Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
In the following exercises, estimate each root between two consecutive whole numbers. 485. a. 68 b. 843In the following exercises, approximate each root and round to two decimal places. 486. a. 37 b. 843 c. 1254In the following exercises, simplify using absolute values as necessary. 487. a. a33 b. b77In the following exercises, simplify using absolute values as necessary. 488. a. a14 b. w24In the following exercises, simplify using absolute values as necessary. 489. a. m84 b. n205In the following exercises, simplify using absolute values as necessary. 490. a. 121m20 b. 64a2In the following exercises, simplify using absolute values as necessary. 491. a. 216a63 b. 32b205In the following exercises, simplify using absolute values as necessary. 492. a. 144x2y2 b. 169w8y10 c. 8a51b63In the following exercises, use the Product Property to simplify radical expressions. 493. 125In the following exercises, use the Product Property to simplify radical expressions. 494. 675In the following exercises, use the Product Property to simplify radical expressions. 495. a. 6253 b. 1286In the following exercises, simplify using absolute value signs as needed. 496. a. a23 b. b83 c. c138In the following exercises, simplify using absolute value signs as needed. 497. a. 80s15 b. 96a75 c. 128b76In the following exercises, simplify using absolute value signs as needed. 498. a. 96r3s3 b. 80x7y63 c. 80x8y94In the following exercises, simplify using absolute value signs as needed. 499. a. 325 b. 18In the following exercises, simplify using absolute value signs as needed. 500. a. 8+96 b. 2+402In the following exercise, use the Quotient Property to simplify square roots. 501. a. 7298 b. 24813 c. 6964In the following exercise, use the Quotient Property to simplify square roots. 502. a. y4y8 b. u 21u 115 c. v 30v 126In the following exercise, use the Quotient Property to simplify square roots. 503. 300m564In the following exercise, use the Quotient Property to simplify square roots. 504. a. 28p7q2 b. 81s8t33 c. 64p 15q 124In the following exercise, use the Quotient Property to simplify square roots. 505. a. 27p2q108p4q3 b. 16c5d7250c2d23 c. 2m9n7128m3n6In the following exercise, use the Quotient Property to simplify square roots. 506. a. 180q55q b. 625353 c. 80m745m4In the following exercises, write as a radical expression. 507. a. r12 b. s13 c. t14In the following exercises, write with a rational exponent. 508. a. 21p b. 8q4 c. 436r6In the following exercises, simplify. 509. a. 62514 b. 24315 c. 3215In the following exercises, simplify. 510. a. (1,000)13 b. 1,00013 c. (1,000)13In the following exercises, simplify. 511. a. (32)15 b. (243)15 c. 12513In the following exercises, write with a rational exponent. 512. a. r74 b. ( 2pq5)3 c. ( 12m 7n )34In the following exercises, simplify. 513. a. 2532 b. 932 c. (64)23In the following exercises, simplify. 514. a. 6432 b. 6432 c. (64)32In the following exercises, simplify. 515. a. 652612 b. (b 15)35 c. w27w97In the following exercises, simplify. 516. a. a34a14a 104 b. ( 27 b 2 3 c 5 2 b 7 3 c 1 2 )13In the following exercises, simplify. 517. a. 7232 b. 7p3+2p3 c. 5x33x3In the following exercises, simplify. 518. a. 11b511b+311b b. 811cd4+511cd4911cd4In the following exercises, simplify. 519. a. 48+27 b. 543+1283 c. 654323204In the following exercises, simplify. 520. a. 80c720c7 b. 2162r104+432r104In the following exercises, simplify. 521. 375y2+8y48300y2In the following exercises, simplify. 522. a. (56)(12) b. (2184)(94)In the following exercises, simplify. 523. a. (32x3)(718x2) b. (620a23)(216a33)In the following exercises, multiply. 524. a. 11(8+411) b. 33(93+183)In the following exercises, multiply. 525. a. (327)(547) b. (x35)(x33)In the following exercises, multiply. 526. (27511)(47+911)In the following exercises, multiply. 527. a. (4+ 11)2 b. (325)2In the following exercises, multiply. 528. (7+10)(710)In the following exercises, multiply. 529. (3x3+2)(3x32)In the following exercises, simplify. 530. a. 4875 b. 813243In the following exercises, simplify. 531. a. 320mn 545m 7n3 b. 16x4y2354x 2y43In the following exercises, rationalize the denominator. 532. a. 83 b. 740 c. 82yIn the following exercises, rationalize the denominator. 533. a. 1113 b. 7543 c. 33x23In the following exercises, rationalize the denominator. 534. a. 144 b. 9324 c. 69x34In the following exercises, simplify. 535. 726In the following exercises, simplify. 536. 5n7In the following exercises, simplify. 537. x+8x8In the following exercises, solve. 538. 4x3=7In the following exercises, solve. 539. 5x+1=3In the following exercises, solve. 540. 4x13=3In the following exercises, solve. 541. u3+3=uIn the following exercises, solve. 542. 4x+532=5In the following exercises, solve. 543. (8x+5)13+2=1In the following exercises, solve. 544. y+4y+2=0In the following exercises, solve. 545. 28r+18=2In the following exercises, solve. 546. 10+2c=4c+16In the following exercises, solve. 547. 2x2+9x183=x2+3x23In the following exercises, solve. 548. r+6=r+8In the following exercises, solve. 549. x+1x2=1In the following exercises, solve. Round approximations to one decimal place. 550. 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=Ato 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. 551. 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 formulas=24dto find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.In the following exercises, evaluate each function. 552. g(x)=16x+1, find a. g(4) b. g(8)In the following exercises, evaluate each function. 553. G(x)=5x1, find a. G(5) b. G(2)In the following exercises, evaluate each function. 554. h(x)=x24,3 find a. h(2) b. h(6)In the following exercises, evaluate each function. 555. For the function g(x)=44x4, find a. g(1) b. g(3)In the following exercises, find the domain of the function and write the domain in interval notation. 556. g(x)=23xIn the following exercises, find the domain of the function and write the domain in interval notation. 557. F(x)=x+3x2In the following exercises, find the domain of the function and write the domain in interval notation. 558. f(x)=4x2163In the following exercises, find the domain of the function and write the domain in interval notation. 559. F(x)=107x4In the following exercises, find the domain of the function graph the function use the graph to determine the range. 560. g(x)=x+4In the following exercises, find the domain of the function graph the function use the graph to determine the range. 561. g(x)=2xIn the following exercises, find the domain of the function graph the function use the graph to determine the range. 562. f(x)=x13In the following exercises, find the domain of the function graph the function use the graph to determine the range. 563. f(x)=x3+3In the following exercises, write each expression in terms of i and simplify if possible. 564. a. 100 b. 13 c. 45In the following exercises, add or subtract. 565. 50+18In the following exercises, add or subtract. 566. (8i)+(6+3i)In the following exercises, add or subtract. 567. (6+i)(24i)In the following exercises, add or subtract. 568. (750)(3218)In the following exercises, multiply. 569. (25i)(4+3i)In the following exercises, multiply. 570. 6i(32i)In the following exercises, multiply. 571. 416In the following exercises, multiply. 572. (512)(3+75)In the following exercises, multiply using the Product of Binomial Squares Pattern. 573. (23i)2In the following exercises, multiply using the Product of Complex Conjugates Pattern. 574. (92i)(9+2i)In the following exercises, divide. 575. 2+i34iIn the following exercises, divide. 576. 432iIn the following exercises, simplify. 577. i48In the following exercises, simplify. 578. i255In the following exercises, simplify using absolute values as necessary. 579. 125x93In the following exercises, simplify using absolute values as necessary. 580. 169x8y6In the following exercises, simplify using absolute values as necessary. 581. 72x8y43In the following exercises, simplify using absolute values as necessary. 582. 45x3y4180x5y2In the following exercises, simplify. Assume all variables are positive. 583. a. 21614 b. 4932In the following exercises, simplify. Assume all variables are positive. 584. 45In the following exercises, simplify. Assume all variables are positive. 585. x14x54x34In the following exercises, simplify. Assume all variables are positive. 586. ( 8 x 2 3 y 5 2 x 7 3 y 1 2 )13In the following exercises, simplify. Assume all variables are positive. 587. 48x575x5In the following exercises, simplify. Assume all variables are positive. 588. 27x24x12+108x2In the following exercises, simplify. Assume all variables are positive. 589. 212x536x3In the following exercises, simplify. Assume all variables are positive. 590. 43(16363)In the following exercises, simplify. Assume all variables are positive. 591. (433)(5+23)In the following exercises, simplify. Assume all variables are positive. 592. 1283543In the following exercises, simplify. Assume all variables are positive. 593. 245xy 445x 4y3In the following exercises, simplify. Assume all variables are positive. 594. 153In the following exercises, simplify. Assume all variables are positive. 595. 32+3In the following exercises, simplify. Assume all variables are positive. 596. 49In the following exercises, simplify. Assume all variables are positive. 597. 4i(23i)In the following exercises, simplify. Assume all variables are positive. 598. 4+i32iIn the following exercises, simplify. Assume all variables are positive. 599. i172In the following exercise, solve. 600. 2x+5+8=6In the following exercise, solve. 601. x+5+1=xIn the following exercise, solve. 602. 2x26x233=x23x+53In the following exercise, find the domain of the function graph the function use the graph to determine the range. 603. g(x)=x+2Solve: x248=0 .Solve: y227=0 .Solve: 2x2=98 .Solve: 5m2=80 .Solve: c2+12=0 .Solve: q2+24=0 .Solve: 12x2+4=24 .Solve: 34y23=18 .Solve: 5r22=34 .Solve: 3t2+6=70 .Solve: 3(a3)2=54 .Solve: 2(b+2)2=80 .Solve: (x12)2=54 .Solve: (y+34)2=716 .Solve: 5(a5)2+4=104 .Solve: 3(b+3)28=88 .Solve: (3r+4)2=8 .Solve: (2t8)2=10 .Solve: 9m212m+4=25 .Solve: 16n2+40n+25=4 .In the following exercises, solve each equation. 1. a2=49In the following exercises, solve each equation. 2. b2=144In the following exercises, solve each equation. 3. r224=0In the following exercises, solve each equation. 4. t275=0In the following exercises, solve each equation. 5. u2300=0In the following exercises, solve each equation. 6. v280=0In the following exercises, solve each equation. 7. 4m2=36In the following exercises, solve each equation. 8. 3n2=48In the following exercises, solve each equation. 9. 43x2=48In the following exercises, solve each equation. 10. 53y2=60In the following exercises, solve each equation. 11. x2+25=0In the following exercises, solve each equation. 12. y2+64=0In the following exercises, solve each equation. 13. x2+63=0In the following exercises, solve each equation. 14. y2+45=0In the following exercises, solve each equation. 15. 43x2+2=110In the following exercises, solve each equation. 16. 23y28=2In the following exercises, solve each equation. 17. 25a2+3=11In the following exercises, solve each equation. 18. 32b27=41In the following exercises, solve each equation. 19. 7p2+10=26In the following exercises, solve each equation. 20. 2q2+5=30In the following exercises, solve each equation. 21. 5y27=25In the following exercises, solve each equation. 22. 3x28=46In the following exercises, solve each equation. 23. (u6)2=64In the following exercises, solve each equation. 24. (v+10)2=121In the following exercises, solve each equation. 25. (m6)2=20In the following exercises, solve each equation. 26. (n+5)2=32In the following exercises, solve each equation. 27. (r12)2=34In the following exercises, solve each equation. 28. (x+15)2=725In the following exercises, solve each equation. 29. (y+23)2=881In the following exercises, solve each equation. 30. (t56)2=1125In the following exercises, solve each equation. 31. (a7)2+5=55In the following exercises, solve each equation. 32. (b1)29=39In the following exercises, solve each equation. 33. 4(x+3)25=27ccIn the following exercises, solve each equation. 34. 5(x+3)27=68In the following exercises, solve each equation. 35. (5c+1)2=27In the following exercises, solve each equation. 36. (8d6)2=24In the following exercises, solve each equation. 37. (4x3)2+11=17In the following exercises, solve each equation. 38. (2y+1)25=23In the following exercises, solve each equation. 39. m24m+4=8In the following exercises, solve each equation. 40. n2+8n+16=27In the following exercises, solve each equation. 41. x26x+9=12In the following exercises, solve each equation. 42. y2+12y+36=32In the following exercises, solve each equation. 43. 25x230x+9=36In the following exercises, solve each equation. 44. 9y2+12y+4=9In the following exercises, solve each equation. 45. 36x224x+4=81In the following exercises, solve each equation. 46. 64x2+144x+81=25In the following exercises, solve using the Square Root Property. 47. 2r2=32In the following exercises, solve using the Square Root Property. 48. 4t2=16In the following exercises, solve using the Square Root Property. 49. (a4)2=28In the following exercises, solve using the Square Root Property. 50. (b+7)2=8In the following exercises, solve using the Square Root Property. 51. 9w224w+16=1In the following exercises, solve using the Square Root Property. 52. 4z2+4z+1=49In the following exercises, solve using the Square Root Property. 53. a218=0In the following exercises, solve using the Square Root Property. 54. b2108=0In the following exercises, solve using the Square Root Property. 55. (p13)2=79In the following exercises, solve using the Square Root Property. 56. (q35)2=34In the following exercises, solve using the Square Root Property. 57. m2+12=0In the following exercises, solve using the Square Root Property. 58. n2+48=0.In the following exercises, solve using the Square Root Property. 59. u214u+49=72In the following exercises, solve using the Square Root Property. 60. v2+18v+81=50In the following exercises, solve using the Square Root Property. 61. (m4)2+3=15In the following exercises, solve using the Square Root Property. 62. (n7)28=64In the following exercises, solve using the Square Root Property. 63. (x+5)2=4In the following exercises, solve using the Square Root Property. 64. (y4)2=64In the following exercises, solve using the Square Root Property. 65. 6c2+4=29In the following exercises, solve using the Square Root Property. 66. 2d24=77In the following exercises, solve using the Square Root Property. 67. (x6)2+7=3In the following exercises, solve using the Square Root Property. 68. (y4)2+10=9In your own words, explain the Square Root Property.In your own words, explain how to use the Square Root Property to solve the quadratic equation (x+2)2=16.Complete the square to make a perfect square trinomial. Then write the result as a binomial squared. (a) a220a (b) m25m (c) p2+14pComplete the square to make a perfect square trinomial. Then write the result as a binomial squared. (a) b24b (b) n2+13n (c) q223qSolve by completing the square: x2+4x=5 .Solve by completing the square: y210y=9 .Solve by completing the square: y210y=35 .Solve by completing the square: z2+8z=19 .Solve by completing the square: x216x=16 .Solve by completing the square: y2+8y=11 .Solve by completing the square: a2+4a+9=30 .Solve by completing the square: b2+8b4=16 .Solve by completing the square: p2=5p+9 .Solve by completing the square: q2=7q3 .Solve by completing the square: (c2)(c+8)=11 .Solve by completing the square: (d7)(d+3)=56 .Solve by completing the square: 2m2+16m+14=0 .Solve by completing the square: 4n224n56=8 .Solve by completing the square: 3r22r=21 .Solve by completing the square: 4t2+2t=20 .Solve by completing the square: 4x2+3x=2 .Solve by completing the square: 3y210y=5 .In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared. 71. (a) m224m (b) x211x (c) p213pIn the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared. 72. (a) n216n (b) y2+15y (c) q2+34qIn the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared. 73. (a) p222p (b) y2+5y (c) m2+25mIn the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared. 74. (a) q26q (b) x27x (c) n223nIn the following exercises, solve by completing the square. 75. u2+2u=3In the following exercises, solve by completing the square. 76. z2+12z=11In the following exercises, solve by completing the square. 77. x220x=21In the following exercises, solve by completing the square. 78. y22y=8In the following exercises, solve by completing the square. 79. m2+4m=44In the following exercises, solve by completing the square. 80. n22n=3In the following exercises, solve by completing the square. 81. r2+6r=11In the following exercises, solve by completing the square. 82. t214t=50In the following exercises, solve by completing the square. 83. a210a=5In the following exercises, solve by completing the square. 84. b2+6b=41In the following exercises, solve by completing the square. 85. x2+5x=2In the following exercises, solve by completing the square. 86. y23y=2In the following exercises, solve by completing the square. 87. u214u+12=1In the following exercises, solve by completing the square. 88. z2+2z5=2In the following exercises, solve by completing the square. 89. r24r3=9In the following exercises, solve by completing the square. 90. t210t6=5In the following exercises, solve by completing the square. 91. v2=9v+2In the following exercises, solve by completing the square. 92. w2=5w1In the following exercises, solve by completing the square. 93. x25=10xIn the following exercises, solve by completing the square. 94. y214=6yIn the following exercises, solve by completing the square. 95. (x+6)(x2)=9In the following exercises, solve by completing the square. 96. (y+9)(y+7)=80In the following exercises, solve by completing the square. 97. (x+2)(x+4)=3In the following exercises, solve by completing the square. 98. (x2)(x6)=5In the following exercises, solve by completing the square. 99. 3m2+30m27=6In the following exercises, solve by completing the square. 100. 2x214x+12=0In the following exercises, solve by completing the square. 101. 2n2+4n=26In the following exercises, solve by completing the square. 102. 5x2+20x=15In the following exercises, solve by completing the square. 103. 2c2+c=6In the following exercises, solve by completing the square. 104. 3d24d=15In the following exercises, solve by completing the square. 105. 2x2+7x15=0In the following exercises, solve by completing the square. 106. 3x214x+8=0In the following exercises, solve by completing the square. 107. 2p2+7p=14In the following exercises, solve by completing the square. 108. 3q25q=9In the following exercises, solve by completing the square. 109. 5x23x=10In the following exercises, solve by completing the square. 110. 7x2+4x=3Solve the equation x2+10x=25 (a) by using the Square Root Property (b) by Completing the Square (c) Which method do you prefer? Why?Solve the equation y2+8y=48 by completing the square and explain all your steps.Solve by using the Quadratic Formula: 3y25y+2=0 .Solve by using the Quadratic Formula: 4z2+2z6=0 .Solve by using the Quadratic Formula: a22a=15 .Solve by using the Quadratic Formula: b2+24=10b .Solve by using the Quadratic Formula: 3m2+12m+7=0 .Solve by using the Quadratic Formula: 5n2+4n4=0 .Solve by using the Quadratic Formula: 4a22a+8=0 .Solve by using the Quadratic Formula: 5b2+2b+4=0 .Solve by using the Quadratic Formula: x(x+2)5=0 .Solve by using the Quadratic Formula: 3y(y2)3=0 .Solve by using the Quadratic Formula: 14c213c=112 .Solve by using the Quadratic Formula: 19d212d=13 .Solve by using the Quadratic Formula: r2+10r+25=0 .Solve by using the Quadratic Formula: 25t240t=16 .Determine the numberand type of solutions to each quadratic equation. (a) 8m23m+6=0 (b) 5z2+6z2=0 (c) 9w2+24w+16=0Determine the numberand type of solutions to each quadratic equation. (a) b2+7b13=0 (b) 5a26a+10=0 (c) 4r220r+25=0Identify the most appropriate method to use to solve each quadratic equation. (a) x2+6x+8=0 (b) (n3)2=16 (c) 5p26p=9Identify the most appropriate method to use to solve each quadratic equation. (a) 8a2+3a9=0 (b) 4b2+4b+1=0 (c) 5c2=125In the following exercises, solve by using the Quadratic Formula. 113. 4m2+m3=0In the following exercises, solve by using the Quadratic Formula. 114. 4n29n+5=0In the following exercises, solve by using the Quadratic Formula. 115. 2p27p+3=0In the following exercises, solve by using the Quadratic Formula. 116. 3q2+8q3=0In the following exercises, solve by using the Quadratic Formula. 117. p2+7p+12=0In the following exercises, solve by using the Quadratic Formula. 118. q2+3q18=0In the following exercises, solve by using the Quadratic Formula. 119. r28r=33In the following exercises, solve by using the Quadratic Formula. 120. t2+13t=40In the following exercises, solve by using the Quadratic Formula. 121. 3u2+7u2=0In the following exercises, solve by using the Quadratic Formula. 122. 2p2+8p+5=0In the following exercises, solve by using the Quadratic Formula. 123. 2a26a+3=0