Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
In the following exercises, simplify. 253. a. 320mn 545m 7n3 b. 16x4y 2354x 2y43In the following exercises, simplify. 254. a. 810c 3d71000cd 1 b. 24a7b 1381a 2b23In the following exercises, simplify. 255. 56x5y42xy3In the following exercises, simplify. 256. 72a3b63ab3In the following exercises, simplify. 257. 48a3b633a 1b33In the following exercises, simplify. 258. 162x 3y632x3y 23In the following exercises, rationalize the denominator. a. 106 b. 427 c. 105xIn the following exercises, rationalize the denominator. 260. a. 83 b. 740 c. 82yIn the following exercises, rationalize the denominator. 261. a. 67 b. 845 c. 123pIn the following exercises, rationalize the denominator. 262. a. 45 b. 2780 c. 186qIn the following exercises, rationalize the denominator. 263. a. 153 b. 5243 c. 436a3In the following exercises, rationalize the denominator. 264. a. 133 b. 5323 c. 749b3In the following exercises, rationalize the denominator. 265. a. 1113 b. 7543 c. 33x23In the following exercises, rationalize the denominator. 266. a. 1133 b. 31283 c. 36y23In the following exercises, rationalize the denominator. 267. a. 174 b. 5324 c. 44x24In the following exercises, rationalize the denominator. 268. a. 144 b. 9324 c. 69x34In the following exercises, rationalize the denominator. 269. a. 194 b. 251284 c. 627a4In the following exercises, rationalize the denominator. 270. a. 184 b. 271284 c. 1664b24In the following exercises, simplify. 271. 815In the following exercises, simplify. 272. 726In the following exercises, simplify. 273. 637In the following exercises, simplify. 274. 5411In the following exercises, simplify. 275. 3m5In the following exercises, simplify. 276. 5n7In the following exercises, simplify. 277. 2x6In the following exercises, simplify. 278. 7y+3In the following exercises, simplify. 279. r+5r5In the following exercises, simplify. 280. s6s+6In the following exercises, simplify. 281. x+8x8In the following exercises, simplify. 282. m3m+3a. 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?Explain what is meant by the word rationalize in the phrase, "rationalize a denominator."Explain why multiplying 2x3 by its conjugate results in an expression with no radicals.Explain why multiplying 7x3 by x3x3 does not rationalize the denominator.Solve: 3m+25=0.Solve: 10z+12=0.Solve: 2r3+5=0.Solve: 7s3+2=0.Solve: x2+2=x.Solve: y5+5=y.Solve: 4x33+8=5Solve: 6x103+1=3Solve: (9x+9)142=1.Solve: (4x8)14+5=7.Solve: m+9m+3=0.Solve: n+1n+1=0.Solve: 24a+416=16.Solve: 32b+325=50.Solve: 5x43=2x+53.Solve: 7x+13=2x53.Solve: 3x=x3.Solve: x+2=x+16.Solve: x1+2=2x+6Solve: x+2=3x+4A 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 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, solve. 287. 5x6=8In the following exercises, solve. 288. 4x3=7In the following exercises, solve. 289. 5x+1=3In the following exercises, solve. 290. 3y4=2In the following exercises, solve. 291. 2x3=2In the following exercises, solve. 292. 4x13=3In the following exercises, solve. 293. 2m35=0In the following exercises, solve. 294. 2n13=0In the following exercises, solve. 295. 6v210=0In the following exercises, solve. 296. 12u+111=0In the following exercises, solve. 297. 4m+2+2=6In the following exercises, solve. 298. 6n+1+4=8In the following exercises, solve. 299. 2u3+2=0In the following exercises, solve. 300. 5v2+5=0In the following exercises, solve. 301. u33=uIn the following exercises, solve. 302. v10+10=vIn the following exercises, solve. 303. r1=r1In the following exercises, solve. 304. s8=s8In the following exercises, solve. 305. 6x+43=4In the following exercises, solve. 306. 11x+43=5In the following exercises, solve. 307. 4x+532=5In the following exercises, solve. 308. 9x131=5In the following exercises, solve. 309. (6x+1)123=4In the following exercises, solve. 310. (3x2)12+1=6In the following exercises, solve. 311. (8x+5)13+2=1In the following exercises, solve. 312. (12x5)13+8=3In the following exercises, solve. 313. (12x3)145=2In the following exercises, solve. 314. (5x4)14+7=9In the following exercises, solve. 315. x+1x+1=0In the following exercises, solve. 316. y+4y+2=0In the following exercises, solve. 317. z+100z=10In the following exercises, solve. 318. w+25w=5In the following exercises, solve. 319. 32x320=7In the following exercises, solve. 320. 25x+18=0In the following exercises, solve. 321. 28r+18=2In the following exercises, solve. 322. 37y+110=8In the following exercises, solve. 323. 3u+7=5u+1In the following exercises, solve. 324. 4v+1=3v+3In the following exercises, solve. 325. 8+2r=3r+10In the following exercises, solve. 326. 10+2c=4c+16In the following exercises, solve. 327. 5x13=x+33In the following exercises, solve. 328. 8x53=3x+53In the following exercises, solve. 329. 2x2+9x183=x2+3x23In the following exercises, solve. 330. x2x+183=2x23x63In the following exercises, solve. 331. a+2=a+4In the following exercises, solve. 332. r+6=r+8In the following exercises, solve. 333. u+1=u+4In the following exercises, solve. 334. x+1=x+2In the following exercises, solve. 335. a+5a=1In the following exercises, solve. 336. 2=d20dIn the following exercises, solve. 337. 2x+1=1+xIn the following exercises, solve. 338. 3x+1=1+2x1In the following exercises, solve. 339. 2x1x1=1In the following exercises, solve. 340. x+1x2=1In the following exercises, solve. 341. x+7x5=2In the following exercises, solve. 342. x+5x3=2In the following exercises, solve. Round approximations to one decimal place. 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. 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. 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. 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. 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. 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.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.For the function f(x)=3x2, find a. f(6) b. f(0).For the function g(x)=5x+5, find a. g(4) b. g(3).For the function g(x)=3x43, find a. g(4) b. g(1).For the function h(x)=5x23, find a. h(2) b. h(5). =For the function f(x)=3x+44, find a. f(4) b. f(1).For the function g(x)=5x+14, find a. g(16) b. g(3).Find the domain of the function, f(x)=6x5, write the domain in interval notation.Find the domain of the function, f(x)45x. Write the domain in interval notation.Find the domain of the function, f(x)=4x+3. Write the domain in interval notation.Find the domain of the function, h(x)=9x5. Write the domain in interval notation.Find the domain of the function, f(x)=3x213. Write the domain in interval notation.Find the domain of the function, g(x)=5x43. Write the domain in interval notation.=For the function f(x)=x+2, (a) find the domain (b) graph the function (c) use the graph to determine the range.For the function f(x)=x2 , (a) find the domain (b) graph the function (c) use the graph to determine the range.For the function f(x)=x3, find the domain (b) graph the function (c) use the graph to determine the range.For the function f(x)=x23, find the domain (b) graph the function (c) use the graph to determine the range.In the following exercises, evaluate each function. 351. f(x)=4x4, find (a) f(5) (b) f(0).In the following exercises, evaluate each function. 352. f(x)=6x5, find (a) f(5) (b) f(1).In the following exercises, evaluate each function. 353. g(x)=6x+1, find (a) g(4) (b) g(8).In the following exercises, evaluate each function. 354. g(x)=3x+1, find (a) g(8) (b) g(5).In the following exercises, evaluate each function. 355. F(x)=32x, find (a) F(1) (b) F(11).In the following exercises, evaluate each function. 356. , F(x)=84x, find (a) F(1) (b) F(2).In the following exercises, evaluate each function. 357. G(x)=5x1, find (a) G(5) (b) G(2).In the following exercises, evaluate each function. 358. G(x)=4x+1, find (a) G(11) (b) G(2).In the following exercises, evaluate each function. 359. g(x)=2x43, find (a) g(6) (b) g(2).In the following exercises, evaluate each function. 360. g(x)=7x13, find (a) g(4) (b) g(1).In the following exercises, evaluate each function. 361. h(x)=x243, find (a) h(2) (b) h(6).In the following exercises, evaluate each function. 362. h(x)=x2+43, find (a) h(2) (b) h(6).In the following exercises, evaluate each function. 363. For the function f(x)=2x34, find (a) f(0) (b) f(2).In the following exercises, evaluate each function. 364. For the function f(x)=3x34, find (a) f(0) (b) f(3)In the following exercises, evaluate each function. 365. For the function g(x)=44x4, find a) g(1) (b) g(3). =In the following exercises, evaluate each function. 366. For the function g(x)=84x4, find (a) g(6) (b) g(2).In the following exercises, find the domain of the function and write the domain in interval notation. 367. f(x)=3x1In the following exercises, find the domain of the function and write the domain in interval notation. 368. f(x)=4x2In the following exercises, find the domain of the function and write the domain in interval notation. 369. g(x)=23xIn the following exercises, find the domain of the function and write the domain in interval notation. 370. g(x)=8xIn the following exercises, find the domain of the function and write the domain in interval notation. 371. h(x)=5x2In the following exercises, find the domain of the function and write the domain in interval notation. 372. h(x)=6x+3In the following exercises, find the domain of the function and write the domain in interval notation. 373. f(x)=x+3x2In the following exercises, find the domain of the function and write the domain in interval notation. 374. f(x)=x1x+4In the following exercises, find the domain of the function and write the domain in interval notation. 375. g(x)=8x13In the following exercises, find the domain of the function and write the domain in interval notation. 376. g(x)=6x+53In the following exercises, find the domain of the function and write the domain in interval notation. 377. f(x)=4x2163In the following exercises, find the domain of the function and write the domain in interval notation. 378. f(x)=6x2253In the following exercises, find the domain of the function and write the domain in interval notation. 379. F(x)=8x+34In the following exercises, find the domain of the function and write the domain in interval notation. 380. F(x)=107x4In the following exercises, find the domain of the function and write the domain in interval notation. 381. G(x)=2x15In the following exercises, find the domain of the function and write the domain in interval notation. 382. G(x)=6x35In the following exercises, find the domain of the function graph the function use the graph to determine the range. 383. f(x)=x+1In the following exercises, find the domain of the function graph the function use the graph to determine the range. 384. f(x)=x1In the following exercises, find the domain of the function graph the function use the graph to determine the range. 385. g(x)=x+4In the following exercises, find the domain of the function graph the function use the graph to determine the range. 386. g(x)=x4In the following exercises, find the domain of the function graph the function use the graph to determine the range. 387. f(x)=x+2In the following exercises, find the domain of the function graph the function use the graph to determine the range. 388. f(x)=x2In the following exercises, find the domain of the function graph the function use the graph to determine the range. 389. g(x)=2xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 390. g(x)=3xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 391. f(x)=3xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 392. f(x)=4xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 393. g(x)=xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 394. g(x)=x+1In the following exercises, find the domain of the function graph the function use the graph to determine the range. 395. f(x)=x+13In the following exercises, find the domain of the function graph the function use the graph to determine the range. 396. f(x)=x13In the following exercises, find the domain of the function graph the function use the graph to determine the range. 397. g(x)=x+23In the following exercises, find the domain of the function graph the function use the graph to determine the range. 398. g(x)=x23In the following exercises, find the domain of the function graph the function use the graph to determine the range. 399. f(x)=x3+3In the following exercises, find the domain of the function graph the function use the graph to determine the range. 400. f(x)=x33In the following exercises, find the domain of the function graph the function use the graph to determine the range. 401. g(x)=x3In the following exercises, find the domain of the function graph the function use the graph to determine the range. 402. g(x)=x3In the following exercises, find the domain of the function graph the function use the graph to determine the range. 403. f(x)=2x3In the following exercises, find the domain of the function graph the function use the graph to determine the range. 404. f(x)=2x3Explain how to find the domain of a fourth root function.Explain how to find the domain of a fifth root function.Explain why y=x3 is a function.Explain why the process of finding the domain of a radical function with an even index is different from the process when the index is odd.Write each expression in terms of i and simplify if possible: (a) 81 (b) 5 (c) 18.Write each expression in term of i and simplify if possible: (a) 36 (b) 3 (c) 27.Add: 8+32.Add: 27+48.Simplify: (a) (2+7i)+(42i) (b) (84i)(2i).Simplify: (a) (32i)+(54i) (b) (4+3i)(26i).Multiply: 4i(53i).Multiply: 3i(2+4i).Multiply: (53i)(12i)Multiply: (43i)(2+i)Multiply using the Binomial Squares pattern: (25i)2.Multiply using the Binomial Squares pattern: (5+4i)2.Multiply: 494.Multiply: 3681.Multiply: (412)(348).Multiply: (2+8)(318).Multiply: (43i)(4+3i).Multiply: (2+5i)(25i).Multiply using the Product of Complex Conjugates Pattern: (310i)(3+10i).Multiply using the Product of Complex Conjugates Pattern: (5+4i)(54i).Divide: 2+5i52i.Divide: 1+6i6i.Divide, writing the answer in standard form: 414i.Divide writing the answer in standard form: 21+2i.Divide: 3+3i2i.Divide: 2+4i5i.Simplify: i75.Simplify: i92.In the following exercises, write each expression in terms of i and simplify if possible. 409. (a) 16 (b) 11 (c) 8In the following exercises, write each expression in terms of i and simplify if possible. 410. (a) 121 (b) 1 (c) 20In the following exercises, write each expression in terms of i and simplify if possible. 411. (a) 100 (b) 13 (c) 45In the following exercises, write each expression in terms of i and simplify if possible. 412. (a) 49 (b) 15 (c) 75In the following exercises, add or subtract. 413. 75+48In the following exercises, add or subtract. 414. 12+75In the following exercises, add or subtract. 415. 50+18In the following exercises, add or subtract. 416. 72+8In the following exercises, add or subtract. 417. (1+3i)+(7+4i)In the following exercises, add or subtract. 418. (6+2i)+(34i)In the following exercises, add or subtract. 419. (8i)+(6+3i)In the following exercises, add or subtract. 420. (74i)+(26i)In the following exercises, add or subtract. 421. (14i)(36i)In the following exercises, add or subtract. 422. (84i)(3+7i)In the following exercises, add or subtract. 423. (6+i)(24i)In the following exercises, add or subtract. 424. (2+5i)(5+6i)In the following exercises, add or subtract. 425. (536)+(249)In the following exercises, add or subtract. 426. (3+64)+(516)In the following exercises, add or subtract. 427. (750)(3018)In the following exercises, add or subtract. 428. (5+27)(448)In the following exercises, multiply. 429. 4i(53i)In the following exercises, multiply. 430. 2i(3+4i)In the following exercises, multiply. 431. 6i(32i)In the following exercises, multiply. 432. i(6+5i)In the following exercises, multiply. 433. (4+3i)(5+6i)In the following exercises, multiply. 434. (25i)(4+3i)In the following exercises, multiply. 435. (3+3i)(27i)In the following exercises, multiply. 436. (62i)(35i)In the following exercises, multiply using the Product of Binomial Squares Pattern. 437. (3+4i)2In the following exercises, multiply using the Product of Binomial Squares Pattern. 438. (1+5i)2In the following exercises, multiply using the Product of Binomial Squares Pattern. 439. (23i)2In the following exercises, multiply using the Product of Binomial Squares Pattern. 440. (65i)2In the following exercises, multiply. 441. 2536In the following exercises, multiply. 442. 416In the following exercises, multiply. 443. 9100In the following exercises, multiply. 444. 649In the following exercises, multiply. 445. (227)(448)In the following exercises, multiply. 446. (512)(3+75)In the following exercises, multiply. 447. (2+8)(4+18)In the following exercises, multiply. 448. (5+18)(250)In the following exercises, multiply. 449. (2i)(2+i)In the following exercises, multiply. 450. (45i)(4+5i)In the following exercises, multiply. 451. (72i)(7+2i)In the following exercises, multiply. 452. (38i)(3+8i)In the following exercises, multiply using the Product of Complex Conjugates Pattern. 453. (7i)(7+i)In the following exercises, multiply using the Product of Complex Conjugates Pattern. 454. (65i)(6+5i)In the following exercises, multiply using the Product of Complex Conjugates Pattern. 455. (92i)(9+2i)In the following exercises, multiply using the Product of Complex Conjugates Pattern. 456. (34i)(3+4i)In the following exercises, divide. 457. 3+4i43iIn the following exercises, divide. 458. 52i2+5iIn the following exercises, divide. 459. 2+i34iIn the following exercises, divide. 460. 32i6+iIn the following exercises, divide. 461. 323iIn the following exercises, divide. 462. 245iIn the following exercises, divide. 463. 432iIn the following exercises, divide. 464. 13+2iIn the following exercises, divide. 465. 1+4i3iIn the following exercises, divide. 466. 4+3i7iIn the following exercises, divide. 467. 23i4iIn the following exercises, divide. 468. 35i2iIn the following exercises, simplify. 469. i41In the following exercises, simplify. 470. i39In the following exercises, simplify. 471. i66In the following exercises, simplify. 472. i48In the following exercises, simplify. 473. i128In the following exercises, simplify. 474. i162In the following exercises, simplify. 475. i137In the following exercises, simplify. 476. i255Explain the relationship between real numbers and complex numbers.Aniket multiplied as follows and he got the wrong answer. What is wrong with his reasoning? 77497Why is 64=8i but 643=4.Explain how dividing complex numbers is similar to rationalizing a denominator.In the following exercises, simplify. 481. a. 225 b. 16In the following exercises, simplify. 482. a. 169 b. 8In the following exercises, simplify. 483. a. 83 b. 814 c. 2435In the following exercises, simplify. 484. a. 5123 b. 814 c. 15