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All Textbook Solutions for Elementary Algebra
In the following exercises, factor completely. 433. 24x3+44x2In the following exercises, factor completely. 434. 24a49a3In the following exercises, factor completely. 435. 16n256mn+49m2In the following exercises, factor completely. 436. 6a225a9In the following exercises, factor completely. 437. 5r2+22r48In the following exercises, factor completely. 438. 5u445u2In the following exercises, factor completely. 439. n481In the following exercises, factor completely. 440. 64j2+225In the following exercises, factor completely. 441. 5x2+5x60In the following exercises, factor completely. 442. b364In the following exercises, factor completely. 443. m3+125In the following exercises, factor completely. 444. 2b22bc+5cb5c2In the following exercises, solve. 445. (a3)(a+7)=0In the following exercises, solve. 446. (b3)(b+10)=0In the following exercises, solve. 447. 3m(2m5)(m+6)=0In the following exercises, solve. 448. 7n(3n+8)(n5)=0In the following exercises, solve. 449. x2+9x+20=0In the following exercises, solve. 450. y2y72=0In the following exercises, solve. 451. 2p211p=40In the following exercises, solve. 452. q3+3q2+2q=0In the following exercises, solve. 453. 144m225=0In the following exercises, solve. 454. 4n2=36In the following exercises, solve. 455. The product of two consecutive numbers is 462. Find the numbers.In the following exercises, solve. 456. The area of a rectangular shaped patio 400 square feet. The length of the patio is 9 feet more than its width. Find the length and width.In the following exercises, find the Greatest Common Factor in each expression. 457. 14y42In the following exercises, find the Greatest Common Factor in each expression. 458. 6x230xIn the following exercises, find the Greatest Common Factor in each expression. 459. 80a2+120a3In the following exercises, find the Greatest Common Factor in each expression. 460. 5m(m1)+3(m1)In the following exercises, factor completely. 461. x2+13x+36In the following exercises, factor completely. 462. p2+pq12q2In the following exercises, factor completely. 463. 3a36a272aIn the following exercises, factor completely. 464. s225s+84In the following exercises, factor completely. 465. 5n2+30n+45In the following exercises, factor completely. 466. 64y249In the following exercises, factor completely. 467. xy8y+7x56In the following exercises, factor completely. 468. 40r2+810In the following exercises, factor completely. 469. 9s212s+4In the following exercises, factor completely. 470. n2+12n+36In the following exercises, factor completely. 471. 100a2In the following exercises, factor completely. 472. 6x211x10In the following exercises, factor completely. 473. 3x275y2In the following exercises, factor completely. 474. c31000d3In the following exercises, factor completely. 475. ab3b2a+6In the following exercises, factor completely. 476. 6u2+3u18In the following exercises, factor completely. 477. 8m2+22m+5In the following exercises, solve. 478. x2+9x+20=0In the following exercises, solve. 479. y2=y+132In the following exercises, solve. 480. 5a2+26a=24In the following exercises, solve. 481. 9b29=0In the following exercises, solve. 482. 16m2=0In the following exercises, solve. 483. 4n2+19+21=0In the following exercises, solve. 484. (x3)(x+2)=6In the following exercises, solve. 485. The product of two consecutive integers is 156. Find the integers.In the following exercises, solve. 486. The area of a rectangular place mat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.Determine the values for which the rational expression is undefined: a.3yx b. 8n53n+1 c. a+10a2+4a+3Determine the values for which the rational expression is undefined: a. 4p5q b. y13y+2 c. m5m2+m6Evaluate y+12y3 for each value: a. y=1b. y=3c. y=0Evaluate 5x12x+1 for each value: a. x=1b. x=1 c. x=0Evaluate x2+1x23x+2 for each value: a. x=0 b. x=1 c. x=3Evaluate x2+x6x29 for each value: a. x=0b. x=2 c. x=1Evaluate 2a3ba2+2ab+b2 for each value: a. a=1,b=2b. a=0,b=1c. a=1,b=12Evaluate a2b28ab3 for each value: a. a=1,b=1 b. a=12,b=1c. a=2,b=1Simplify: 4581 .Simplify: 4254Simplify: 4x2y12xy2 .Simplify: 16x2y2xy2 .Simplify: 3x62x4 .Simplify: 7y+355y+25 .Simplify: x2x2x23x+2 .Simplify: x23x10x2+x2Simplify: x2+x6x24Simplify: x2+8x+7x249 .Simplify: y33y2+y3y2y6 .Simplify: p3p2+2p2p2+4p5 .Simplify: 2n210n4n216n20 .Simplify: 4x216x8x216x64 .Simplify: 2x212x+183x227 .Simplify: 5y230y+252y250 .Simplify : p364p216 .Simplify: x3+8x24 .Simplify: y22y .Simplify: n99n .Simplify: 102yy225 .Simplify: 3y2781y2 .Simplify: x24x525x2 .Simplify: x2+x21x2 .In the following exercises, determine the values for which the rational expression is undefined. 1.a. 2xz a. 4p16p5 b. n3n2+2n8In the following exercises, determine the values for which the rational expression is undefined. 2. a. 10m11n b. 6y+134y9 c. b8b236In the following exercises, determine the values for which the rational expression is undefined. 3. a. 4x2y3y b. 3x22x+1 c. u1u23u28In the following exercises, determine the values for which the rational expression is undefined. 4. a. 5pq29q b. 7a43a+5 c. 1x24In the following exercises, evaluate the rational expression for the given values. 5. 2xx1 a. x=0 b. x=2 c. x=1In the following exercises, evaluate the rational expression for the given values. 6. 4y15y3 a. y=0 b. y=2 c. y=1In the following exercises, evaluate the rational expression for the given values. 7. 2p+3p2+1 a. p=0 b. p=1 c. p=2In the following exercises, evaluate the rational expression for the given values. 8. x+323x a. x=0 b. x=1 c. x=2In the following exercises, evaluate the rational expression for the given values. 9. y2+5y+6y21 a. y=0 b. y=2 c. y=2In the following exercises, evaluate the rational expression for the given values. 10. z2+3z10z21 a. z=0 b. z=2 c. z=2In the following exercises, evaluate the rational expression for the given values. 11. a24a2+5a+4 a. a=0 b. a=1 c. a=2In the following exercises, evaluate the rational expression for the given values. 12. b2+2b23b4 a. b=0 b. b=2 c. b=2In the following exercises, evaluate the rational expression for the given values. 13. x2+3xy+2y22x3y a. x=1,y=1 b. x=2,y=1 c. x=1,y=2In the following exercises, evaluate the rational expression for the given values. 14. c2+cd2d2cd3 a. c=2,d=1 b. c=1,d=1 c. c=1,d=2In the following exercises, evaluate the rational expression for the given values. 15. m24n25mn3 a. m=2,n=1 b. m=1,n=1 c. m=3,n=2In the following exercises, evaluate the rational expression for the given values. 16. 2s2ts29t2 a. s=4,t=1 b. s=1,t=1 c. s=0,t=2In the following exercises, simplify. 17. 452In the following exercises, simplify. 18. 4455In the following exercises, simplify. 19. 5663In the following exercises, simplify. 20. 65104In the following exercises, simplify. 21. 6ab212a2bIn the following exercises, simplify. 22. 15xy3x3y3In the following exercises, simplify. 23. 8m3n12mn2In the following exercises, simplify. 24. 36v3w227vw3In the following exercises, simplify. 25. 3a+64a+8In the following exercises, simplify. 26. 5b+56b+6In the following exercises, simplify. 27. 3c95c15In the following exercises, simplify. 28. 4d+89d+18In the following exercises, simplify. 29. 7m+635m+45In the following exercises, simplify. 30. 8n963n36In the following exercises, simplify. 31. 12p2405p100In the following exercises, simplify. 32. 6q+2105q+175In the following exercises, simplify. 33. a2a12a28a+16In the following exercises, simplify. 34. x2+4x5x22x+1In the following exercises, simplify. 35. y2+3y4y26y+5In the following exercises, simplify. 36. v2+8v+15v2v12In the following exercises, simplify. 37. x225x2+2x15In the following exercises, simplify. 38. a24a2+6a16In the following exercises, simplify. 39. y22y3y29In the following exercises, simplify. 40. b2+9b+18b236In the following exercises, simplify. 41. y3+y2+y+1y2+2y+1In the following exercises, simplify. 42. p3+3p2+4p+12p2+p6In the following exercises, simplify. 43. x32x225x+50x225In the following exercises, simplify. 44. q3+3q24q12q24In the following exercises, simplify. 45. 3a2+15a6a2+6a36In the following exercises, simplify. 46. 8b232b2b26b80In the following exercises, simplify. 47. 5c210c10c2+30c+100In the following exercises, simplify. 48. 4d224d2d24d48In the following exercises, simplify. 49. 3m2+30m+754m2100In the following exercises, simplify. 50. 5n2+30n+452n218In the following exercises, simplify. 51. 5r2+30r35r249In the following exercises, simplify. 52. 3s2+30s+243s248In the following exercises, simplify. 53. t327t29In the following exercises, simplify. 54. v31v21In the following exercises, simplify. 55. w3+216w236In the following exercises, simplify. 56. v3+125v225In the following exercises, simplify each rational expression. 57. a55aIn the following exercises, simplify each rational expression. 58. b1212bIn the following exercises, simplify each rational expression. 59. 11cc11In the following exercises, simplify each rational expression. 60. 5dd5In the following exercises, simplify each rational expression. 61. 122xx236In the following exercises, simplify each rational expression. 62. 205yy216In the following exercises, simplify each rational expression. 63. 4v3264v2In the following exercises, simplify each rational expression. 64. 7w219w2In the following exercises, simplify each rational expression. 65. y211y+249y2In the following exercises, simplify each rational expression. 66. z29z+2016z2In the following exercises, simplify each rational expression. 67. a25z3681a2In the following exercises, simplify each rational expression. 68. b2+b4236b2Tax Rates For the tax year 2015, the amount of tax owed by a single person earning between $37,450 and $90,750, can be found by evaluating the formula 0.25x4206.25 , where x is income. The average tax rate for this income can be found by evaluating the formula 0.25x4206.25x . What would be the average tax rate for a single person earning $50,000?Work The length of time it takes for two people for perform the same task if they work together can be found by evaluating the formula xyx+y . If Tom can paint the den in x=45 minutes and his brother Bobby can paint it in y=60 minutes, how many minutes will it take them if they work together?Explain how you find the values of x for which the rational expression x2x20x24 is undefined.Explain all the steps you take to simplify the rational expression p2+4p219p2 .Multiply: 6101512 .Multiply: 201568 .Multiply: 3pqq25p2q6pq .Multiply: 6x3y7x22xy3x2yMultiply: 5xx2+5x+6x2410x .Multiply: 9x2x2+11x+30x2363x2 .Multiply: x225x23x10x+2x .Multiply: x24xx2+5x+6x+2x .Multiply: 12x6x2x2+8xx2+11x+24x24 .Multiply: 9v3v29v+36v2+7v+12v29 .Multiply: 3a21a29a+14a243a+6 .Multiply: b2bb2+9b10b2100b210b .Divide: c+35cc29c5 .Divide: 2dd44d24d .Divide: 2m2m28m8m2+24mm2+m6 .Divide: 15n23n2+33n5n5n2+9n22 .Divide: 3a28a3a2253a214a5a2+10a+25 .Divide: 4b2+7b21b24b2+15b4b22b+1 .Divide: x383x26x+12x246 .Divide: 2z2z21z3z2+zz31 .Divide: 2x214x164(x2+2x+1) .Divide: y26y+8y24y(3y212y) .Divide: 3x2+7x+24x+243x214x5x2+x30 .Divide: y2362y2+11y62y22y608y4 .Divide: 4m+43m15m23m10m24m3212m366m48 .Divide: 2n2+10nn1n2+10n+24n2+8n9n+48n2+12n .In the following exercises, multiply. 73. 1216410In the following exercises, multiply. 74. 3251624In the following exercises, multiply. 75. 1810430In the following exercises, multiply. 76. 21364524In the following exercises, multiply. 77. 5x2y412xy36x220y2In the following exercises, multiply. 78. 8w3y9y23y4w4In the following exercises, multiply. 79. 12a3bb22ab29b3In the following exercises, multiply. 80. 4mn25n3mn38m2n2In the following exercises, multiply. 81. 5p2p25p36p21610pIn the following exercises, multiply. 82. 3q2q2+q6q299qIn the following exercises, multiply. 83. 4rr23r10r2258r2In the following exercises, multiply. 84. ss29s+14s2497s2In the following exercises, multiply. 85. x27xx2+6x+9x+34xIn the following exercises, multiply. 86. 2y210yy2+10y+25y+56yIn the following exercises, multiply. 87. z2+3zz23z4z4z2In the following exercises, multiply. 88. 2a2+8aa29a+20a5a2In the following exercises, multiply. 89. 284b3b3b2+8b9b249In the following exercises, multiply. 90. 18c2c26c+30c2+7c+10c281In the following exercises, multiply. 91. 35d7d2d2+7dd2+12d+35d225In the following exercises, multiply. 92. 72m12m28m+32m2+10m+24m236In the following exercises, multiply. 93. 4n+20n2+n20n2164n+16In the following exercises, multiply. 94. 6p26pp2+7p18p2813p227pIn the following exercises, multiply. 95. q22qq2+6q16q264q28qIn the following exercises, multiply. 96. 2r22rr2+4r5r2252r210rthe following exercises, divide. 97. t63tt29t5In the following exercises, divide. 98. v511vv225v11In the following exercises, divide. 99. 10+ww8100w28wIn the following exercises, divide. 100. 7+xx649x2x+6In the following exercises, divide. 101. 27y23y213y2+18y2+13y+42In the following exercises, divide. 102. 24z22z84z28z211z+28In the following exercises, divide. 103. 16a24a+364a224aa2+4a45In the following exercises, divide. 104. 24b22b412b2+36bb211b+18In the following exercises, divide. 105. 5c2+9c+2c2253c214c5c2+10c+25In the following exercises, divide. 106. 2d2+d3d2162d29d18d28d+16In the following exercises, divide. 107. 6m22m109m26m2+29m20m26m+9In the following exercises, divide. 108. 2n23n1425n22n213n+21n210n+25In the following exercises, divide. 109. 3s2s216s34s2+16ss364In the following exercises, divide. 110. r2915r3275r2+15r+45In the following exercises, divide. 111. p3+q33p2+3pq+3q2p2q212In the following exercises, divide. 112. v38w32v2+4vw+8w2v24w24In the following exercises, divide. 113. t292t(t26t+9)In the following exercises, divide. 114. x2+3x104x(2x2+20x+50)In the following exercises, divide. 115. 2y210yz48z22y1(4y232yz)In the following exercises, divide. 116. 2m298n22m+6(m27mn)In the following exercises, divide. 117. 2a2a215a+20a2+7a+12a2+8a+16In the following exercises, divide. 118. 3b2+2b812b+183b2+2b82b27b15In the following exercises, divide. 119. 12c2122c23c+14c+46c213c+5In the following exercises, divide. 120. 4d2+7d235d+10d247d212d4In the following exercises, divide. 121. 10m2+80m3m9m2+4m21m29m+205m2+10m2m10In the following exercises, divide. 122. 4n2+32n3n+23n2n2n2+n30108n224nn+6In the following exercises, divide. 123. 12p2+3pp+3p2+2p63p2p12p79p39p2In the following exercises, divide. 124. 6q+39q29qq2+14q+33q2+4q54q2+12q12q+6Probability The director of large company is interviewing applicants for two identical jobs. If w = the number of women applicants and m = the number of men applicants, then the probability that two women are selected for the jobs is ww+mw1w+m1 . a. Simplify the probability by multiplying the two rational expressions. b.Find the probability that two women are selected when w = 5 and m = 10.Area of a triangle The area of a triangle with base b and height h is bh2 . If the triangle is stretched to make a new triangle with base and height three times as much as in the original triangle, the area is 9bh2 . Calculate how the area of the new triangle compares to the area of the original triangle by dividing 9bh2 by bh2 .Multiply a. 74910 and explain all your steps. b. Multiply nn39n+3 and explain all your steps. c. Evaluate your answer to part (b) when n=7 . Did you get the same answer you get in part (a)? Why or why not?a. Divide 2456and explain all your steps. b. Divide x21x(x+1) and explain all your steps. c. Evaluate your answer to part (b) when x=5 . Did you get the same answer you get in part (a)? Why or why not?Add: 716+516 .Add: 310+110 .Add: 5x2x+3+22x+3 .Add; xx2+1x2 .Add; 9x+14x+7+x2x+7 .Add: x2+8xx+5+15x+5 .Subtract: x2x+39x+3 .Subtract: 4x22x5252x5 .Subtract: n2n4n+12n4 .Subtract: y2y19y8y1 .Subtract: 4x211x+8x23x+23x2+x3x23x+2 .Subtract: 6x2x+20x2815x2+11x7x281 .Add: 8x152x5+2x52x .Add: 6y2+7y104y7+2y2+2y+1174y .Subtract: y25yy246y64y2 .Subtract: 2n2+8n1n21n27n11n2 .In the following exercises, add. 129. 215+715In the following exercises, add. 130. 421+321In the following exercises, add. 131. 724+1124In the following exercises, add. 132. 736+1336In the following exercises, add. 133. 3aab+1abIn the following exercises, add. 134. 3c4c5+54c5In the following exercises, add. 135. dd+8+5d+8In the following exercises, add. 136. 7m2m+n+42m+nIn the following exercises, add. 137. p2+10pp+2+16p+2In the following exercises, add. 138. q2+12qq+3+27q+3In the following exercises, add. 139. 2r22r1+15r82r1In the following exercises, add. 140. 3s23s2+13s103s2In the following exercises, add. 141. 8t2t+4+32tt+4In the following exercises, add. 142. 6v2v+5+30vv+5In the following exercises, add. 143. 2w2w216+8ww216In the following exercises, add. 144. 7x2x29+21xx29In the following exercises, subtract. 145. y2y+864y+8In the following exercises, subtract. 146. z2z+24z+2In the following exercises, subtract. 147. 9a23a7493a7In the following exercises, subtract. 148. 25b25b6365b6In the following exercises, subtract. 149. c2c86c+16c8In the following exercises, subtract. 150. d2d96d+27d9In the following exercises, subtract. 151. 3m26m3021m306m30In the following exercises, subtract. 152. 2n24n3230n164n32In the following exercises, subtract. 153. 6p2+3p+4p2+4p55p2+p+7p2+4p5In the following exercises, subtract. 154. 5q2+3q9q2+6q+84q2+9q+7q2+6q+8In the following exercises, subtract. 155. 5r2+7r33r2494r25r30r249In the following exercises, subtract. 156. 7t2t4t2256t2+2t1t225In the following exercises, add. 157. 10v2v1+2v+412vIn the following exercises, add. 158. 20w5w2+5w+625wIn the following exercises, add. 159. 10x2+16x78x3+2x2+3x138xIn the following exercises, add. 160. 6y2+2y113y7+3y23y+1773yIn the following exercises, subtract. 161. z2+6zz2253z+2025z2In the following exercises, subtract. 162. a2+3aa293a279a2In the following exercises, subtract. 163. 2b2+30b13b2492b25b849b2In the following exercises, subtract. 164. c2+5c10c216c28c1016c2Sarah ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. If r represents Sarah’s speed when she ran, then her running time is modeled by the expression 8r and her biking time is modeled by the expression 24r+4 . Add the rational expressions 8r+24r+4 to get an expression for the total amount of time Sarah ran and biked.If Pete can paint a wall in p hours, then in one hour he can paint 1p of the wall. It would take Penelope 3 hours longer than Pete to paint the wall, so in one hour she can paint 1p+3 of the wall. Add the rational expressions 1p+1p+3 to get an expression for the part of the wall Pete and Penelope would paint in one hour if they worked together.Donald thinks that 3x+4x is 72x . Is Donald correct? Explain.Explain how you find the Least Common Denominator of x2+5x+4 and x216 .Find the LCD for 2x2x12 , 1x216 .Find the LCD for xx2+8x+15 , 5x2+9x+18 .Rewrite as equivalent rational expressions with denominator (x+3)(x4)(x+4) : 2x2x12 , 1x216 .Rewrite as equivalent rational expressions with denominator (x+3)(x+5)(x+6) : xx2+8x+15 , 5x2+9x+18 .