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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Elementary Algebra

In the following exercises, rationalize the denominator. 692. 66 In the following exercises, rationalize the denominator. 693. 535 In the following exercises, rationalize the denominator. 694. 1026 In the following exercises, rationalize the denominator. 695. 328 In the following exercises, rationalize the denominator. 696. 975 In the following exercises, rationalize the denominator. 697. 44+27 In the following exercises, rationalize the denominator. 698. 5210 In the following exercises, rationalize the denominator. 699. 425 In the following exercises, rationalize the denominator. 700. 548 In the following exercises, rationalize the denominator. 701. 2p+3 In the following exercises, rationalize the denominator. 702. x2x+2 In the following exercises, solve the equation. 703. 7z+1=6 In the following exercises, solve the equation. 704. 4u24=0 In the following exercises, solve the equation. 705. 6m+45=0 In the following exercises, solve the equation. 706. 2u3+2=0 In the following exercises, solve the equation. 707. u4+4=u In the following exercises, solve the equation. 708. v9+9=0 In the following exercises, solve the equation. 709. r4r=10 In the following exercises, solve the equation. 710. s9s=9 In the following exercises, solve the equation. 711. 22x74=8 In the following exercises, solve the equation. 712. 2x=2x7 In the following exercises, solve the equation. 713. a+3=a+9 In the following exercises, solve the equation. 714. r+3=r+4 In the following exercises, solve the equation. 715. u+2=u+5 In the following exercises, solve the equation. 716. n+111=n+4 In the following exercises, solve the equation. 717. y+5+1=2y+3 In the following exercises, solve. Round approximations to one decimal place. 718. A pallet of sod will cover an area of about 600 square feet. Trinh wants to order a pallet of sod to make a square lawn in his backyard. Use the formula s=A to find the length of each side of his lawn.In the following exercises, solve. Round approximations to one decimal place. 719. A helicopter dropped a package from a height of 900 feet above a stranded hiker. Use the formula t=h4 to find how many seconds it took for the package to reach the hiker.In the following exercises, solve. Round approximations to one decimal place. 720. Officer Morales measured the skid marks of one of the cars involved in an accident. The length of the skid marks was 245 feet. Use the formula s=24d to find the speed of the car before the brakes were applied.In the following exercises, simplify. 721. (a) 646 (b) 643 In the following exercises, simplify. 722. (a) 273 (b) 644 In the following exercises, simplify. 723. (a) d99 (b) v88 In the following exercises, simplify. 724. (a) a105 (b) b273 In the following exercises, simplify. 725. (a) 16x84 (b) 64y126 In the following exercises, simplify. 726. (a) 128r147 (b) 81s244 In the following exercises, simplify. 727. (a) d99 (b) m1711 In the following exercises, simplify. 728. (a) 543 (b) 1284 In the following exercises, simplify. 729. (a) 64c85 (b) 48d74 In the following exercises, simplify. 730. (a) 343q73 (b) 192r96 In the following exercises, simplify. 731. (a) 5003 (b) 164 In the following exercises, simplify. 732. r 10r55 In the following exercises, simplify. 733. w 12w23 In the following exercises, simplify. 734. 64y84y54 In the following exercises, simplify. 735. 54z92z33 In the following exercises, simplify. 736. 64a7b26 In the following exercises, simplify. 737. 42052205 In the following exercises, simplify. 738. 4183+3183 In the following exercises, simplify. 739. 125041624 In the following exercises, simplify. 740. 640c5380c33 In the following exercises, simplify. 741. 96t85+486t45 In the following exercises, write as a radical expression. 742. r18 In the following exercises, write as a radical expression. 743. s110 In the following exercises, write with a rational exponent. 744. u5 In the following exercises, write with a rational exponent. 745. v6 In the following exercises, write with a rational exponent. 746. 9m3 In the following exercises, write with a rational exponent. 747. 10z6 In the following exercises, simplify. 748. 1614 In the following exercises, simplify. 749. 3215 In the following exercises, simplify. 750. (125)13 In the following exercises, simplify. 751. (125)13 In the following exercises, simplify. 752. (9)12 In the following exercises, simplify. 753. (36)12 In the following exercises, write with a rational exponent. 754. q53 In the following exercises, write with a rational exponent. 755. n85 In the following exercises, simplify. 756. 2723 In the following exercises, simplify. 757. 6452 In the following exercises, simplify. 758. 3632 In the following exercises, simplify. 759. 8152 In the following exercises, simplify. 760. 345365 In the following exercises, simplify. 761. (x6)43 In the following exercises, simplify. 762. z52z75 In the following exercises, simplify. 763. (16s 9 4 )14 In the following exercises, simplify. 764. (m8n 12)14 In the following exercises, simplify. 765. z23z13z53 In the following exercises, simplify. 766. 81+144 In the following exercises, simplify. 767. 169m4n2 In the following exercises, simplify. 768. 36n13 In the following exercises, simplify. 769. 313+52+13 In the following exercises, simplify. 770. 520+2125 In the following exercises, simplify. 771. (36y)(250y3)In the following exercises, simplify. 772. (25x)(3+x)In the following exercises, simplify. 773. (12q)2 In the following exercises, simplify. 774. (a) a124 (b) b213 In the following exercises, simplify. 775. (a) 81x124 (b) 64y186 In the following exercises, simplify. 776. 64r 1225r6 In the following exercises, simplify. 777. 14y37y In the following exercises, simplify. 778. 256x754x25 In the following exercises, simplify. 779. 51242324 In the following exercises, simplify. 780. (a) 25614 (b) 24315 In the following exercises, simplify. 781. 4932 In the following exercises, simplify. 782. 2552 In the following exercises, simplify. 783. w34w74 In the following exercises, simplify. 784. (27s 3 5 )13 In the following exercises, rationalize the denominator. 785. 326 In the following exercises, rationalize the denominator. 786. 3x+5 In the following exercises, solve. 787. 32x320=7 In the following exercises, solve. 788. 3u2=5u+1 In the following exercise, solve. 789. A helicopter flying at an altitude of 600 feet dropped a package to a lifeboat. Use the formula t=h4 to find how many seconds it took for the package to reach the hiker. Round your answer to the nearest tenth of a second.Solve: x2=81 .Solve: y2=121 .Solve: x250=0 .Solve: y227=0 .Solve: 2x2=98 .Solve: 3z2=108 .Solve: c2+12=0 .Solve: d2+81=0 .Solve: 12x2+4=24 .Solve: 34y23=18 .Solve: 5r22=34 .Solve: 3t2+6=70 .Solve: (q+5)2=1 .Solve: (r3)2=25 .Solve: (a3)2=18 .Solve: (b+2)2=40 .Solve: (x13)2=59 .Solve: (y34)2=716 .Solve: (a5)2+4=24 .Solve: (b3)28=24 .Solve: (3r+4)2=8 .Solve: (3r+4)2=8 .Solve: x26x+9=12 .Solve: y2+12y+36=32 .Solve: 9m212m+4=25 .Solve: 16n2+40n+25=4 .In the following exercises, solve the following quadratic equations. 1. a2=49 In the following exercises, solve the following quadratic equations. 2. b2=144 In the following exercises, solve the following quadratic equations. 3. r224=0 In the following exercises, solve the following quadratic equations. 4. t275=0 In the following exercises, solve the following quadratic equations. 5. u2300=0 In the following exercises, solve the following quadratic equations. 6. v280=0 In the following exercises, solve the following quadratic equations. 7. 4m2=36 In the following exercises, solve the following quadratic equations. 8. 3n2=48 In the following exercises, solve the following quadratic equations. 9. x2+20=0 In the following exercises, solve the following quadratic equations. 10. y2+64=0 In the following exercises, solve the following quadratic equations. 11. 25a2+3=11 In the following exercises, solve the following quadratic equations. 12. 32b27=41 In the following exercises, solve the following quadratic equations. 13. 7p2+10=26 In the following exercises, solve the following quadratic equations. 14. 2q2+5=30 In the following exercises, solve the following quadratic equations. 15. (x+2)2=9 In the following exercises, solve the following quadratic equations. 16. (y5)2=36 In the following exercises, solve the following quadratic equations. 17. (u6)2=64 In the following exercises, solve the following quadratic equations. 18. (v+10)2=121 In the following exercises, solve the following quadratic equations. 19. (m6)2=20 In the following exercises, solve the following quadratic equations. 20. (n+5)2=32 In the following exercises, solve the following quadratic equations. 21. (r12)2=34 In the following exercises, solve the following quadratic equations. 22. (t56)2=1125 In the following exercises, solve the following quadratic equations. 23. (a7)2+5=55 In the following exercises, solve the following quadratic equations. 24. (b1)29=39 In the following exercises, solve the following quadratic equations. 25. (5c+1)2=27 In the following exercises, solve the following quadratic equations. 26. (8d6)2=24 In the following exercises, solve the following quadratic equations. 27. m24m+4=8 In the following exercises, solve the following quadratic equations. 28. n2+8n+16=27 In the following exercises, solve the following quadratic equations. 29. 25x230x+9=36 In the following exercises, solve the following quadratic equations. 30. 9y2+12y+4=9 In the following exercises, solve using the Square Root Property. 31. 2r2=32 In the following exercises, solve using the Square Root Property. 32. 4t2=16 In the following exercises, solve using the Square Root Property. 33. (a4)2=28 In the following exercises, solve using the Square Root Property. 34. (b+7)2=8 In the following exercises, solve using the Square Root Property. 35. 9w224w+16=1 In the following exercises, solve using the Square Root Property. 36. 4z2+4z+1=49 In the following exercises, solve using the Square Root Property. 37. a218=0 In the following exercises, solve using the Square Root Property. 38. b2108=0 In the following exercises, solve using the Square Root Property. 39. (p13)2=79 In the following exercises, solve using the Square Root Property. 40. (q35)2=34 In the following exercises, solve using the Square Root Property. 41. m2+12=0 In the following exercises, solve using the Square Root Property. 42. n2+48=0 In the following exercises, solve using the Square Root Property. 43. u214u+49=72 In the following exercises, solve using the Square Root Property. 44. v2+18v+81=50 In the following exercises, solve using the Square Root Property. 45. (m4)2+3=15 In the following exercises, solve using the Square Root Property. 46. (n7)28=64 In the following exercises, solve using the Square Root Property. 47. (x+5)2=4 In the following exercises, solve using the Square Root Property. 48. (y4)2=64 In the following exercises, solve using the Square Root Property. 49. 6c2+4=29 In the following exercises, solve using the Square Root Property. 50. 2d24=77 In the following exercises, solve using the Square Root Property. 51. (x6)2+7=3 In the following exercises, solve using the Square Root Property. 52. (y4)2+10=9 Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation 3s2=48 to find s, the length of each garden side.Kathy is drawing up the blueprints for a house she is designing. She wants to have four square windows of equal size in the living room, with a total area of 64 square feet. Solve the equation 4s2=64 to find s, the length of the sides of the windows.Explain why the equation x2+12=8 has no solution.Explain why the equation y2+8=12 has two solutions.Complete the square to make a perfect square trinomial. Write the result as a binomial square. y2+12y Complete the square to make a perfect square trinomial. Write the result as a binomial square. z2+8z Complete the square to make a perfect square trinomial. Write the result as a binomial square. a220a Complete the square to make a perfect square trinomial. Write the result as a binomial square. b24b Complete the square to make a perfect square trinomial. Write the result as a binomial square. m25m Complete the square to make a perfect square trinomial. Write the result as a binomial square. n2+13n Complete the square to make a perfect square trinomial. Write the result as a binomial square. p2+14p Complete the square to make a perfect square trinomial. Write the result as a binomial square. q223q Solve c2+4c=5 by completing the square.Solve d2+10d=9 by completing the square.Solve r24r=12 by completing the square.Solve t210t=11 by completing the square.Solve y210y=35 by completing the square.Solve z2+8z=19 by completing the square.Solve x216x=16 by completing the square.Solve y2+8y=11 by completing the square.Solve a2+4a+9=30 by completing the square.Solve b2+8b4=16 by completing the square.Solve p2=5p+9 by completing the square.Solve q2=7q3 by completing the square.Solve (c2)(c+8)=7 by completing the square.Solve (d7)(d+3)=56 by completing the square.Solve 2m2+16m8=0 by completing the square.Solve 4n224n56=8 by completing the square.Solve 3r22r=21 by completing the square.Solve 4t2+2t=20 by completing the square.Solve 4x2+3x=12 by completing the square.Solve 5y2+3y=10 by completing the square.In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 57. a2+10a In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 58. b2+12b In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 59. m2+18m In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 60. n2+16n In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 61. m224m In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 62. n216n In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 63. p222p In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 64. q26q In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 65. x29x In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 66. y2+11y In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 67. p213p In the following exercises, complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. 68. q2+34q In the following exercises, solve by completing the square. 69. v2+6v=40 In the following exercises, solve by completing the square. 70. w2+8w=65 In the following exercises, solve by completing the square. 71. u2+2u=3 In the following exercises, solve by completing the square. 72. z2+12z=11 In the following exercises, solve by completing the square. 73. c212c=13 In the following exercises, solve by completing the square. 74. d28d=9 In the following exercises, solve by completing the square. 75. x220x=21 In the following exercises, solve by completing the square. 76. y22y=8 In the following exercises, solve by completing the square. 77. m2+4m=44 In the following exercises, solve by completing the square. 78. n22n=3 In the following exercises, solve by completing the square. 79. r2+6r=11 In the following exercises, solve by completing the square. 80. t214t=50 In the following exercises, solve by completing the square. 81. a210a=5 In the following exercises, solve by completing the square. 82. b2+6b=41 In the following exercises, solve by completing the square. 83. u214u+12=1 In the following exercises, solve by completing the square. 84. z2+2z5=2 In the following exercises, solve by completing the square. 85. v2=9v+2 In the following exercises, solve by completing the square. 86. w2=5w1 In the following exercises, solve by completing the square. 87. (x+6)(x2)=9 In the following exercises, solve by completing the square. 88. (y+9)(y+7)=79 In the following exercises, solve by completing the square. 89. 3m2+30m27=6 In the following exercises, solve by completing the square. 90.2n2+4n26=0 In the following exercises, solve by completing the square. 91. 2c2+c=6 In the following exercises, solve by completing the square. 92. 3d24d=15 In the following exercises, solve by completing the square. 93. 2p2+7p=14 In the following exercises, solve by completing the square. 94. 3q25q=9 Rafi is designing a rectangular playground to have an area of 320 square feet. He wants one side of the playground to be four feet longer than the other side. Solve the equation p2+4p=320 for p, the length of one side of the playground. What is the length of the other side?Yvette wants to put a square swimming pool in the corner of her backyard. She will have a 3 foot deck on the south side of the pool and a 9 foot deck on the west side of the pool. She has a total area of 1080 square feet for the pool and two decks. Solve the equation (s+3)(s+9)=1080 for s, the length of a side of the pool.Solve the equation x2+10x=25 (a) by using the Square Root Property and (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 3y25y+2=0 by using the Quadratic Formula.Solve 4z2+2z6=0 by using the Quadratic Formula.Solve a22a15=0 by using the Quadratic Formula.Solve b2+10b+24=0 by using the Quadratic Formula.Solve 2p2+8p+5=0 by using the Quadratic Formula.Solve 5q211q+3=0 by using the Quadratic Formula.Solve 3m2+12m+7=0 by using the Quadratic Formula.Solve 5n2+4n4=0 by using the Quadratic Formula.Solve 4a23a+8=0 by using the Quadratic Formula.Solve 5b2+2b+4=0 by using the Quadratic Formula.Solve x(x+2)5=0 by using the Quadratic Formula.Solve y(3y1)2=0 by using the Quadratic Formula.Solve 14c213c=112 by using the Quadratic Formula.Solve 19d212d=12 by using the Quadratic Formula.Solve r2+10r+25=0 by using the Quadratic Formula.Solve 25t240t=16 by using the Quadratic Formula.Determine the number of solutions to each quadratic equation: (a) 8m23m+6=0 (b) 5z2+6z2=0 (c) 9w2+24w+16=0 (d) 9u22u+4=0 Determine the number of solutions to each quadratic equation: (a) b2+7b13=0 (b) 5a26a+10=0 (c) 4r220r+25=0 (d) 7t211t+3=0 Identify the most appropriate method to use to solve each quadratic equation: (a) x2+6x+8=0 (b) (n3)2=16 (c) 5p26p=9 Identify the most appropriate method to use to solve each quadratic equation: (a) 8a2+3a9=0 (b) 4b2+4b+1=0 (c) 5c2=125 In the following exercises, solve by using the Quadratic Formula. 99. 4m2+m3=0 In the following exercises, solve by using the Quadratic Formula. 100. 4n29n+5=0 In the following exercises, solve by using the Quadratic Formula. 101. 2p27p+3=0 In the following exercises, solve by using the Quadratic Formula. 102. 3q2+8q3=0 In the following exercises, solve by using the Quadratic Formula. 103. p2+7p+12=0 In the following exercises, solve by using the Quadratic Formula. 104. q2+3q18=0 In the following exercises, solve by using the Quadratic Formula. 105. r28r33=0 In the following exercises, solve by using the Quadratic Formula. 106.t2+13t+40=0 In the following exercises, solve by using the Quadratic Formula. 107. 3u2+7u2=0 In the following exercises, solve by using the Quadratic Formula. 108. 6z29z+1=0 In the following exercises, solve by using the Quadratic Formula. 109.2a26a+3=0 In the following exercises, solve by using the Quadratic Formula. 110. 5b2+2b4=0 In the following exercises, solve by using the Quadratic Formula. 111. 2x2+3x+9=0 In the following exercises, solve by using the Quadratic Formula. 112. 6y25y+2=0 In the following exercises, solve by using the Quadratic Formula. 113. v(v+5)10=0 In the following exercises, solve by using the Quadratic Formula. 114. 3w(w2)8=0 In the following exercises, solve by using the Quadratic Formula. 115. 13m2+112m=14 In the following exercises, solve by using the Quadratic Formula. 116. 13n2+n=12 In the following exercises, solve by using the Quadratic Formula. 117. 16c2+24c+9=0 In the following exercises, solve by using the Quadratic Formula. 118. 25d260d+36=0 In the following exercises, solve by using the Quadratic Formula. 119. 5m2+2m7=0 In the following exercises, solve by using the Quadratic Formula. 120. 8n23n+3=0 In the following exercises, solve by using the Quadratic Formula. 121. p26p27=0 In the following exercises, solve by using the Quadratic Formula. 122. 25q2+30q+9=0 In the following exercises, solve by using the Quadratic Formula. 123. 4r2+3r5=0 In the following exercises, solve by using the Quadratic Formula. 124. 3t(t2)=2 In the following exercises, solve by using the Quadratic Formula. 125. 2a2+12a+5=0 In the following exercises, solve by using the Quadratic Formula. 126. 4d27d+2=0 In the following exercises, solve by using the Quadratic Formula. 127. 34b2+12b=38 In the following exercises, solve by using the Quadratic Formula. 128. 19c2+23c=3

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