Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 63. f(x)=6x212xx2+7x18 g(x)=x2813x227xFor the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 64. f(x)=x22xx2+6x16 g(x)=x264x28xFor the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 65. f(x)=4xx23x10 g(x)=x2258x2For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 66. f(x)=2x2+8xx29x+20 g(x)=x5x2For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 67. f(x)=27x23x21 g(x)=3x2+18xx2+13x+42For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 68. f(x)=24x22x8 g(x)=4x3+28x2x2+11x+28For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 69. f(x)=16x24x+36 g(x)=4x224xx2+4x45For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given. 70. f(x)= 24 x 2 2x4g(x)= 12 x 2 +36x x 2 11x+18Explain 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 .(a) Multiply 7494 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 got in part (a)? Why or why not?(a) Divide 2456 and 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 got in part (a)? Why or why not?Simplify: 9x+14x+7+x2x+7 .Simplify: x2+8xx+5+15x+5 .Subtract: 4x211x+8x23x+23x2+x3x23x+2 .Subtract: 6x2x+20x2815x2+11x7x281 .Subtract: y25yy246y64y2 .Subtract: 2n2+8n1n21n27n11n2 .(a) Find the LCD for the expressions 2x2x12,1x216 (b) rewrite them as equivalent rational expressions with the lowest common denominator.(a) Find the LCD for the expressions 3xx23x+10,5x2+3x+2 (b) rewrite them as equivalent rational expressions with the lowest common denominator.Add: 2x2+5x+3 .Add: 4m+3+3m+4 .Add: 1m2m2+5mm2+3m+2 .Add: 2nn23n10+6n2+5n+6 .Subtract: 2xx241x+2 .Subtract: 3z+36zz29 .Subtract: 3x1x25x626x .Subtract: 2y2y2+2y8y12y .Subtract: 3b24b52b26b+5 .Subtract: 4x243x2x2 .Simplify: vv+1+3v16v21 .Simplify: 3ww+2+2w+717w+4w2+9w+14 .Find R(x)=f(x)g(x) where f(x)=x+1x+3 and g(x)=x+17x2x12 .Find R(x)=f(x)+g(x) where f(x)=x4x+3 and g(x)=4x+6x29 .In the following exercises, add. 75. 215+715In the following exercises, add. 76. 724+1124In the following exercises, add. 77. 3c4c5+54c5In the following exercises, add. 78. 7m2m+n+42m+nIn the following exercises, add. 79. 2r22r1+15r82r1In the following exercises, add. 80. 3s23s2+13s103s2In the following exercises, add. 81. 2w2w216+8ww216In the following exercises, add. 82. 7x2x29+21xx29In the following exercises, subtract. 83. 9a23a7493a7In the following exercises, subtract. 84. 25b25b6365b6In the following exercises, subtract. 85. 3m26m3021m306m30In the following exercises, subtract. 86. 2n24n3218n164n32In the following exercises, subtract. 87. 6p2+3p+4p2+4p55p2+p+7p2+4p5In the following exercises, subtract. 88. 5q2+3q9q2+6q+84q2+9q+7q2+6q+8In the following exercises, subtract. 89. 5r2+7r33r2494r2+5r+30r249In the following exercises, subtract. 90. 7t2t4t2256t2+12t44t225In the following exercises, add or subtract. 91. 10v2v1+2v+412vIn the following exercises, add or subtract. 92. 20w5w2+5w+625wIn the following exercises, add or subtract. 93. 10x2+16x78x3+2x2+3x138xIn the following exercises, add or subtract. 94. 6y2+2y113y7+3y23y+1773yIn the following exercises, add or subtract. 95. z2+6zz2253z+2025z2In the following exercises, add or subtract. 96. a2+3aa293a279a2In the following exercises, add or subtract. 97. 2b2+30b13b2492b25b849b2In the following exercises, add or subtract. 98. c2+5c10c216c28c1016c2In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 99. 5x22x8,2xx2x12In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 100. 8y2+12y+35,3yy2+y42In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 101. 9z2+2z8,4zz24In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 102. 6a2+14a+45,5aa281In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 103. 4b2+6b+9,2bb22b15In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 104. 5c24c+4,3cc27c+10In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 105. 23d2+14d5,5d3d219d+6In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator. 106. 35m23m2,6m5m2+17m+6In the following exercises, perform the indicated operations. 107. 710x2y+415xy2In the following exercises, perform the indicated operations. 108. 112a3b2+59a2b3In the following exercises, perform the indicated operations. 109. 3r+4+2r5In the following exercises, perform the indicated operations. 110. 4s7+5s+3In the following exercises, perform the indicated operations. 111. 53w2+1w+1In the following exercises, perform the indicated operations. 112. 42x+5+2x1In the following exercises, perform the indicated operations. 113. 2yy+3+3y1In the following exercises, perform the indicated operations. 114. 3zz2+1z+5In the following exercises, perform the indicated operations. 115. 5ba2b2a2+2bb24In the following exercises, perform the indicated operations. 116. 4cd+3c+1d29In the following exercises, perform the indicated operations. 117. 3m3m3+5mm2+3m4In the following exercises, perform the indicated operations. 118. 84n+4+6n2n2In the following exercises, perform the indicated operations. 119. 3rr2+7r+6+9r2+4r+3In the following exercises, perform the indicated operations. 120. 2ss2+2s8+4s2+3s10In the following exercises, perform the indicated operations. 121. tt6t2t+6In the following exercises, perform the indicated operations. 122. x3x+6xx+3In the following exercises, perform the indicated operations. 123. 5aa+3a+2a+6In the following exercises, perform the indicated operations. 124. 3bb2b6b8In the following exercises, perform the indicated operations. 125. 6m+612mm236In the following exercises, perform the indicated operations. 126. 4n+48nn216In the following exercises, perform the indicated operations. 127. 9p17p24p21p+17pIn the following exercises, perform the indicated operations. 128. 7q+8q22q24q+24qIn the following exercises, perform the indicated operations. 129. 2r16r2+6r1652rIn the following exercises, perform the indicated operations. 130. 2t30t2+6t2723tIn the following exercises, perform the indicated operations. 131. 2x+710x1+3In the following exercises, perform the indicated operations. 132. 8y45y+26In the following exercises, perform the indicated operations. 133. 3x23x42x25x+4In the following exercises, perform the indicated operations. 134. 4x26x+53x27x+10In the following exercises, perform the indicated operations. 135. 5x2+8x94x2+10x+9In the following exercises, perform the indicated operations. 136. 32x2+5x+212x2+3x+1In the following exercises, perform the indicated operations. 137. 5aa2+9a2a+18a22aIn the following exercises, perform the indicated operations. 138. 2bb5+32b2b152b210bIn the following exercises, perform the indicated operations. 139. cc+2+5c211cc24In the following exercises, perform the indicated operations. 140. 6dd5+1d+47d5d2d20In the following exercises, perform the indicated operations. 141. 3dd+2+4dd+8d2+2dIn the following exercises, perform the indicated operations. 142. 2qq+5+3q313q+15q2+2q15In the following exercises, find (a) R(x)=f(x)+g(x)(b) R(x)=f(x)g(x). 143. f(x)=5x5x2+x6 and g(x)=x+12xIn the following exercises, find (a) R(x)=f(x)+g(x)(b) R(x)=f(x)g(x). 144. f(x)=4x24x2+x30 and g(x)=x+75xIn the following exercises, find (a) R(x)=f(x)+g(x)(b) R(x)=f(x)g(x). 145. f(x)=6xx264 and g(x)=3x8In the following exercises, find (a) R(x)=f(x)+g(x)(b) R(x)=f(x)g(x). 146. f(x)=5x+7 and g(x)=10xx249Donald thinks that 3x+4x is 72x . Is Donald correct? Explain.Explain how you find the Least Common Denominator of x2+5x+4 and x216 .Felipe thinks 1x+1y is 2x+y . (a) Choose numerical values for x and y and evaluate 1x+1y . (b) Evaluate 2x+y for the same values of x and y you used in part ?. (c) Explain why Felipe is wrong. (d) Find the correct expression for 1x+1y .Simplify the expression 4n2+6n+91n29 and explain all your steps.Simplify the complex rational expression by writing it as division: 2x213x+1 .Simplify the complex rational expression by writing it as division: 1x27x+122x4 .Simplify the complex rational expression by writing it as division: 12+2356+112 .Simplify the complex rational expression by writing it as division: 341318+56 .Simplify the complex rational expression by writing it as division: 1x+1y1x1y .Simplify the complex rational expression by writing it as division: 1a+1b1a21b2 .Simplify the complex rational expression by writing it as division: b3bb+52b+5+1b5 .Simplify the complex rational expression by writing it as division: 13c+41c+4+c3 .Simplify the complex rational expression by writing it as division: 12+15110+15 .Simplify the complex rational expression by using the LCD: 14+3812516 .Simplify the complex rational expression by using the LCD: 1a+1bab+ba .Simplify the complex rational expression by using the LCD: 1x21y21x+1y .Simplify the complex rational expression by using the LCD: 3x+25x23x24 .Simplify the complex rational expression by using the LCD: 2x71x+76x+71x249 .Simplify the complex rational expression by using the LCD: 3x2+7x+104x+2+1x+5 .Simplify the complex rational expression by using the LCD: 4yy+5+2y+63yy2+11y+30 .Simplify the complex rational expression by using the LCD: xx+31+1x+3 .In the following exercises, simplify each complex rational expression by writing it as division. 151. 2aa+44a2a216In the following exercises, simplify each complex rational expression by writing it as division. 152. 3bb5b2b225In the following exercises, simplify each complex rational expression by writing it as division. 153. 5c2+5c1410c+7In the following exercises, simplify each complex rational expression by writing it as division. 154. 8d2+9d+1812d+6In the following exercises, simplify each complex rational expression by writing it as division. 155. 12+5623+79In the following exercises, simplify each complex rational expression by writing it as division. 156. 12+3435+710In the following exercises, simplify each complex rational expression by writing it as division. 157. 231934+56In the following exercises, simplify each complex rational expression by writing it as division. 158. 121623+34In the following exercises, simplify each complex rational expression by writing it as division. 159. nm+1n1nnmIn the following exercises, simplify each complex rational expression by writing it as division. 160. 1p+pqqp1qIn the following exercises, simplify each complex rational expression by writing it as division. 161. 1r+1t1r21t2In the following exercises, simplify each complex rational expression by writing it as division. 162. 2v+2w1v21w2In the following exercises, simplify each complex rational expression by writing it as division. 163. x2xx+31x+3+1x3In the following exercises, simplify each complex rational expression by writing it as division. 164. y2yy42y4+2y+4In the following exercises, simplify each complex rational expression by writing it as division. 165. 22a+31a+3+a2In the following exercises, simplify each complex rational expression by writing it as division. 166. 4+4b51b5+b4In the following exercises, simplify each complex rational expression by using the LCD. 167. 13+1814+112In the following exercises, simplify each complex rational expression by using the LCD. 168. 14+1916+112In the following exercises, simplify each complex rational expression by using the LCD. 169. 56+2971813In the following exercises, simplify each complex rational expression by using the LCD. 170. 16+4153512In the following exercises, simplify each complex rational expression by using the LCD. 171. cd+1d1ddcIn the following exercises, simplify each complex rational expression by using the LCD. 172. 1m+mnnm1nIn the following exercises, simplify each complex rational expression by using the LCD. 173. 1p+1q1p21q2In the following exercises, simplify each complex rational expression by using the LCD. 174. 2r+2t1r21t2In the following exercises, simplify each complex rational expression by using the LCD. 175. 2x+53x5+1x225In the following exercises, simplify each complex rational expression by using the LCD. 176. 5y43y+4+2y216In the following exercises, simplify each complex rational expression by using the LCD. 177. 5z264+3z+81z+8+2z8In the following exercises, simplify each complex rational expression by using the LCD. 178. 3s+6+5s61s236+4s+6In the following exercises, simplify each complex rational expression by using the LCD. 179. 4a22a151a5+2a+3In the following exercises, simplify each complex rational expression by using the LCD. 180. 5b26b273b9+1b+3In the following exercises, simplify each complex rational expression by using the LCD. 181. 5c+23c+75cc2+9c+14In the following exercises, simplify each complex rational expression by using the LCD. 182. 6d42d+72dd2+3d28In the following exercises, simplify each complex rational expression by using the LCD. 183. 2+1p35p3In the following exercises, simplify each complex rational expression by using the LCD. 184. nn23+5n2In the following exercises, simplify each complex rational expression by using the LCD. 185. mm+54+1m5In the following exercises, simplify each complex rational expression by using the LCD. 186. 7+2q21q+2In the following exercises, simplify each complex rational expression using either method. 187. 342712+514In the following exercises, simplify each complex rational expression using either method. 188. vw+1v1vvwIn the following exercises, simplify each complex rational expression using either method. 189. 2a+41a216In the following exercises, simplify each complex rational expression using either method. 190. 3b23b405b+52b8In the following exercises, simplify each complex rational expression using either method. 191. 3m+3n1m21n2In the following exercises, simplify each complex rational expression using either method. 192. 2r91r+9+3r281In the following exercises, simplify each complex rational expression using either method. 193. x3xx+23x+2+3x2In the following exercises, simplify each complex rational expression using either method. 194. yy+32+1y3In this section, you learned to simplify the complex fraction 3x+2xx24 two ways: rewriting it as a division problem or multiplying the numerator and denominator by the LCD. Which method do you prefer? Why?Efraim wants to start simplifying the complex fraction 1a+1b1a1b by cancelling the variables from the numerator and denominator, 1a+1b1a1b . Explain what is wrong with Efraim’s plan.Solve: 1y+23=15 .Solve: 23+15=1x .Solve: 12x=15x2 .Solve: 14y=12y2 .Solve: 2x+1+1x1=1x21 .Solve: 5y+3+2y3=5y29 .Solve: x+13x27x+10=6x54x2 .Solve: y6y2+3y4=2y+4+7y1 .Solve: xx+4=32x216+5 .Solve: yy+8=128y264+9 .Solve: y5y1053y+6=2y219y+5415y260 .Solve: z2z+834z8=3z216z168z2+2z64 .Solve: 15x2+x63x2=2x+3 .Solve: 5x2+2x33x2+x2=1x2+5x+6 .For rational function, f(x)=8xx27x+12 , (a) find the domain of the function (b) solve f(x)=3 (c) find the points on the graph at this function value.For rational function, f(x)=x1x26x+5 , (a) find the domain of the function (b) solve f(x)=4 (c) find the points on the graph at this function value.Solve: m=y5x4 for y.Solve: m=y1x+5 for y.Solve: 1a+1b=c for a.Solve: 2x+13=1y for y.In the following exercises, solve each rational equation. 197. 1a+25=12In the following exercises, solve each rational equation. 198. 632d=49In the following exercises, solve each rational equation. 199. 45+14=2vIn the following exercises, solve each rational equation. 200. 38+2y=14In the following exercises, solve each rational equation. 201. 12m=8m2In the following exercises, solve each rational equation. 202. 1+4n=21n2In the following exercises, solve each rational equation. 203. 1+9p=20p2In the following exercises, solve each rational equation. 204. 17q=6q2In the following exercises, solve each rational equation. 205. 53v2=74vIn the following exercises, solve each rational equation. 206. 82w+1=3wIn the following exercises, solve each rational equation. 207. 3x+4+7x4=8x216In the following exercises, solve each rational equation. 208. 5y9+1y+9=18y281In the following exercises, solve each rational equation. 209. 8z107z+10=5z2100In the following exercises, solve each rational equation. 210. 9a+116a11=6a2121In the following exercises, solve each rational equation. 211. 10q27q+4=1In the following exercises, solve each rational equation. 212. 2s+7ss3=1In the following exercises, solve each rational equation. 213. v10v25v+4=3v16v4In the following exercises, solve each rational equation. 214. w+8w211w+28=5w7+2w4In the following exercises, solve each rational equation. 215. x10x2+8x+12=3x+2+4x+6In the following exercises, solve each rational equation. 216. y5y24y5=1y+1+1y5In the following exercises, solve each rational equation. 217. b+33b+b24=1bIn the following exercises, solve each rational equation. 218. c+312c+c36=14cIn the following exercises, solve each rational equation. 219. dd+3=18d29+4In the following exercises, solve each rational equation. 220. mm+5=50m225+6In the following exercises, solve each rational equation. 221. nn+23=8n24In the following exercises, solve each rational equation. 222. pp+78=98p249In the following exercises, solve each rational equation. 223. q3q934q+12=7q2+6q+6324q2216In the following exercises, solve each rational equation. 224. r3r1514r+20=3r2+17r+4012r2300In the following exercises, solve each rational equation. 225. s2s+625s+5=5s23s710s2+40s+30In the following exercises, solve each rational equation. 226. t6t1252t+10=t223t+7012t2+36t120In the following exercises, solve each rational equation. 227. 2x2+2x81x2+9x+20=4x2+3x10In the following exercises, solve each rational equation. 228. 5x2+4x+3+2x2+x6=3x2x2In the following exercises, solve each rational equation. 229. 3x25x6+3x27x+6=6x21In the following exercises, solve each rational equation. 230. 2x2+2x3+3x2+4x+3=6x21For rational function f(x)=x2x2+6x+8 , (a) find the domain of the function (b) solve f(x)=5 (c) find the points on the graph at this function value.For rational function, f(x)=x+1x22x3 , (a) find the domain of the function (b) solve f(x)=1 (c) find the points on the graph at this function value.For rational function, f(x)=2xx27x+10 , (a) find the domain of the function (b) solve f(x)=2 (c) find the points on the graph at this function value.For rational function, f(x)=5xx2+5x+6 , (a) find the domain of the function (b) solve f(x)=3 (c) find the points on the graph at this function value.In the following exercises, solve 235. Cr=2 for r.In the following exercises, solve 236. Ir=P for r.In the following exercises, solve 237. v+3w1=12 for w.In the following exercises, solve 238. x+52y=43 for y.In the following exercises, solve 239. a=b+3c2 for c.In the following exercises, solve 240. m=n2n for n.In the following exercises, solve 241. 1p+2q=4 for p.In the following exercises, solve 242. 3s+1t=2 for s.In the following exercises, solve 243. 2v+15=3w for w.In the following exercises, solve 244. 6x+23=1y for y.In the following exercises, solve 245. m+3n2=45 for n.In the following exercises, solve 246. r=s3t for t.In the following exercises, solve 247. Ec=m2 for c.In the following exercises, solve 248. RT=W for T.In the following exercises, solve 249. 3x5y=14 for y.In the following exercises, solve 250. c=2a+b5fora.Your class mate is having trouble in this section. Write down the steps you would use to explain how to solve a rational equation.Alek thinks the equation yy+6=72y236+4 has two solutions, y=6 and y=4 . Explain why Alek is wrong.Solve the proportion: yy+55=38 .Solve the proportion: zz84=15 .Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?For every 1 kilogram (kg) of a child’s weight, pediatricians prescribe 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe?Find the actual distance from Seattle to Portland.Find the actual distance from Portland to Boise.A telephone pole casts a shadow that is 50 feet long. Nearby, an 8 foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?A pine tree casts a shadow of 80 feet next to a 30 foot tall building which casts a 40 feet shadow. How tall is the pine tree?Link can ride his bike 20 miles into a 3 mph headwind in the same amount of time he can ride 30 miles with a 3 mph tailwind. What is Link’s biking speed?Danica can sail her boat 5 miles into a 7 mph headwind in the same amount of time she can sail 12 miles with a 7 mph tailwind. What is the speed of Danica’s boat without a wind?Dennis went cross-country skiing for 6 hours on Saturday. He skied 20 mile uphill and then 20 miles back downhill, returning to his starting point. His uphill speed was 5 mph slower than his downhill speed. What was Dennis’ speed going uphill and his speed going downhill?Joon drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on country roads. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads?Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed. Find Kayla’s biking speed.Victoria jogs 12 miles to the park along a flat trail and then returns by jogging on an 20 mile hilly trail. She jogs 1 mile per hour slower on the hilly trail than on the flat trail, and her return trip takes her two hours longer. Find her rate of jogging on the flat trail.One gardener can mow a golf course in 4 hours, while another gardener can mow the same golf course in 6 hours. How long would it take if the two gardeners worked together to mow the golf course?Daria can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them working together?Alice can paint a room in 6 hours. If Kristina helps her it takes them 4 hours to paint the room. How long would it take Kristina to paint the room by herself?Tracy can lay a slab of concrete in 3 hours, with Jordan’s help they can do it in 2 hours. If Jordan works alone, how long will it take?The number of calories, c, burned varies directly with the amount of time, t, spent exercising. Arnold burned 312 calories in 65 minutes exercising. (a) Write the equation that relates c and t. (b) How many calories would he burn if he exercises for 90 minutes?The distance a moving body travels, d, varies directly with time, t, it moves. A train travels 100 miles in 2 hours (a) Write the equation that relates d and t. (b) How many miles would it travel in 5 hours?The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees Celsius. (a) Write the equation of variation. (b) How many hours would it take for the same block of ice to melt if the temperature was 78 degrees?Xander’s new business found that the daily demand for its product was inversely proportional to the price, p. When the price is $5, the demand is 700 units. (a) Write the equation of variation. (b) What is the demand if the price is raised to $7?In the following exercises, solve each proportion. 253. x56=78In the following exercises, solve each proportion. 254. 5672=y9In the following exercises, solve each proportion. 255. 98154=7pIn the following exercises, solve each proportion. 256. 72156=6qIn the following exercises, solve each proportion. 257. aa+12=47In the following exercises, solve each proportion. 258. bb16=119In the following exercises, solve each proportion. 259. m+9025=m+3015In the following exercises, solve each proportion. 260. n+104=40n6In the following exercises, solve each proportion. 261. 2p+48=p+186In the following exercises, solve each proportion. 262. q22=2q718In the following exercises, solve. 263. Kevin wants to keep his heart rate at 160 beats per minute while training. During his workout he counts 27 beats in 10 seconds. (a) How many beats per minute is this? (b) Has Kevin met his target heart rate?In the following exercises, solve. 264. Jesse’s car gets 30 miles per gallon of gas. (a) If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home? (b) If gas is $3.09 per gallon, what is the total cost of the gas for the trip?In the following exercises, solve. 265. Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 pounds?In the following exercises, solve. 266. A veterinarian prescribed Sunny, a 65-pound dog, an antibacterial medicine in case an infection emerges after her teeth were cleaned. If the dosage is 5 mg for every pound, how much medicine was Sunny given?In the following exercises, solve. 267. A new energy drink advertises 106 calories for 8 ounces. How many calories are in 12 ounces of the drink?In the following exercises, solve. 268. One 12-ounce can of soda has 150 calories. If Josiah drinks the big 32-ounce size from the local mini-mart, how many calories does he get?In the following exercises, solve. 269. Kyra is traveling to Canada and will change $250 US dollars into Canadian dollars. At the current exchange rate, $1 US is equal to $1.3 Canadian. How many Canadian dollars will she get for her trip?In the following exercises, solve. 270. Maurice is traveling to Mexico and needs to exchange $450 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip?In the following exercises, solve. 271. Ronald needs a morning breakfast drink that will give him at least 390 calories. Orange juice has 130 calories in one cup. How many cups does he need to drink to reach his calorie goal?In the following exercises, solve. 272. Sonya drinks a 32-ounce energy drink containing 80 calories per 12 ounce. How many calories did she drink?In the following exercises, solve. 273. Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 square feet. How many bags of fertilizer will he have to buy?In the following exercises, solve. 274. An oatmeal cookie recipe calls for 12 cup of butter to make 4 dozen cookies. Hilda needs to make 10 dozen cookies for the bake sale. How many cups of butter will she need?In the following exercises, the triangles are similar. Find the length of the indicated side. 275. (a) side x (b) side bIn the following exercises, the triangles are similar. Find the length of the indicated side. 276. (a) side d (b) side qIn the following exercises, use the map shown. On the map, New York City, Chicago, and Memphis form a triangle. The actual distance from New York to Chicago is 800 miles. 277. Find the actual distance from New York to Memphis.In the following exercises, use the map shown. On the map, New York City, Chicago, and Memphis form a triangle. The actual distance from New York to Chicago is 800 miles. 278. Find the actual distance from Chicago to Memphis.In the following exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle. The actual distance from Atlanta to New Orleans is 420 miles. 279. Find the actual distance from New Orleans to Miami.In the following exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle. The actual distance from Atlanta to New Orleans is 420 miles. 280. Find the actual distance from Atlanta to Miami.In the following exercises, answer each question. 281. A 2-foot-tall dog casts a 3-foot shadow at the same time a cat casts a one foot shadow. How tall is the cat?