Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 8.9, Problem 481E
In the following exercises, solve.
481. The area of a
a. Write the equation that relates the area to the radius.
b. What is the area of a personal pizza with a radius 4 inches?
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Chapter 8 Solutions
Elementary Algebra
Ch. 8.1 - Determine the values for which the rational...Ch. 8.1 - Determine the values for which the rational...Ch. 8.1 - Evaluate y+12y3 for each value: a. y=1b. y=3c. y=0Ch. 8.1 - Evaluate 5x12x+1 for each value: a. x=1b. x=1 c....Ch. 8.1 - Evaluate x2+1x23x+2 for each value: a. x=0 b. x=1 ...Ch. 8.1 - Evaluate x2+x6x29 for each value: a. x=0b. x=2 c....Ch. 8.1 - Evaluate 2a3ba2+2ab+b2 for each value: a....Ch. 8.1 - Evaluate a2b28ab3 for each value: a. a=1,b=1 b....Ch. 8.1 - Simplify: 4581 .Ch. 8.1 - Simplify: 4254
Ch. 8.1 - Simplify: 4x2y12xy2 .Ch. 8.1 - Simplify: 16x2y2xy2 .Ch. 8.1 - Simplify: 3x62x4 .Ch. 8.1 - Simplify: 7y+355y+25 .Ch. 8.1 - Simplify: x2x2x23x+2 .Ch. 8.1 - Simplify: x23x10x2+x2Ch. 8.1 - Simplify: x2+x6x24Ch. 8.1 - Simplify: x2+8x+7x249 .Ch. 8.1 - Simplify: y33y2+y3y2y6 .Ch. 8.1 - Simplify: p3p2+2p2p2+4p5 .Ch. 8.1 - Simplify: 2n210n4n216n20 .Ch. 8.1 - Simplify: 4x216x8x216x64 .Ch. 8.1 - Simplify: 2x212x+183x227 .Ch. 8.1 - Simplify: 5y230y+252y250 .Ch. 8.1 - Simplify : p364p216 .Ch. 8.1 - Simplify: x3+8x24 .Ch. 8.1 - Simplify: y22y .Ch. 8.1 - Simplify: n99n .Ch. 8.1 - Simplify: 102yy225 .Ch. 8.1 - Simplify: 3y2781y2 .Ch. 8.1 - Simplify: x24x525x2 .Ch. 8.1 - Simplify: x2+x21x2 .Ch. 8.1 - In the following exercises, determine the values...Ch. 8.1 - In the following exercises, determine the values...Ch. 8.1 - In the following exercises, determine the values...Ch. 8.1 - In the following exercises, determine the values...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, evaluate the rational...Ch. 8.1 - In the following exercises, simplify. 17. 452Ch. 8.1 - In the following exercises, simplify. 18. 4455Ch. 8.1 - In the following exercises, simplify. 19. 5663Ch. 8.1 - In the following exercises, simplify. 20. 65104Ch. 8.1 - In the following exercises, simplify. 21....Ch. 8.1 - In the following exercises, simplify. 22....Ch. 8.1 - In the following exercises, simplify. 23....Ch. 8.1 - In the following exercises, simplify. 24....Ch. 8.1 - In the following exercises, simplify. 25. 3a+64a+8Ch. 8.1 - In the following exercises, simplify. 26. 5b+56b+6Ch. 8.1 - In the following exercises, simplify. 27. 3c95c15Ch. 8.1 - In the following exercises, simplify. 28....Ch. 8.1 - In the following exercises, simplify. 29....Ch. 8.1 - In the following exercises, simplify. 30. 8n963n36Ch. 8.1 - In the following exercises, simplify. 31....Ch. 8.1 - In the following exercises, simplify. 32....Ch. 8.1 - In the following exercises, simplify. 33....Ch. 8.1 - In the following exercises, simplify. 34....Ch. 8.1 - In the following exercises, simplify. 35....Ch. 8.1 - In the following exercises, simplify. 36....Ch. 8.1 - In the following exercises, simplify. 37....Ch. 8.1 - In the following exercises, simplify. 38....Ch. 8.1 - In the following exercises, simplify. 39. y22y3y29Ch. 8.1 - In the following exercises, simplify. 40....Ch. 8.1 - In the following exercises, simplify. 41....Ch. 8.1 - In the following exercises, simplify. 42....Ch. 8.1 - In the following exercises, simplify. 43....Ch. 8.1 - In the following exercises, simplify. 44....Ch. 8.1 - In the following exercises, simplify. 45....Ch. 8.1 - In the following exercises, simplify. 46....Ch. 8.1 - In the following exercises, simplify. 47....Ch. 8.1 - In the following exercises, simplify. 48....Ch. 8.1 - In the following exercises, simplify. 49....Ch. 8.1 - In the following exercises, simplify. 50....Ch. 8.1 - In the following exercises, simplify. 51....Ch. 8.1 - In the following exercises, simplify. 52....Ch. 8.1 - In the following exercises, simplify. 53. t327t29Ch. 8.1 - In the following exercises, simplify. 54. v31v21Ch. 8.1 - In the following exercises, simplify. 55....Ch. 8.1 - In the following exercises, simplify. 56....Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - In the following exercises, simplify each rational...Ch. 8.1 - Tax Rates For the tax year 2015, the amount of tax...Ch. 8.1 - Work The length of time it takes for two people...Ch. 8.1 - Explain how you find the values of x for which the...Ch. 8.1 - Explain all the steps you take to simplify the...Ch. 8.2 - Multiply: 6101512 .Ch. 8.2 - Multiply: 201568 .Ch. 8.2 - Multiply: 3pqq25p2q6pq .Ch. 8.2 - Multiply: 6x3y7x22xy3x2yCh. 8.2 - Multiply: 5xx2+5x+6x2410x .Ch. 8.2 - Multiply: 9x2x2+11x+30x2363x2 .Ch. 8.2 - Multiply: x225x23x10x+2x .Ch. 8.2 - Multiply: x24xx2+5x+6x+2x .Ch. 8.2 - Multiply: 12x6x2x2+8xx2+11x+24x24 .Ch. 8.2 - Multiply: 9v3v29v+36v2+7v+12v29 .Ch. 8.2 - Multiply: 3a21a29a+14a243a+6 .Ch. 8.2 - Multiply: b2bb2+9b10b2100b210b .Ch. 8.2 - Divide: c+35cc29c5 .Ch. 8.2 - Divide: 2dd44d24d .Ch. 8.2 - Divide: 2m2m28m8m2+24mm2+m6 .Ch. 8.2 - Divide: 15n23n2+33n5n5n2+9n22 .Ch. 8.2 - Divide: 3a28a3a2253a214a5a2+10a+25 .Ch. 8.2 - Divide: 4b2+7b21b24b2+15b4b22b+1 .Ch. 8.2 - Divide: x383x26x+12x246 .Ch. 8.2 - Divide: 2z2z21z3z2+zz31 .Ch. 8.2 - Divide: 2x214x164(x2+2x+1) .Ch. 8.2 - Divide: y26y+8y24y(3y212y) .Ch. 8.2 - Divide: 3x2+7x+24x+243x214x5x2+x30 .Ch. 8.2 - Divide: y2362y2+11y62y22y608y4 .Ch. 8.2 - Divide: 4m+43m15m23m10m24m3212m366m48 .Ch. 8.2 - Divide: 2n2+10nn1n2+10n+24n2+8n9n+48n2+12n .Ch. 8.2 - In the following exercises, multiply. 73. 1216410Ch. 8.2 - In the following exercises, multiply. 74. 3251624Ch. 8.2 - In the following exercises, multiply. 75. 1810430Ch. 8.2 - In the following exercises, multiply. 76. 21364524Ch. 8.2 - In the following exercises, multiply. 77....Ch. 8.2 - In the following exercises, multiply. 78....Ch. 8.2 - In the following exercises, multiply. 79....Ch. 8.2 - In the following exercises, multiply. 80....Ch. 8.2 - In the following exercises, multiply. 81....Ch. 8.2 - In the following exercises, multiply. 82....Ch. 8.2 - In the following exercises, multiply. 83....Ch. 8.2 - In the following exercises, multiply. 84....Ch. 8.2 - In the following exercises, multiply. 85....Ch. 8.2 - In the following exercises, multiply. 86....Ch. 8.2 - In the following exercises, multiply. 87....Ch. 8.2 - In the following exercises, multiply. 88....Ch. 8.2 - In the following exercises, multiply. 89....Ch. 8.2 - In the following exercises, multiply. 90....Ch. 8.2 - In the following exercises, multiply. 91....Ch. 8.2 - In the following exercises, multiply. 92....Ch. 8.2 - In the following exercises, multiply. 93....Ch. 8.2 - In the following exercises, multiply. 94....Ch. 8.2 - In the following exercises, multiply. 95....Ch. 8.2 - In the following exercises, multiply. 96....Ch. 8.2 - the following exercises, divide. 97. t63tt29t5Ch. 8.2 - In the following exercises, divide. 98....Ch. 8.2 - In the following exercises, divide. 99....Ch. 8.2 - In the following exercises, divide. 100....Ch. 8.2 - In the following exercises, divide. 101....Ch. 8.2 - In the following exercises, divide. 102....Ch. 8.2 - In the following exercises, divide. 103....Ch. 8.2 - In the following exercises, divide. 104....Ch. 8.2 - In the following exercises, divide. 105....Ch. 8.2 - In the following exercises, divide. 106....Ch. 8.2 - In the following exercises, divide. 107....Ch. 8.2 - In the following exercises, divide. 108....Ch. 8.2 - In the following exercises, divide. 109....Ch. 8.2 - In the following exercises, divide. 110....Ch. 8.2 - In the following exercises, divide. 111....Ch. 8.2 - In the following exercises, divide. 112....Ch. 8.2 - In the following exercises, divide. 113....Ch. 8.2 - In the following exercises, divide. 114....Ch. 8.2 - In the following exercises, divide. 115....Ch. 8.2 - In the following exercises, divide. 116....Ch. 8.2 - In the following exercises, divide. 117....Ch. 8.2 - In the following exercises, divide. 118....Ch. 8.2 - In the following exercises, divide. 119....Ch. 8.2 - In the following exercises, divide. 120....Ch. 8.2 - In the following exercises, divide. 121....Ch. 8.2 - In the following exercises, divide. 122....Ch. 8.2 - In the following exercises, divide. 123....Ch. 8.2 - In the following exercises, divide. 124....Ch. 8.2 - Probability The director of large company is...Ch. 8.2 - Area of a triangle The area of a triangle with...Ch. 8.2 - Multiply a. 74910 and explain all your steps. b....Ch. 8.2 - a. Divide 2456and explain all your steps. b....Ch. 8.3 - Add: 716+516 .Ch. 8.3 - Add: 310+110 .Ch. 8.3 - Add: 5x2x+3+22x+3 .Ch. 8.3 - Add; xx2+1x2 .Ch. 8.3 - Add; 9x+14x+7+x2x+7 .Ch. 8.3 - Add: x2+8xx+5+15x+5 .Ch. 8.3 - Subtract: x2x+39x+3 .Ch. 8.3 - Subtract: 4x22x5252x5 .Ch. 8.3 - Subtract: n2n4n+12n4 .Ch. 8.3 - Subtract: y2y19y8y1 .Ch. 8.3 - Subtract: 4x211x+8x23x+23x2+x3x23x+2 .Ch. 8.3 - Subtract: 6x2x+20x2815x2+11x7x281 .Ch. 8.3 - Add: 8x152x5+2x52x .Ch. 8.3 - Add: 6y2+7y104y7+2y2+2y+1174y .Ch. 8.3 - Subtract: y25yy246y64y2 .Ch. 8.3 - Subtract: 2n2+8n1n21n27n11n2 .Ch. 8.3 - In the following exercises, add. 129. 215+715Ch. 8.3 - In the following exercises, add. 130. 421+321Ch. 8.3 - In the following exercises, add. 131. 724+1124Ch. 8.3 - In the following exercises, add. 132. 736+1336Ch. 8.3 - In the following exercises, add. 133. 3aab+1abCh. 8.3 - In the following exercises, add. 134. 3c4c5+54c5Ch. 8.3 - In the following exercises, add. 135. dd+8+5d+8Ch. 8.3 - In the following exercises, add. 136. 7m2m+n+42m+nCh. 8.3 - In the following exercises, add. 137....Ch. 8.3 - In the following exercises, add. 138....Ch. 8.3 - In the following exercises, add. 139....Ch. 8.3 - In the following exercises, add. 140....Ch. 8.3 - In the following exercises, add. 141....Ch. 8.3 - In the following exercises, add. 142....Ch. 8.3 - In the following exercises, add. 143....Ch. 8.3 - In the following exercises, add. 144....Ch. 8.3 - In the following exercises, subtract. 145....Ch. 8.3 - In the following exercises, subtract. 146....Ch. 8.3 - In the following exercises, subtract. 147....Ch. 8.3 - In the following exercises, subtract. 148....Ch. 8.3 - In the following exercises, subtract. 149....Ch. 8.3 - In the following exercises, subtract. 150....Ch. 8.3 - In the following exercises, subtract. 151....Ch. 8.3 - In the following exercises, subtract. 152....Ch. 8.3 - In the following exercises, subtract. 153....Ch. 8.3 - In the following exercises, subtract. 154....Ch. 8.3 - In the following exercises, subtract. 155....Ch. 8.3 - In the following exercises, subtract. 156....Ch. 8.3 - In the following exercises, add. 157....Ch. 8.3 - In the following exercises, add. 158....Ch. 8.3 - In the following exercises, add. 159....Ch. 8.3 - In the following exercises, add. 160....Ch. 8.3 - In the following exercises, subtract. 161....Ch. 8.3 - In the following exercises, subtract. 162....Ch. 8.3 - In the following exercises, subtract. 163....Ch. 8.3 - In the following exercises, subtract. 164....Ch. 8.3 - Sarah ran 8 miles and then biked 24 miles. Her...Ch. 8.3 - If Pete can paint a wall in p hours, then in one...Ch. 8.3 - Donald thinks that 3x+4x is 72x . Is Donald...Ch. 8.3 - Explain how you find the Least Common Denominator...Ch. 8.4 - Find the LCD for 2x2x12 , 1x216 .Ch. 8.4 - Find the LCD for xx2+8x+15 , 5x2+9x+18 .Ch. 8.4 - Rewrite as equivalent rational expressions with...Ch. 8.4 - Rewrite as equivalent rational expressions with...Ch. 8.4 - Add: 1130+712 .Ch. 8.4 - Add: 38+920 .Ch. 8.4 - Add: 215a2b+56ab2 .Ch. 8.4 - Add: 516c+38cd2 .Ch. 8.4 - Add: 2x2+5x+3 .Ch. 8.4 - Add: 4m+3+3m+4 .Ch. 8.4 - Add: 5xxyy2+2xx2+y2 .Ch. 8.4 - Add: 72m+6+4m2+4m+3 .Ch. 8.4 - Add: 1m2m2+5mm2+3m+2 .Ch. 8.4 - Add: 2nn23n10+6n2+5n+6 .Ch. 8.4 - Subtract: yy+4y2y5 .Ch. 8.4 - Subtract: z+3z+2zz+3 .Ch. 8.4 - Subtract: 2xx241x+2 .Ch. 8.4 - Subtract: 3z+36zz29 .Ch. 8.4 - Subtract: 3x1x25x626x .Ch. 8.4 - Subtract: 2y2y2+2y8y12y .Ch. 8.4 - Subtract: 2x+1x73 .Ch. 8.4 - Subtract: 4y+32y15Ch. 8.4 - Simplify: vv+1+3v16v21 .Ch. 8.4 - Simplify: 3ww+2+2w+717w+4w2+9w+14 .Ch. 8.4 - In the following exercises, find the LCD. 169....Ch. 8.4 - In the following exercises, find the LCD. 170....Ch. 8.4 - In the following exercises, find the LCD. 171....Ch. 8.4 - In the following exercises, find the LCD. 172....Ch. 8.4 - In the following exercises, find the LCD. 173....Ch. 8.4 - the following exercises, find the LCD. 174....Ch. 8.4 - In the following exercises, find the LCD. 175....Ch. 8.4 - In the following exercises, find the LCD. 176....Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, write as equivalent...Ch. 8.4 - In the following exercises, add. 185. 524+1136Ch. 8.4 - In the following exercises, add. 186. 730+1345Ch. 8.4 - In the following exercises, add. 187. 920+1130Ch. 8.4 - In the following exercises, add. 188. 827+718Ch. 8.4 - In the following exercises, add. 189....Ch. 8.4 - In the following exercises, add. 190....Ch. 8.4 - In the following exercises, add. 191. 12m+78m2nCh. 8.4 - In the following exercises, add. 192. 56p2q+14pCh. 8.4 - In the following exercises, add. 193. 3r+4+2r5Ch. 8.4 - In the following exercises, add. 194. 4s7+5s+3Ch. 8.4 - In the following exercises, add. 195. 8t+5+6t5Ch. 8.4 - In the following exercises, add. 196. 7v+5+9v5Ch. 8.4 - In the following exercises, add. 197. 53w2+2w+1Ch. 8.4 - In the following exercises, add. 198. 42x+5+2x1Ch. 8.4 - In the following exercises, add. 199. 2yy+3+3y1Ch. 8.4 - In the following exercises, add. 200. 3zz2+1z+5Ch. 8.4 - In the following exercises, add. 201....Ch. 8.4 - In the following exercises, add. 202. 4cd+3c+1d29Ch. 8.4 - In the following exercises, add. 203....Ch. 8.4 - In the following exercises, add. 204. 34n+4+6n2n2Ch. 8.4 - In the following exercises, add. 205....Ch. 8.4 - In the following exercises, add. 206....Ch. 8.4 - In the following exercises, add. 207....Ch. 8.4 - In the following exercises, add. 208....Ch. 8.4 - In the following exercises, subtract. 209....Ch. 8.4 - In the following exercises, subtract. 210....Ch. 8.4 - In the following exercises, subtract. 211....Ch. 8.4 - In the following exercises, subtract. 212....Ch. 8.4 - In the following exercises, subtract. 213....Ch. 8.4 - In the following exercises, subtract. 214....Ch. 8.4 - In the following exercises, subtract. 215....Ch. 8.4 - In the following exercises, subtract. 216....Ch. 8.4 - In the following exercises, subtract. 217....Ch. 8.4 - In the following exercises, subtract. 218....Ch. 8.4 - In the following exercises, subtract. 219....Ch. 8.4 - In the following exercises, subtract. 220....Ch. 8.4 - In the following exercises, subtract. 221....Ch. 8.4 - In the following exercises, subtract. 222....Ch. 8.4 - In the following exercises, subtract. 223....Ch. 8.4 - In the following exercises, subtract. 224....Ch. 8.4 - In the following exercises, subtract. 225. 5v2v+34Ch. 8.4 - In the following exercises, subtract. 226....Ch. 8.4 - In the following exercises, subtract. 227....Ch. 8.4 - In the following exercises, subtract. 228....Ch. 8.4 - In the following exercises, add and subtract. 229....Ch. 8.4 - In the following exercises, add and subtract. 230....Ch. 8.4 - In the following exercises, add and subtract. 231....Ch. 8.4 - In the following exercises, add and subtract. 232....Ch. 8.4 - In the following exercises, simplify. 233....Ch. 8.4 - In the following exercises, simplify. 234....Ch. 8.4 - In the following exercises, simplify. 235....Ch. 8.4 - In the following exercises, simplify. 236....Ch. 8.4 - In the following exercises, simplify. 237....Ch. 8.4 - In the following exercises, simplify. 238....Ch. 8.4 - In the following exercises, simplify. 239....Ch. 8.4 - In the following exercises, simplify. 240....Ch. 8.4 - In the following exercises, simplify. 241....Ch. 8.4 - In the following exercises, simplify. 242....Ch. 8.4 - In the following exercises, simplify. 243....Ch. 8.4 - In the following exercises, simplify. 244....Ch. 8.4 - In the following exercises, simplify. 245....Ch. 8.4 - In the following exercises, simplify. 246. 3y1y+42Ch. 8.4 - In the following exercises, simplify. 247....Ch. 8.4 - In the following exercises, simplify. 248....Ch. 8.4 - In the following exercises, simplify. 249....Ch. 8.4 - In the following exercises, simplify. 250....Ch. 8.4 - Decorating cupcakes Victoria can decorate an order...Ch. 8.4 - Kayaking When Trina kayaks upriver, it takes her...Ch. 8.4 - Felipe thinks 1x+1y is 2x+y . a. Choose numerical...Ch. 8.4 - Simplify the expression 4n2+6n+91n29 and explain...Ch. 8.5 - Simplify: 2x213x+1 .Ch. 8.5 - Simplify: 1x27x+122x4 .Ch. 8.5 - Simplify: 12+2356+112 .Ch. 8.5 - Simplify: 341318+56 .Ch. 8.5 - Simplify: 1x+1y1x1y .Ch. 8.5 - Simplify: 1a+1b1a21b2 .Ch. 8.5 - Simplify: b3bb+52b+5+1b5 .Ch. 8.5 - Simplify: 13c+41c+4+c3 .Ch. 8.5 - Simplify: 12+15110+15 .Ch. 8.5 - Simplify: 14+3812516 .Ch. 8.5 - Simplify: 1a+1babba .Ch. 8.5 - Simplify: 1x21y21x+1y .Ch. 8.5 - Simplify: 3x+25x2+3x24 .Ch. 8.5 - Simplify: 2x71x+76x+71x249 .Ch. 8.5 - Simplify: 3x2+7x+104x+2+1x+5Ch. 8.5 - Simplify: 4yy+5+2y+63yy2+11y+30 .Ch. 8.5 - Simplify: xx+31+1x+3 .Ch. 8.5 - Simplify: 1+1x13x+1 .Ch. 8.5 - In the following exercises, simplify. 255....Ch. 8.5 - In the following exercises, simplify. 256....Ch. 8.5 - In the following exercises, simplify. 257....Ch. 8.5 - In the following exercises, simplify. 258....Ch. 8.5 - In the following exercises, simplify. 259....Ch. 8.5 - In the following exercises, simplify. 260....Ch. 8.5 - In the following exercises, simplify. 261....Ch. 8.5 - In the following exercises, simplify. 262....Ch. 8.5 - In the following exercises, simplify. 263....Ch. 8.5 - In the following exercises, simplify. 264....Ch. 8.5 - In the following exercises, simplify. 265....Ch. 8.5 - In the following exercises, simplify. 266....Ch. 8.5 - In the following exercises, simplify. 267....Ch. 8.5 - In the following exercises, simplify. 268....Ch. 8.5 - In the following exercises, simplify. 269....Ch. 8.5 - In the following exercises, simplify. 270....Ch. 8.5 - In the following exercises, simplify. 271....Ch. 8.5 - In the following exercises, simplify. 272....Ch. 8.5 - In the following exercises, simplify. 273....Ch. 8.5 - In the following exercises, simplify. 274....Ch. 8.5 - In the following exercises, simplify. 275....Ch. 8.5 - In the following exercises, simplify. 276....Ch. 8.5 - In the following exercises, simplify. 277....Ch. 8.5 - In the following exercises, simplify. 278....Ch. 8.5 - In the following exercises, simplify. 279....Ch. 8.5 - In the following exercises, simplify. 280....Ch. 8.5 - In the following exercises, simplify. 281....Ch. 8.5 - In the following exercises, simplify. 282....Ch. 8.5 - In the following exercises, simplify. 283....Ch. 8.5 - In the following exercises, simplify. 284....Ch. 8.5 - In the following exercises, simplify. 285....Ch. 8.5 - In the following exercises, simplify. 286....Ch. 8.5 - In the following exercises, simplify. 287....Ch. 8.5 - In the following exercises, simplify. 288....Ch. 8.5 - In the following exercises, simplify. 289....Ch. 8.5 - In the following exercises, simplify. 290....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - In the following exercises, use either method....Ch. 8.5 - Electronics The resistance of a circuit formed by...Ch. 8.5 - Ironing Lenore can do the ironing for her family’s...Ch. 8.5 - In this section, you learned to simplify the...Ch. 8.5 - Efraim wants to start simplifying the complex...Ch. 8.6 - Solve: 1y+23=15 .Ch. 8.6 - Solve: 23+15=1x .Ch. 8.6 - Solve: 12a=15a2 .Ch. 8.6 - Solve: 14b=12b2 .Ch. 8.6 - Solve: 1x1=23x .Ch. 8.6 - Solve: 35n+1=23n .Ch. 8.6 - Solve: 2x+1+1x1=1x21 .Ch. 8.6 - Solve: 5y+3+2y3=5y29 .Ch. 8.6 - Solve: 2x+51x1=1 .Ch. 8.6 - Solve: 3x+82x2=1 .Ch. 8.6 - Solve: x+13x27x+10=6x54x2 .Ch. 8.6 - Solve: y14y2+3y4=2y+4+7y1 .Ch. 8.6 - Solve: x18+x+69x=23x .Ch. 8.6 - Solve: y+55y+y15=1y .Ch. 8.6 - Solve: xx+4=32x216+5 .Ch. 8.6 - Solve: yy+8=128y264+9 .Ch. 8.6 - Solve: y5y1053y+6=2y219y+5415y260 .Ch. 8.6 - Solve: z2z+834z8=3z216z68z2+8z64 .Ch. 8.6 - Solve: AL=W for L.Ch. 8.6 - Solve: FA=W for A.Ch. 8.6 - Solve: y2x+1=23 for x.Ch. 8.6 - Solve: x=y1y for y.Ch. 8.6 - Solve: 1a+1b=c for a.Ch. 8.6 - Solve: 2x+13=1y for y.Ch. 8.6 - In the following exercises, solve. 303. 1a+25=12Ch. 8.6 - In the following exercises, solve. 304. 56+3b=13Ch. 8.6 - In the following exercises, solve. 305. 521c=34Ch. 8.6 - In the following exercises, solve. 306. 632d=49Ch. 8.6 - In the following exercises, solve. 307. 45+14=2vCh. 8.6 - In the following exercises, solve. 308. 37+23=1wCh. 8.6 - In the following exercises, solve. 309. 79+1x=23Ch. 8.6 - In the following exercises, solve. 310. 38+2y=14Ch. 8.6 - In the following exercises, solve. 311. 12m=8m2Ch. 8.6 - In the following exercises, solve. 312. 1+4n=21n2Ch. 8.6 - In the following exercises, solve. 313. 1+9p=20p2Ch. 8.6 - In the following exercises, solve. 314. 17q=6q2Ch. 8.6 - In the following exercises, solve. 315. 1r+3=42rCh. 8.6 - In the following exercises, solve. 316. 3t6=1tCh. 8.6 - In the following exercises, solve. 317. 53v2=74vCh. 8.6 - In the following exercises, solve. 318. 82w+1=3wCh. 8.6 - In the following exercises, solve. 319....Ch. 8.6 - In the following exercises, solve. 320....Ch. 8.6 - In the following exercises, solve. 321....Ch. 8.6 - In the following exercises, solve. 322....Ch. 8.6 - In the following exercises, solve. 323. 1q+47q2=1Ch. 8.6 - In the following exercises, solve. 324. 3r+104r4=1Ch. 8.6 - In the following exercises, solve. 325. 1t+75t5=1Ch. 8.6 - In the following exercises, solve. 326. 2s+73s3=1Ch. 8.6 - In the following exercises, solve. 327....Ch. 8.6 - In the following exercises, solve. 328....Ch. 8.6 - In the following exercises, solve. 329....Ch. 8.6 - In the following exercises, solve. 330....Ch. 8.6 - In the following exercises, solve. 331....Ch. 8.6 - In the following exercises, solve. 332....Ch. 8.6 - In the following exercises, solve. 333....Ch. 8.6 - In the following exercises, solve. 334....Ch. 8.6 - In the following exercises, solve. 335....Ch. 8.6 - In the following exercises, solve. 336....Ch. 8.6 - In the following exercises, solve. 337....Ch. 8.6 - In the following exercises, solve. 338....Ch. 8.6 - In the following exercises, solve. 339....Ch. 8.6 - In the following exercises, solve. 340....Ch. 8.6 - In the following exercises, solve. 341....Ch. 8.6 - In the following exercises, solve. 342....Ch. 8.6 - In the following exercises, solve. 343. Cr=2 for rCh. 8.6 - In the following exercises, solve. 344. Ir=P for rCh. 8.6 - In the following exercises, solve. 345. Vh=lw for...Ch. 8.6 - In the following exercises, solve. 346. 2Ab=h for...Ch. 8.6 - In the following exercises, solve. 347. v+3w1=12...Ch. 8.6 - In the following exercises, solve. 348. x+52y=43...Ch. 8.6 - In the following exercises, solve. 349. a=b+3c2...Ch. 8.6 - In the following exercises, solve. 350. m=n2n for...Ch. 8.6 - In the following exercises, solve. 351. 1p+2q=4...Ch. 8.6 - In the following exercises, solve. 352. 3s+1t=2...Ch. 8.6 - In the following exercises, solve. 353. 2v+15=12...Ch. 8.6 - In the following exercises, solve. 354. 6x+23=1y...Ch. 8.6 - In the following exercises, solve. 354. m+3n2=45...Ch. 8.6 - In the following exercises, solve. 356. Ec=m2 for...Ch. 8.6 - In the following exercises, solve. 357. 3x5y=14...Ch. 8.6 - In the following exercises, solve. 358. RT=W for TCh. 8.6 - In the following exercises, solve. 359. r=s3t for...Ch. 8.6 - In the following exercises, solve. 360. c=2a+b5...Ch. 8.6 - House Painting Alain can paint a house in 4 days....Ch. 8.6 - Boating An can drive his boat 18 miles with the...Ch. 8.6 - Why is there no solution to the equation 3x2=5x2 ?Ch. 8.6 - Pete thinks the equation yy+6=72y236+4 has two...Ch. 8.7 - Solve the proportion: n84=1112 .Ch. 8.7 - Solve the proportion: y96=1312 .Ch. 8.7 - Solve the proportion: 91b=75 .Ch. 8.7 - Solve the proportion: 39c=138 .Ch. 8.7 - Solve the proportion: yy+55=38 .Ch. 8.7 - Solve the proportion: zz84=15 .Ch. 8.7 - Solve : v+308=v+6612 .Ch. 8.7 - Solve: 2x+159=7x+315 .Ch. 8.7 - Pediatricians prescribe 5 milliliters (ml) of...Ch. 8.7 - For every 1 kilogram (kg) of a child’s weight...Ch. 8.7 - At a fast-food restaurant, a 22-ounce chocolate...Ch. 8.7 - Yaneli loves Starburst candies, but wants to keep...Ch. 8.7 - yurianna is going to Europe and wants to change...Ch. 8.7 - Corey and Nicole are traveling to Japan and need...Ch. 8.7 - ABC is similar to XYZ The lengths of two sides of...Ch. 8.7 - ABC is similar to XYZ. The lengths of two sides of...Ch. 8.7 - On the map, Seattle. Portland, and Boise form a...Ch. 8.7 - Using the map above, find the distance from...Ch. 8.7 - A telephone pole casts a shadow that s 50 feet...Ch. 8.7 - A pine tree casts a shadow of 80 feet next to a...Ch. 8.7 - In the following exercises, solve. 365. x56=78Ch. 8.7 - In the following exercises, solve. 366. n91=813Ch. 8.7 - In the following exercises, solve. 367. 4963=z9Ch. 8.7 - In the following exercises, solve. 368. 5672=y9Ch. 8.7 - In the following exercises, solve. 369. 5a=65117Ch. 8.7 - In the following exercises, solve. 370. 4b=64144Ch. 8.7 - In the following exercises, solve. 371. 98154=7pCh. 8.7 - In the following exercises, solve. 372. 72156=6qCh. 8.7 - In the following exercises, solve. 373. a8=4248Ch. 8.7 - In the following exercises, solve. 374. b7=3042Ch. 8.7 - In the following exercises, solve. 375....Ch. 8.7 - In the following exercises, solve. 376....Ch. 8.7 - In the following exercises, solve. 377. aa+12=47Ch. 8.7 - In the following exercises, solve. 278. bb16=119Ch. 8.7 - In the following exercises, solve. 379. cc104=58Ch. 8.7 - In the following exercises, solve. 380. dd48=133Ch. 8.7 - In the following exercises, solve. 381....Ch. 8.7 - In the following exercises, solve. 382. n+104=40n6Ch. 8.7 - In the following exercises, solve. 383....Ch. 8.7 - In the following exercises, solve. 384. q22=2q718Ch. 8.7 - In the following exercises, solve. 385....Ch. 8.7 - In the following exercises, solve. 386. Brianna,...Ch. 8.7 - In the following exercises, solve. 387. A...Ch. 8.7 - In the following exercises, solve.388. Belle, a 13...Ch. 8.7 - In the following exercises, solve. 389. A new...Ch. 8.7 - In the following exercises, solve. 390. One 12...Ch. 8.7 - In the following exercises, solve. 391. A new 7...Ch. 8.7 - In the following exercises, solve. 392. Reese...Ch. 8.7 - In the following exercises, solve. 393. Janice is...Ch. 8.7 - In the following exercises, solve. 394. Todd is...Ch. 8.7 - In the following exercises, solve. 395. Steve...Ch. 8.7 - In the following exercises, solve. 396. Martha...Ch. 8.7 - In the following exercises, solve. 397. When...Ch. 8.7 - In the following exercises, solve. 398. A...Ch. 8.7 - In the following exercises, solve. 399. Ronald...Ch. 8.7 - In the following exercises, solve. 400. Sarah...Ch. 8.7 - In the following exercises, solve. 401. Elizabeth...Ch. 8.7 - In the following exercises, solve. 402. Ben needs...Ch. 8.7 - In the following exercises, solve. 403. A golden...Ch. 8.7 - In the following exercises, solve. 404....Ch. 8.7 - In the following exercises, solve. 405. Karen eats...Ch. 8.7 - In the following exercises, solve. 406. An oatmeal...Ch. 8.7 - In the following exercises, ABC is similar to XYZ...Ch. 8.7 - In the following exercises, ABC is similar to XYZ...Ch. 8.7 - In the following exercises, DEF is similar to NPQ...Ch. 8.7 - In the following exercises, DEF is similar to NPQ...Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - In the following two exercises, use the map shown....Ch. 8.7 - Heart Rate At the gym, Carol takes her pulse for...Ch. 8.7 - Heart Rate Kevin wants to keep his heart rate at...Ch. 8.7 - Cost of a Road Trip Jesse’s car gets 30 miles per...Ch. 8.7 - Cost of a Road Trip Danny wants to drive to...Ch. 8.7 - Lawn Fertilizer Phil wants to fertilize his lawn....Ch. 8.7 - House Paint April wants to paint the exterior of...Ch. 8.7 - Cooking Natalia’s pasta recipe calls for 2 pounds...Ch. 8.7 - Heating Oil A 275 gallon oil tank costs $400 to...Ch. 8.7 - Marisol solves the proportion 144a=94 by ‘cross...Ch. 8.7 - Find a printed map and then write and solve an...Ch. 8.8 - Link can ride his bike 20 miles into a 3 mph...Ch. 8.8 - Judy can sail her boat 5 miles into a 7 mph...Ch. 8.8 - Dennis went cross-country skiing for 6 hours on...Ch. 8.8 - Tony drove 4 hours to his home, driving 208 miles...Ch. 8.8 - Kayla rode her bike 75 miles home from college one...Ch. 8.8 - Victoria jogs 12 miles to the park along a flat...Ch. 8.8 - One gardener can mow a golf course in 4 hours,...Ch. 8.8 - Carrie can weed the garden in 7 hours, while her...Ch. 8.8 - Two hoses can fill a swimming pool in 10 hours. It...Ch. 8.8 - Cara and Cindy, working together, can rake the...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve uniform motion...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - In the following exercises, solve work...Ch. 8.8 - Dana enjoys taking her dog for a walk, but...Ch. 8.8 - Ken and Joe leave their apartment to go to a...Ch. 8.8 - In Example 8.83, the solution h=4 is crossed out....Ch. 8.8 - Paula and Yuki are roommates. It takes Paula 3...Ch. 8.9 - If y varies directly as x and y=3 , when x=10 ,...Ch. 8.9 - If y varies directly as x and y=12 when x=4 find...Ch. 8.9 - The number of calories, c, burned varies directly...Ch. 8.9 - The distance a moving body travels, d, varies...Ch. 8.9 - The distance that Brad travels varies directly...Ch. 8.9 - The weight of a liquid varies directly as its...Ch. 8.9 - The distance an object falls is directly...Ch. 8.9 - The area of a circle varies directly as the square...Ch. 8.9 - If p varies inversely with q and p=30 when q=12...Ch. 8.9 - If y varies inversely with x and y=8 when x=2 find...Ch. 8.9 - A car’s value varies inversely with its age. Elena...Ch. 8.9 - The time required to empty a pool varies inversely...Ch. 8.9 - The number of hours it takes for ice to melt...Ch. 8.9 - The force needed to break a board varies inversely...Ch. 8.9 - In the following exercises, solve. 463. If y...Ch. 8.9 - In the following exercises, solve. 464. If p...Ch. 8.9 - In the following exercises, solve. 465. If v...Ch. 8.9 - In the following exercises, solve. 466. If a...Ch. 8.9 - In the following exercises, solve. 467. If p...Ch. 8.9 - In the following exercises, solve. 468. If y...Ch. 8.9 - In the following exercises, solve. 469. If a...Ch. 8.9 - In the following exercises, solve. 470. If V...Ch. 8.9 - In the following exercises, solve. 471. The amount...Ch. 8.9 - In the following exercises, solve. 472. The price,...Ch. 8.9 - In the following exercises, solve. 473. Terri...Ch. 8.9 - In the following exercises, solve. 474. Joseph is...Ch. 8.9 - In the following exercises, solve. 475. The price...Ch. 8.9 - In the following exercises, solve. 476. The...Ch. 8.9 - In the following exercises, solve. 477. The mass...Ch. 8.9 - In the following exercises, solve. 478. The length...Ch. 8.9 - In the following exercises, solve. 479. The...Ch. 8.9 - In the following exercises, solve. 480. The...Ch. 8.9 - In the following exercises, solve. 481. The area...Ch. 8.9 - In the following exercises, solve. 482. The...Ch. 8.9 - In the following exercises, solve. 483. If v...Ch. 8.9 - In the following exercises, solve. 484. If p...Ch. 8.9 - In the following exercises, solve. 485. If v...Ch. 8.9 - In the following exercises, solve. 486. If a...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - Write an inverse variation equation to solve the...Ch. 8.9 - If y varies directly as x and y=5, when x=3 .,...Ch. 8.9 - If v varies directly as w and v=21 , when w=8 ....Ch. 8.9 - If p vanes inversely with q and p=5when q=6 , find...Ch. 8.9 - If y varies inversely with x and y=11 when x=3...Ch. 8.9 - If p varies directly as q and p=10 , when q=2 ....Ch. 8.9 - If v varies inversely with w and v=18 when w=13...Ch. 8.9 - The force needed to break a board varies inversely...Ch. 8.9 - The number of hours it takes for ice to melt...Ch. 8.9 - The length a spring stretches varies directly with...Ch. 8.9 - The amount that June gets paid varies directly the...Ch. 8.9 - The fuel consumption (mpg) of a car varies...Ch. 8.9 - The volume of a gas in a container varies...Ch. 8.9 - The distance an object falls varies directly to...Ch. 8.9 - The area of the face of a Ferris wheel varies...Ch. 8.9 - Ride Service It costs $35 for a ride from the city...Ch. 8.9 - Road Trip The number of hours it takes Jack to...Ch. 8.9 - In your own words, explain the difference between...Ch. 8.9 - Make up an example from your life experience of...Ch. 8 - In the following exercises, determine the values...Ch. 8 - In the following exercises, determine the values...Ch. 8 - In the following exercises, determine the values...Ch. 8 - In the following exercises, determine the values...Ch. 8 - In the following exercises, evaluate the rational...Ch. 8 - In the following exercises, evaluate the rational...Ch. 8 - In the following exercises, evaluate the rational...Ch. 8 - In the following exercises, evaluate the rational...Ch. 8 - In the following exercises, simplify. 521. 1024Ch. 8 - In the following exercises, simplify. 522....Ch. 8 - In the following exercises, simplify. 523. 14a14a1Ch. 8 - In the following exercises, simplify. 524....Ch. 8 - In the following exercises, simplify. 525. c2c24c2Ch. 8 - In the following exercises, simplify. 526. d1616dCh. 8 - In the following exercises, simplify. 527....Ch. 8 - In the following exercises, simplify. 528....Ch. 8 - In the following exercises, multiply. 529. 38215Ch. 8 - In the following exercises, multiply. 530....Ch. 8 - In the following exercises, multiply. 531....Ch. 8 - In the following exercises, multiply. 532....Ch. 8 - In the following exercises, divide. 533....Ch. 8 - In the following exercises, divide. 534....Ch. 8 - In the following exercises, divide. 535....Ch. 8 - In the following exercises, divide. 536....Ch. 8 - In the following exercises, divide. 537....Ch. 8 - In the following exercises, divide. 538....Ch. 8 - In the following exercises, add. 539. 35+25Ch. 8 - In the following exercises, add. 540. 4a22a112a1Ch. 8 - In the following exercises, add. 541....Ch. 8 - In the following exercises, add. 542. 3xx1+2x1Ch. 8 - In the following exercises, subtract. 543....Ch. 8 - In the following exercises, subtract. 544....Ch. 8 - In the following exercises, subtract. 545....Ch. 8 - In the following exercises, subtract. 546....Ch. 8 - In the following exercises, add and subtract. 547....Ch. 8 - In the following exercises, add and subtract. 548....Ch. 8 - In the following exercises, add and subtract. 549....Ch. 8 - In the following exercises, add and subtract. 550....Ch. 8 - In the following exercises, find the LCD. 551....Ch. 8 - In the following exercises, find the LCD. 552....Ch. 8 - In the following exercises, find the LCD. 553....Ch. 8 - In the following exercises, rewrite as equivalent...Ch. 8 - In the following exercises, rewrite as equivalent...Ch. 8 - In the following exercises, rewrite as equivalent...Ch. 8 - In the following exercises, add. 557. 23+35Ch. 8 - In the following exercises, add. 558. 75a+32bCh. 8 - In the following exercises, add. 559. 2c2+9c+3Ch. 8 - In the following exercises, add. 560....Ch. 8 - In the following exercises, add. 561....Ch. 8 - In the following exercises, add. 562....Ch. 8 - In the following exercises, subtract and add. 563....Ch. 8 - In the following exercises, subtract and add. 564....Ch. 8 - In the following exercises, subtract and add. 565....Ch. 8 - In the following exercises, subtract and add. 566....Ch. 8 - In the following exercises, subtract and add. 567....Ch. 8 - In the following exercises, subtract and add. 568....Ch. 8 - In the following exercises, simplify. 569....Ch. 8 - In the following exercises, simplify. 570....Ch. 8 - In the following exercises, simplify. 571....Ch. 8 - In the following exercises, simplify. 572....Ch. 8 - In the following exercises, simplify. 573....Ch. 8 - In the following exercises, simplify. 574....Ch. 8 - In the following exercises, simplify. 575....Ch. 8 - In the following exercises, simplify. 576....Ch. 8 - In the following exercises, solve. 577. 12+23=1xCh. 8 - In the following exercises, solve. 578. 12m=8m2Ch. 8 - In the following exercises, solve. 579....Ch. 8 - In the following exercises, solve. 580. 3q+82q2=1Ch. 8 - In the following exercises, solve. 581....Ch. 8 - In the following exercises, solve. 582....Ch. 8 - In the following exercises, solve for the...Ch. 8 - In the following exercises, solve for the...Ch. 8 - In the following exercises, solve for the...Ch. 8 - In the following exercises, solve for the...Ch. 8 - In the following exercises, solve. 587. x4=35Ch. 8 - In the following exercises, solve. 588. 3y=95Ch. 8 - In the following exercises, solve. 589. ss+20=37Ch. 8 - In the following exercises, solve. 590. t35=t+29Ch. 8 - In the following exercises, solve using...Ch. 8 - In the following exercises, solve using...Ch. 8 - In the following exercises, solve. 593. ABC is...Ch. 8 - In the following exercises, solve. 594. On a map...Ch. 8 - In the following exercises, solve. 595. Tony is...Ch. 8 - In the following exercises, solve. 596. The height...Ch. 8 - In the following exercises, solve. 597. When...Ch. 8 - In the following exercises, solve. 598. Mark is...Ch. 8 - In the following exercises, solve. 599. John can...Ch. 8 - In the following exercises, solve. 600. Mark was...Ch. 8 - In the following exercises, solve. 601. Jerry can...Ch. 8 - In the following exercises, solve. 602. Lisa takes...Ch. 8 - In the following exercises, solve. 603. Jeffrey...Ch. 8 - In the following exercises, solve. 604. Sue and...Ch. 8 - In the following exercises, solve. 605. If y...Ch. 8 - In the following exercises, solve. 606. If y...Ch. 8 - In the following exercises, solve. 607. If m...Ch. 8 - In the following exercises, solve. 608. Vanessa is...Ch. 8 - In the following exercises, solve. 609. If the...Ch. 8 - In the following exercises, solve. 610. The...Ch. 8 - In the following exercises, solve. 611. The number...Ch. 8 - In the following exercises, solve. 612. On a...Ch. 8 - In the following exercises, simplify. 613....Ch. 8 - In the following exercises, simplify. 614....Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, perform the indicated...Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve. 626. If y...Ch. 8 - In the following exercises, solve. 627. If y...Ch. 8 - In the following exercises, solve. 628. If y...Ch. 8 - In the following exercises, solve. 629. The...Ch. 8 - In the following exercises, solve each equation....Ch. 8 - In the following exercises, solve. 631. Kurt can...Ch. 8 - In the following exercises, solve. 632. Amanda...Ch. 8 - In the following exercises, solve. 633. An...Ch. 8 - In the following exercises, solve. 634. Josh can...Ch. 8 - In the following exercises, solve. 635. The price...Ch. 8 - In the following exercises, solve. 636. The volume...Ch. 8 - In the following exercises, solve. 637. The cities...
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- Select the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forwardWhich of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward
- (20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forwardAssume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the abovearrow_forward
- Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the abovearrow_forwardLet H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardSolve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8arrow_forward
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