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All Textbook Solutions for Intermediate Algebra

Is 4,962 divisible by (a) 2? (b) 3? (c) 5? (d) 6? (e)10?Is 3,765 divisible by (a) 2? (b) 3? (c) 5? (d) 6? (e) 10?Find the prime factorization of 80.Find the prime factorization of 60.Find the LCM of 9 and 12 using the Prime Factors Method.Find the LCM of 18 and 24 using the Prime Factors Method.Simplify: 305+10(32) .Simplify: 7010+4(62) .Simplify: 9+53[4(9+3)].Simplify: 722[4(5+1)].Evaluate when x=3 , (a) x2 (b) 4x (c) 3x2+4x+1 .Evaluate when x=6 , (a) x3 (b) 2x (c) 6x24x7 .Simplify: 3x2+7x+9+7x2+9x+8 .Simplify: 4y2+5y+2+8y2+4y+5 .Translate the English phrase into an algebraic expression: (a) the difference of 14x2and 13 (b) the quotient of 12x and 2 (c) 13 more than z (d) 18 less than 8x Translate the English phrase into an algebraic expression: (a) the sum of 17y2and 19 (b) the product of 7 and y (c) Eleven more than x (d) Fourteen less than 11a Translate the English phrase into an algebraic expression: (a) four times the sum of p and q(b) the sum of four times p and q.Translate the English phrase into an algebraic expression: (a) the difference of two times x and 8 (b) two times thedifference of x and 8.The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.The width of a rectangle is 6 less than the length. Let I represent the length of the rectangle. Write an expression for the width of the rectangle.Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 1. 84 In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 2. 96 In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 3. 896 In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 4. 942 In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 5. 22,335 In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10. 6. 39,075 In the following exercises, find the prime factorization. 7. 86 In the following exercises, find the prime factorization. 8. 78 In the following exercises, find the prime factorization. 9. 455 In the following exercises, find the prime factorization. 10. 400 In the following exercises, find the prime factorization. 11. 432 In the following exercises, find the prime factorization. 12. 627 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 13. 8, 12 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 14. 12, 16 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 15. 28, 40 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 16. 84, 90 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 17. 55, 88 In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 18. 60, 72 In the following exercises, simplify each expression. 19. 2312(95)In the following exercises, simplify each expression. 20. 3218(115)In the following exercises, simplify each expression. 21. 2+8(6+1)In the following exercises, simplify each expression. 22. 4+6(3+6)In the following exercises, simplify each expression. 23. 204+6(51)In the following exercises, simplify each expression. 24. 333+4(72)In the following exercises, simplify each expression. 25. 3(1+96)42 In the following exercises, simplify each expression. 26. 5(2+84)72 In the following exercises, simplify each expression. 27. 2[1+3(102)]In the following exercises, simplify each expression. 28. 5[2+4(32)]In the following exercises, simplify each expression. 29. 8+2[72(53)]32 In the following exercises, simplify each expression. 30. 10+3[62(42)]24 In the following exercises, evaluate the following expressions. 31. When x=2 , (a) x6 (b) 4x (c) 2x2+3x7 In the following exercises, evaluate the following expressions. 32. When x=3 , (a) x5 (b) 5x (c) 3x24x8 In the following exercises, evaluate the following expressions. 33. When x=4,y=1 x2+3xy7y2 In the following exercises, evaluate the following expressions. 34. When x=3,y=2 6x2+3xy9y2 In the following exercises, evaluate the following expressions. 35. When x=10,y=7 (xy)2 In the following exercises, evaluate the following expressions. 36. When a=3,b=8 a2+b2 In the following exercises, simplify the following expressions by combining like terms. 37. 7x+2+3x+4 In the following exercises, simplify the following expressions by combining like terms. 38. 8y+5+2y4 In the following exercises, simplify the following expressions by combining like terms. 39. 10a+7+5a2+7a4 In the following exercises, simplify the following expressions by combining like terms. 40. 7c+4+6c3+9c1 In the following exercises, simplify the following expressions by combining like terms. 41. 3x2+12x+11+14x2+8x+5 In the following exercises, simplify the following expressions by combining like terms. 42. 5b2+9b+10+2b2+3b4 In the following exercises, translate the phrases into algebraic expressions. 43. (a)the difference of 5x2and 6xy (b)the quotient of 6y2and 5x (c) Twenty-one more than y2 (d) 6x less than 81x2 In the following exercises, translate the phrases into algebraic expressions. 44. (a)the difference of 17x2and 5xy (b)the quotient of 8y3and 3x (c) Eighteen more than a2; (d) 11b less than 100b2 In the following exercises, translate the phrases into algebraic expressions. 45. (a)the sum of 4ab2and 3a2b (b)the product of 4y2and 5x (c) Fifteen more than m (d) 9x less than 121x2 In the following exercises, translate the phrases into algebraic expressions. 46. (a)the sum of 3x2y and 7xy2 (b)the product of 6xy2and 4z (c) Twelve more than 3x2 (d) 7x2less than 63x3 In the following exercises, translate the phrases into algebraic expressions. 47. (a)eight times the difference of y and nine (b)the difference of eight times y and 9 In the following exercises, translate the phrases into algebraic expressions. 48. (a)seven times the difference of y and one (b)the difference of seven times y and 1 In the following exercises, translate the phrases into algebraic expressions. 49. (a)five times the sum of 3x and y (b)the sum of five times 3x and y In the following exercises, translate the phrases into algebraic expressions. 50. (a)eleven times the sum of 4x2and 5x (b)the sum of eleven times 4x2and 5x In the following exercises, translate the phrases into algebraic expressions. 51. Eric has rock and country songs on his playlist. The number of rock songs is 14 more than twice the number of country songs. Let c represent the number of country songs. Write an expression for the number of rock songs.In the following exercises, translate the phrases into algebraic expressions. 52. The number of women in a Statistics class is 8 more than twice the number of men. Let m represent the number of men. Write an expression for the number of women.In the following exercises, translate the phrases into algebraic expressions. 53. Greg has nickels and pennies in his pocket. The number of pennies is seven less than three the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.In the following exercises, translate the phrases into algebraic expressions. 54. Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.Explain in your own words how to find the prime factorization of a composite number.Why is it important to use the order of operations to simplify an expression?Explain how you identify the like terms in the expression 8a2+4a+9a21 .Explain the difference between the phrases “4 times the sum of x and y” and “the sum of 4 times x and y”.Fill in < ,> , or = for each of the following pairs of numbers: (a) 9 __ |9| (b) 2 __ |2| (c) 8 __ |8| (d) (9) __ |9| .Fill in < , > , or = for each of the following pairs of numbers: (a) 7 __ |7| (b) (10) __ |10| (c) |4| __ |4| (d) 1 __ |1| .Simplify: 19|114(31)| .Simplify: 9|84(75)| .Add: (a) 2+(4) (b) 2+4 (c) 2+(4) .Add: (a) 2+(5) (b) 2+5 (c) 2+(5) .Subtract: (a) 64 (b) 6(4) (c) 64 (d) 6(4) .Subtract: (a) 74 (b) 7(4) (c) 74 (d) 7(4) .Simplify: (a) 2113 and 21+(13) (b) -11 - 7 and 11+(7) (c) 6(13) and 6+13 (d) 5(1) and 5+1 .Simplify: (a) 157 and 15+(7) (b) 148 and 14+(8) (c) 4(19) and 4+19 (d) 4(7) and 4+7 .Simplify: 8(31)9 .Simplify: 12(96)14 .Multiply or divide: (a) 115(5) (b) 512 (c) 9(7) (d) 637 .Multiply or divide: (a) 117(3) (b) 313 (c) 7(4) (d) 426 .Simplify: (a) (3)4 (b) 34 .Simplify: (a) (7)2 (b) 72 .Simplify: (a) 12(9)(3)3 (b) 273+(5)(6) .Simplify: (a) 18(4)(2)3 (b) 324+(2)(7) .Evaluate: 3x22xy+6y2 when x=1,y=2 .Evaluate: 4x2xy+5y2 when x=2,y=3 .Translate and simplify the sum of 9 and 16 , increased by 4.Translate and simplify the sum of 8 and 12 , increased by 7.The temperature in Anchorage, Alaska one morning was 15 degrees. By mid-afternoon the temperature haddropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?The temperature in Denver was 6 degrees at lunchtime. By sunset the temperature had dropped to 15 degrees. What was the difference in the lunchtime and sunset temperatures?In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 59. (a) |7| ___ |7| (b) 6 ___ |6| (c) |11| ___ 11 (d) (13) ___ |13|In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 60. (a) |9| ___ |9| (b) 8 ___ |8| (c) |1| ___ 1 (d) (14) ___ |14|In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 61. (a) |2| ___ |2| (b) 12 ___ |12| (c) |3| ___ 3 (d) (19) ___ |19|In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 62. (a) |4| ___ |4| (b) 5 ___ |5| (c) |10| ___ 10 (d) |0| ___ (0)In the following exercises, simplify. 63. |157||146|In the following exercises, simplify. 64. |178||134|In the following exercises, simplify. 65. 18|2(83)|In the following exercises, simplify. 66. 15|3(85)|In the following exercises, simplify. 67. 18|124(41)+3|In the following exercises, simplify. 68. 27|19+4(31)7|In the following exercises, simplify. 69. 103|93(31)|In the following exercises, simplify. 70. 132|112(52)|In the following exercises, simplify each expression. 71. (a) 7+(4) (b) 7+4 (c) 7+(4) .In the following exercises, simplify each expression. 72. (a) 5+(9) (b) 5+9 (c) 5+(9)In the following exercises, simplify each expression. 73. 48+(16)In the following exercises, simplify each expression. 74. 34+(19)In the following exercises, simplify each expression. 75. 14+(12)+4 In the following exercises, simplify each expression. 76. 17+(18)+6 In the following exercises, simplify each expression. 77. 19+2(3+8)In the following exercises, simplify each expression. 78. 24+3(5+9)In the following exercises, simplify each expression. 79. (a) 137 (b) 13(7) (c) 137 (d) 13(7)In the following exercises, simplify each expression. 80. (a) 158 (b) 15(8) (c) 158 (d) 15(8)In the following exercises, simplify each expression. 81. 1742 In the following exercises, simplify each expression. 82. 58(67)In the following exercises, simplify each expression. 83. 14(27)+9 In the following exercises, simplify each expression. 84. 64+(17)9 In the following exercises, simplify each expression. 85. (a) 4428 (b)44+(28)In the following exercises, simplify each expression. 86. (a) 3516 (b) 35+(16)In the following exercises, simplify each expression. 87. (a) 27(18) (b) 27+18 In the following exercises, simplify each expression. 88. (a) 46(37) (b) 46+37 In the following exercises, simplify each expression. 89. (27)(38)In the following exercises, simplify each expression. 90. (18)(29)In the following exercises, simplify each expression. 91. (68)(24)In the following exercises, simplify each expression. 92. (45)(78)In the following exercises, simplify each expression. 93. 25[10(312)]In the following exercises, simplify each expression. 94. 32[5(1520)]In the following exercises, multiply or divide. 95. (a) 48 (b) 13(5) (c) 246 (d) 52(4)In the following exercises, multiply or divide. 96. (a) 39 (b) 9(7) (c) 35(7) (d) -84 ÷ (-6)In the following exercises, multiply or divide. 97. (a) 287 (b) 18015 (c) 3(13) (d) 1(14)In the following exercises, multiply or divide. 98. (a) 364 (b) 19212 (c) 9(7) (d) 1(19)In the following exercises, simplify each expression. 99. (a) (2)6 (b) 26 In the following exercises, simplify each expression. 100. (a) (3)5 (b)35 In the following exercises, simplify each expression. 101. 5(6)+7(2)3 In the following exercises, simplify each expression. 102. 8(4)+5(4)6 In the following exercises, simplify each expression. 103. 3(5)(6)In the following exercises, simplify each expression. 104. 4(6)(3)In the following exercises, simplify each expression. 105. (811)(912)In the following exercises, simplify each expression. 106. (611)(813)In the following exercises, simplify each expression. 107. 263(27)In the following exercises, simplify each expression. 108. 232(46)In the following exercises, simplify each expression. 109. 65(5)+(28)(7)In the following exercises, simplify each expression. 110. 52(4)+(32)(8)In the following exercises, simplify each expression. 111. 92[38(2)]In the following exercises, simplify each expression. 112. 113[74(2)]In the following exercises, simplify each expression. 113. 8|24(41)+3|In the following exercises, simplify each expression. 114. 7|53(41)6|In the following exercises, simplify each expression. 115. 93|2(26)(37)|In the following exercises, simplify each expression. 116. 52|2(14)(25)|In the following exercises, simplify each expression. 117. (3)224(82)In the following exercises, simplify each expression. 118. (4)232(124)In the following exercises, evaluate each expression. 119. y+(14) when (a) y=33 (b) y=30 In the following exercises, evaluate each expression. 120. x+(21) when (a) x=27 (b) x=44 In the following exercises, evaluate each expression. 121. (x+y)2 when x=3,y=14 In the following exercises, evaluate each expression. 122. (y+z)2 when y=3,z=15 In the following exercises, evaluate each expression. 123. 9a2b8 When a=6 and b=3 In the following exercises, evaluate each expression. 124. 7m4n2 when m=4 and n=9 In the following exercises, evaluate each expression. 125. 3x24xy+2y2 when x=2,y=3 In the following exercises, evaluate each expression. 126. 4x2xy+3y2 when x=3,y=2 In the following exercises, translate to an algebraic expression and simplify if possible. 127. the sum of 3 and 15 , increased by 7 In the following exercises, translate to an algebraic expression and simplify if possible. 128. the sum of 8 and 9 , increased by 23 In the following exercises, translate to an algebraic expression and simplify if possible. 129. (a) the difference of 10 and18 (b) subtract 11 from 25 In the following exercises, translate to an algebraic expression and simplify if possible. 130. (a) the difference of 5 and 30 (b) subtract 6 from 13 In the following exercises, translate to an algebraic expression and simplify if possible. 131. the quotient of 6 and the sum of a and b In the following exercises, translate to an algebraic expression and simplify if possible. 132. the product of 13 and the difference of c and d In the following exercises, solve. 133. Temperature On January 15, the high temperature in Anaheim, California, was 84°. That same day, the high temperature in Embarrass, Minnesota, was 12 . What was the difference between the temperature in Anaheim and the temperature in Embarrass?In the following exercises, solve. 134. Temperature On January 21, the high temperature in Palm Springs, California, was 89°, and the high temperature in Whitefield, New Hampshire, was 31 . What was the difference between the temperature in Palm Springs and the temperature in Whitefield?In the following exercises, solve. 135. Football On the first down, the Chargers had the ball on their 25-yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?In the following exercises, solve. 136. Football On the first down, the Steelers had the ball on their 30-yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?In the following exercises, solve. 137. Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?In the following exercises, solve. 138. Checking Account Reymonte has a balance of 49 in his checking account. He deposits $281 to the account. What is the new balance?Explain why the sum of 8 and 2 is negative, but the sum of 8 and 2 is positive.Give an example from your life experience of adding two negative numbers.In your own words, state the rules for multiplying and dividing integers.Why is 43=(4)3 ?Simplify: 69120 .Simplify: 120192 .Multiply: 113(9a) .Multiply: 137(14b) .Divide: 727(3536) .Divide: 514(1528) .Simplify: a8ab6 .Simplify: p2pq8 .Add: 712+1115.Add: 1315+1720 .Simplify: (a) 3a489 (b) 3a489 .Simplify: (a) 4k516 (b) 4k516 .Simplify: 8(2)+4(3)5(2)+3 .Simplify: 7(1)+9(3)5(3)2 .Simplify: ( 1 3 )223+2 .Simplify: 1+42( 1 4 )2.Simplify: 13+123413 .Simplify: 231214+13 .Evaluate 3ab2 when a=23 and b=12 .Evaluate 4c3d when c=12 and d=43 .In the following exercises, simplify. 143. 10863 In the following exercises, simplify. 144. 10448 In the following exercises, simplify. 145. 120252 In the following exercises, simplify. 146. 182294 In the following exercises, simplify. 147. 14x221y In the following exercises, simplify. 148. 24a32b2 In the following exercises, simplify. 149. 210a2110ab2 In the following exercises, simplify. 150. 30x2105y2 In the following exercises, perform the indicated operation. 151. 34(49)In the following exercises, perform the indicated operation. 152. 38415 In the following exercises, perform the indicated operation. 153. (1415)(920)In the following exercises, perform the indicated operation. 154. (910)(2533)In the following exercises, perform the indicated operation. 155.(6384)(4490)In the following exercises, perform the indicated operation. 156. (3360)(4088)In the following exercises, perform the indicated operation. 157. 3721n In the following exercises, perform the indicated operation. 158. 5630m In the following exercises, perform the indicated operation. 159. 34x11 In the following exercises, perform the indicated operation. 160.25y9 In the following exercises, perform the indicated operation. 161. 518(1524)In the following exercises, perform the indicated operation. 162.718(1427)In the following exercises, perform the indicated operation. 163. 8u1512v25 In the following exercises, perform the indicated operation. 164. 12r2518s35 In the following exercises, perform the indicated operation. 165. 34(12)In the following exercises, perform the indicated operation. 166. 15(53)In the following exercises, simplify. 167. 8211235 In the following exercises, simplify. 168. 9163340 In the following exercises, simplify. 169.452 In the following exercises, simplify. 170.5310 In the following exercises, simplify. 171. m3n2 In the following exercises, simplify. 172. 38y12 In the following exercises, add or subtract. 173.712+58 In the following exercises, add or subtract. 174.512+38 In the following exercises, add or subtract. 175. 712916 In the following exercises, add or subtract. 176. 716512 In the following exercises, add or subtract. 177. 1330+2542 In the following exercises, add or subtract. 178. 2330+548 In the following exercises, add or subtract. 179. 39562235 In the following exercises, add or subtract. 180. 33491835 In the following exercises, add or subtract. 181. 23(34)In the following exercises, add or subtract. 182. 34(45)In the following exercises, add or subtract. 183. x3+14 In the following exercises, add or subtract. 184. x514 In the following exercises, add or subtract. 185. (a) 23+16 (b) 2316 In the following exercises, add or subtract. 186. (a) 2518 (b) 2518 In the following exercises, add or subtract. 187. (a) 5n6815 (b) 5n6815 In the following exercises, add or subtract. 188. (a) 3a8712 (b) 3a8712 In the following exercises, add or subtract. 189. (a) 4x956 (b) 4k956 In the following exercises, add or subtract. 190. (a)3y843 (b) 3y843 In the following exercises, add or subtract. 191. (a) 5a3+(106) (b) 5a3(106)In the following exercises, add or subtract. 192. (a) 2b5+815 (b) 2b5815 In the following exercises, simplify. 193. 56344523 In the following exercises, simplify. 194 8976 5692 In the following exercises, simplify. 195. 523235 In the following exercises, simplify. 196. 624246 In the following exercises, simplify. 197. 742(85)9335 In the following exercises, simplify. 198. 973(128)8766 In the following exercises, simplify. 199. 9(82)3(157)6(71)3(179)In the following exercises, simplify. 200. 8(92)4(149)7(83)3(169)In the following exercises, simplify. 201.23+42( 2 3 )2 In the following exercises, simplify. 202.3332( 3 4 )2 In the following exercises, simplify. 203. ( 3 5 )2( 3 7 )2 In the following exercises, simplify. 204. ( 3 4 )2( 5 8 )2 In the following exercises, simplify. 205. 213+15 In the following exercises, simplify. 206. 514+13 drymlIn the following exercises, simplify. 207. 782312+38 In the following exercises, simplify. 208. 343514+25 In the following exercises, simplify. 209. 38(310)In the following exercises, simplify. 210. 312(59)In the following exercises, simplify. 211.] 38+512 In the following exercises, simplify. 212. 18+712 In the following exercises, simplify. 213. 715y4 In the following exercises, simplify. 214. 38x11 In the following exercises, simplify. 215.1112a9a16 In the following exercises, simplify. 216. 10y13815y In the following exercises, simplify. 217. 12+23512 In the following exercises, simplify. 218. 13+2534 In the following exercises, simplify. 219. 135110 In the following exercises, simplify. 220. 156112 In the following exercises, simplify. 221. 3816+34 In the following exercises, simplify. 222. 25+5834 In the following exercises, simplify. 223. 12(920415)In the following exercises, simplify. 224. 8(151656)In the following exercises, simplify. 225. 58+161924 In the following exercises, simplify. 226. 16+3101430 In the following exercises, simplify. 227. (59+16)(2312)In the following exercises, simplify. 228. (34+16)(5813)In the following exercises, evaluate. 229. 710w when(a) w=12 (b)w=12 In the following exercises, evaluate. 230. 512w when(a) w=14 (b)w=14 In the following exercises, evaluate. 231. 2x2y3 when x=23 and y=12 In the following exercises, evaluate. 232. 8u2v3 when u=34 and v=12 In the following exercises, evaluate. 233. a+bab when a=3,b=8 In the following exercises, evaluate. 234. rsr+s when r=10,s=5

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