 235. (a) 714 (b) (48)(58)In the following exercises, simplify. 236. (a) 612 (b) (25)(210)In the following exercises, simplify. 237. (52)(36)In the following exercises, simplify. 238. (23)(46)In the following exercises, simplify. 239. (23)(318)In the following exercises, simplify. 240. (45)(510)In the following exercises, simplify. 241. (56)(12)In the following exercises, simplify. 242. (62)(10)In the following exercises, simplify. 243. (27)(214)In the following exercises, simplify. 244. (211)(422)In the following exercises, simplify. 245. (a) (15y)(15y3) (b) (2n2)(18n3)In the following exercises, simplify. 246. (a) (14x3)(7x3) (b) (3q2)(48q3)In the following exercises, simplify. 247. (a) (16y2)(8y4) (b) (11s6)(11s)In the following exercises, simplify. 248. (a) (8x3)(3x) (b) (7r)(7r8)In the following exercises, simplify. 249. (25b3)(415b)In the following exercises, simplify. 250. (38c5)(26c3)In the following exercises, simplify. 251. (63d3)(412d5)In the following exercises, simplify. 252. (25b3)(415b)In the following exercises, simplify. 253. (63d3)(412d5)In the following exercises, simplify. 254. (27z3)(314z8)In the following exercises, simplify. 255. (42k5)(332k6)In the following exercises, simplify. 256. (a) (7)2 (b) ( 15)2In the following exercises, simplify. 257. (a) ( 11)2 (b) ( 21)2In the following exercises, simplify. 258. (a) ( 19)2 (b) (5)2In the following exercises, simplify. 259. (a) ( 23)2 (b) (3)2In the following exercises, simplify. 260. (a) (411)(311) (b) (53)2In the following exercises, simplify. 261. (a) (213)(913) (b) (65)2In the following exercises, simplify. 262. (a) (312)(26) (b) (4 10)2In the following exercises, simplify. 263. (a) (75)(310) (b) (2 14)2In the following exercises, simplify. 264. (a) 3(43) (b) 2(46)In the following exercises, simplify. 265. (a) 4(611) (b) 2(512)In the following exercises, simplify. 266. (a) 5(37) (b) 3(415)In the following exercises, simplify. 267. (a) 7(211) (b) 7(614)In the following exercises, simplify. 268. (a) 7(5+27) (b) 5(10+18)In the following exercises, simplify. 269. (a) 11(8+411) (b) 3(12+27)In the following exercises, simplify. 270. (a) 11(3+411) (b) 3(1518)In the following exercises, simplify. 271. (a) 2(5+92) (b) 7(321)In the following exercises, simplify. 272. (8+3)(23)In the following exercises, simplify. 273. (7+3)(93)In the following exercises, simplify. 274. (82)(3+2)In the following exercises, simplify. 275. (92)(6+2)In the following exercises, simplify. 276. (37)(57)In the following exercises, simplify. 277. (57)(47)In the following exercises, simplify. 278. (1+310)(5210)In the following exercises, simplify. 279. (725)(4+95)In the following exercises, simplify. 280. (3+10)(3+210)In the following exercises, simplify. 281. (11+5)(11+65)In the following exercises, simplify. 282. (27511)(47+911)In the following exercises, simplify. 283. (46+713)(86313)In the following exercises, simplify. 284. (5u)(3+u)In the following exercises, simplify. 285. (9w)(2+w)In the following exercises, simplify. 286. (7+2m)(4+9m)In the following exercises, simplify. 287. (6+5n)(11+3n)In the following exercises, simplify. 288. (a) (3+5)2 (b) (253)2In the following exercises, simplify. 289. (a) (4+ 11)2 (b) (325)2In the following exercises, simplify. 290. (a) (96)2 (b) (10+37)2In the following exercises, simplify. 291. (a) (5 10)2 (b) (8+32)2In the following exercises, simplify. 292. (35)(3+5)In the following exercises, simplify. 293. (103)(10+3)In the following exercises, simplify. 294. (4+2)(42)In the following exercises, simplify. 295. (7+10)(710)In the following exercises, simplify. 296. (4+93)(493)In the following exercises, simplify. 297. (1+82)(182)In the following exercises, simplify. 298. (1255)(12+55)In the following exercises, simplify. 299. (943)(9+43)In the following exercises, simplify. 300. 321In the following exercises, simplify. 301. (46)(18)In the following exercises, simplify. 302. (5+7)(6+21)In the following exercises, simplify. 303. (57)(621)In the following exercises, simplify. 304. (42)(218)In the following exercises, simplify. 305. (35y3)(7y3)In the following exercises, simplify. 306. (412x5)(26x3)In the following exercises, simplify. 307. ( 29)2In the following exercises, simplify. 308. (417)(317)In the following exercises, simplify. 309. (4+17)(3+17)A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.An artist wants to make a small monument in the shape of a square base topped by a right triangle, as shown below. The square base will be adjacent to one leg of the triangle. The other leg of the triangle will measure 2 feet and the hypotenuse will be 5 feet. (a) Use the Pythagorean Theorem to find the length of a side of the square base. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the face of the square base.A square garden will be made with a stone border on one edge. If only 3+10 feet of stone are available, simplify (3+ 10)2 to determine the area of the largest such garden.A garden will be made so as to contain two square sections, one section with side length 5+6 yards and one section with side length 2+3 yards. Simplify (5+6)(2+3) to determine the total area of the garden.Suppose a third section will be added to the garden in the previous exercise. The third section is to have a width of 432 feet. Write an expression that gives the total area of the garden.(a) Explain why (n)2 is always positive, for n0 . (b) Explain why (n)2 is always negative, for n0 .Use the binomial square pattern to simplify (3+2)2 . Explain all your steps.Simplify: 328 .Simplify: 7515 .Simplify: 84010 .Simplify: 107520 .Simplify: 48108 .Simplify: 9654 .Simplify: 12r36r .Simplify: 14p92p5 .Simplify: 50s3128s .Simplify: 75q5108q .Simplify: 162x 10y22x6y6 .Simplify: 300m3n73m5n .Simplify: 53 .Simplify: 65 .Simplify: 525 .Simplify: 943 .Simplify: 718 .Simplify: 332 .Simplify: 327 .Simplify: 1050 .Simplify: 22+3 .Simplify: 55+3 .Simplify: 315 .Simplify: 246 .Simplify: 5x+2 .Simplify: 10y3 .Simplify:. p+2p2 .Simplify: q10q+10 .In the following exercises, simplify. 317. 276In the following exercises, simplify. 318. 5010In the following exercises, simplify. 319. 729In the following exercises, simplify. 320. 2436In the following exercises, simplify. 321. 2328In the following exercises, simplify. 322. 3+279In the following exercises, simplify. 323. 6+456In the following exercises, simplify. 324. 1020020In the following exercises, simplify. 325. 80125In the following exercises, simplify. 326. 72200In the following exercises, simplify. 327. 12872In the following exercises, simplify. 328. 4875In the following exercises, simplify. 329. (a) 8x62x2 (b) 200m598mIn the following exercises, simplify. 330. (a) 10y35y (b) 108n7243n3In the following exercises, simplify. 331. 75r3108rIn the following exercises, simplify. 332. 196q5484qIn the following exercises, simplify. 333. 108p5q234p3q6In the following exercises, simplify. 334. 98rs 102r3s4In the following exercises, simplify. 335. 320mn545m7n3In the following exercises, simplify. 336. 810c3d71000c5dIn the following exercises, simplify. 337. 9814In the following exercises, simplify. 338. 7218In the following exercises, simplify. 339. 5+12515In the following exercises, simplify. 340. 64512In the following exercises, simplify. 341. 96150In the following exercises, simplify. 342. 2863In the following exercises, simplify. 343. 26y72yIn the following exercises, simplify. 344. 15x33xIn the following exercises, simplify and rationalize the denominator. 345. 106In the following exercises, simplify and rationalize the denominator. 346. 83In the following exercises, simplify and rationalize the denominator. 347. 67In the following exercises, simplify and rationalize the denominator. 348. 45In the following exercises, simplify and rationalize the denominator. 349. 313In the following exercises, simplify and rationalize the denominator. 350. 1011In the following exercises, simplify and rationalize the denominator. 351. 10310In the following exercises, simplify and rationalize the denominator. 352. 252In the following exercises, simplify and rationalize the denominator. 353. 495In the following exercises, simplify and rationalize the denominator. 354. 927In the following exercises, simplify and rationalize the denominator. 355. 923In the following exercises, simplify and rationalize the denominator. 356. 836In the following exercises, simplify and rationalize the denominator. 357. 320In the following exercises, simplify and rationalize the denominator. 358. 427In the following exercises, simplify and rationalize the denominator. 359. 740In the following exercises, simplify and rationalize the denominator. 360. 845In the following exercises, simplify and rationalize the denominator. 361. 19175In the following exercises, simplify and rationalize the denominator. 362. 17192In the following exercises, simplify by rationalizing the denominator. 363. (a) 33+11 (b) 815In the following exercises, simplify by rationalizing the denominator. 364. (a) 44+7 (b) 726In the following exercises, simplify by rationalizing the denominator. 365. (a) 55+6 (b) 637In the following exercises, simplify by rationalizing the denominator. 366. (a) 66+5 (b) 5411In the following exercises, simplify by rationalizing the denominator. 367. 3m5In the following exercises, simplify by rationalizing the denominator. 368. 5n7In the following exercises, simplify by rationalizing the denominator. 369. 2x6In the following exercises, simplify by rationalizing the denominator. 370. 7y+3In the following exercises, simplify by rationalizing the denominator. 371. r+5r5In the following exercises, simplify by rationalizing the denominator. 372. s6s+6In the following exercises, simplify by rationalizing the denominator. 373. 150x2y66x4y2In the following exercises, simplify by rationalizing the denominator. 374. 80p3q5pq5In the following exercises, simplify by rationalizing the denominator. 375. 155In the following exercises, simplify by rationalizing the denominator. 376. 358In the following exercises, simplify by rationalizing the denominator. 377. 854In the following exercises, simplify by rationalizing the denominator. 378. 1220In the following exercises, simplify by rationalizing the denominator. 379. 35+5In the following exercises, simplify by rationalizing the denominator. 380. 2043In the following exercises, simplify by rationalizing the denominator. 381. 2x3In the following exercises, simplify by rationalizing the denominator. 382. 5y7In the following exercises, simplify by rationalizing the denominator. 383. x+8x8In the following exercises, simplify by rationalizing the denominator. 384. m3m+3A supply kit is dropped from an airplane flying at an altitude of 250 feet. Simplify 25016 to determine how many seconds it takes for the supply kit to reach the ground.A flare is dropped into the ocean from an airplane flying at an altitude of 1,200 feet. Simplify 120016 to determine how many seconds it takes for the flare to reach the ocean.(a) Simplify 273 and explain all your steps. (b) Simplify 275 and explain all your steps. (c) Why are the two methods of simplifying square roots different?(a) Approximate 12 by dividing 11.414 using long division without a calculator. (b) Rationalizing the denominator of 12 gives 22 . Approximate 22 by dividing 1.4142 using long division without a calculator. (c) Do you agree that rationalizing the denominator makes calculations easier? Why or why not?For the equation x+6=x : (a) Is x=2 a solution? (b) Is x=3 a solution?For the equation x+2=x : (a) Is x=2 a solution? (b) Is x=1 a solution?Solve: 3x5=5 .Solve: 4x+8=6 .Solve: 3m+25=0 .Solve: 10z+12=0 .Solve: 3p+3+3=5 .Solve: 5q+1+4=6 .Solve: 2r3+5=0 .Solve: 7s3+2=0 .Solve: x2+2=x .Solve: y5+5=y .Solve: m+9m+3=0 .Solve: n+1n+1=0 .Solve: 24a+216=16 .Solve: 36b+325=50 .Solve: 2x5=5x+3 .Solve: 7y+1=2y5 .Solve: x+3=x+5 .Solve: m+5=m+16 .Solve: y3+2=4y+2 .Solve: n4+5=3n+3 .Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of 370 square feet. Use the formula s=A to find the length of each side of her lawn. Round your answer to the nearest tenth of a foot.Sergio wants to make a square mosaic as an inlay for a table he is building. He has enough tile to cover an area of 2704 square centimeters. Use the formula s=A to find the length of each side of his mosaic. Round your answer to the nearest tenth of a foot.A helicopter dropped a rescue package from a height of 1,296 feet. Use the formula t=h4 to find how many seconds it took for the package to reach the ground.A window washer dropped a squeegee from a platform 196 feet above the sidewalk Use the formula t=h4 to find how many seconds it took for the squeegee to reach the sidewalk.An accident investigator measured the skid marks of the car. The length of the skid marks was 76 feet. Use the formula s=24d to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.The skid marks of a vehicle involved in an accident were 122 feet long. Use the formula s=24d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.In the following exercises, check whether the given values are solutions. 389. For the equation x+12=x : (a) Is x=4 a solution? (b) Is x=3 a solution?In the following exercises, check whether the given values are solutions. 390. For the equation y+20=y : (a) Is y=4 a solution? (b) Is y=5 a solution?In the following exercises, check whether the given values are solutions. 391. For the equation t+6=t : (a) Is t=2 a solution? (b) Is t=3 a solution?In the following exercises, check whether the given values are solutions. 392. For the equation u+42=u : (a) Is u=6 a solution? (b) Is u=7 a solution?In the following exercises, solve. 393. 5y+1=4In the following exercises, solve. 394. 7z+15=6In the following exercises, solve. 395. 5x6=8In the following exercises, solve. 396. 4x3=7In the following exercises, solve. 397. 2m35=0In the following exercises, solve. 398. 2n13=0In the following exercises, solve. 399. 6v210=0In the following exercises, solve. 400. 4u+26=0In the following exercises, solve. 401. 5q+34=0In the following exercises, solve. 402. 4m+2+2=6In the following exercises, solve. 403. 6n+1+4=8In the following exercises, solve. 404. 2u3+2=0In the following exercises, solve. 405. 5v2+5=0In the following exercises, solve. 406. 3z5+2=0In the following exercises, solve. 407. 2m+1+4=0In the following exercises, solve. 408. (a) u3+3=u (b) x+1x+1=0In the following exercises, solve. 409. (a) v10+10=v (b) y+4y+2=0In the following exercises, solve. 410. (a) r1r=1 (b) z+100z+10=0In the following exercises, solve. 411. (a) s8s=8 (b) w+25w+5=0In the following exercises, solve. 412. 32x320=7In the following exercises, solve. 413. 25x+18=0In the following exercises, solve. 414. 28r+18=2In the following exercises, solve. 415. 37y+110=8In the following exercises, solve. 416. 3u2=5u+1In the following exercises, solve. 417. 4v+3=v6In the following exercises, solve. 418. 8+2r=3r+10In the following exercises, solve. 419. 12c+6=104cIn the following exercises, solve. 420. (a) a+2=a+4 (b) b2+1=3b+2In the following exercises, solve. 421. (a) r+6=r+8 (b) s3+2=s+4In the following exercises, solve. 422. (a) u+1=u+4 (b) n5+4=3n+7In the following exercises, solve. 423. (a) x+10=x+2 (b) y2+2=2y+4In the following exercises, solve. 424. 2y+4+6=0In the following exercises, solve. 425. 8u+1+9=0In the following exercises, solve. 426. a+1=a+5In the following exercises, solve. 427. d2=d20In the following exercises, solve. 428. 6s+4=8s28In the following exercises, solve. 429. 9p+9=10p6In the following exercises, solve. Round approximations to one decimal place. 430. Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. Use the formula s=A to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.In the following exercises, solve. Round approximations to one decimal place. 431. Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. Use the formula s=A to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.In the following exercises, solve. Round approximations to one decimal place. 432. Gravity While putting up holiday decorations, Renee dropped a light bulb from the top of a 64 foot tall tree. Use the formula t=h4 to find how many seconds it took for the light bulb to reach the ground.In the following exercises, solve. Round approximations to one decimal place. 433. Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Use the formula t=h4 to find how many seconds it took for the flare to reach the water.In the following exercises, solve. Round approximations to one decimal place. 434. Gravity A hang glider dropped his cell phone from a height of 350 feet. Use the formula t=h4 to find how many seconds it took for the cell phone to reach the ground.In the following exercises, solve. Round approximations to one decimal place. 435. Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, 4000 feet above the Colorado River. Use the formula t=h4 to find how many seconds it took for the hammer to reach the river.In the following exercises, solve. Round approximations to one decimal place. 436. Accident investigation The skid marks for a car involved in an accident measured 54 feet. Use the formula s=24d to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.In the following exercises, solve. Round approximations to one decimal place. 437. Accident investigation The skid marks for a car involved in an accident measured 216 feet. Use the formula s=24d to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.In the following exercises, solve. Round approximations to one decimal place. 438. Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula s=24d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.In the following exercises, solve. Round approximations to one decimal place. 439. Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117 feet. Use the formula s=24d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.Explain why an equation of the form x+1=0 has no solution.(a) Solve the equation r+4r+2=0 . (b) Explain why one of the “solutions” that was found was not actually a solution to the equation.Simplify: (a) 273 (b) 2564 (c) 2435 .Simplify: (a) 10003 (b) 164 (c) 325 .Simplify: (a) 1253 (b) 164 (c) 325 .Simplify: (a) 2163 (b) 814 (c) 10245 .Simplify: (a) b2 (b) w33 (c) m44 (d) q55 .Simplify: (a) y2 (b) p33 (c) z44 (d) q55 .Simplify: (a) u124 (b) v153 .Simplify: (a) c205 (b) d246 .Simplify: (a) 27x273 (b) 81q284 .Simplify: (a) 125p93 (b) 243q255 .