Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
Write the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.In your own words, define a parabola.Is the parabola y=x2 a function? Is the parabola x=y2 a function? Explain why or why not.Write the equation of a parabola that opens up or down in standard form and the equation of a parabola that opens left or right in standard form. Provide a sketch of the parabola for each one, label the vertex and axis of symmetry.Explain in your own words, how you can tell from its equation whether a parabola opens up, down, left or right.Graph: x24+y216=1.Graph: x29+y216=1.Graph 9x2+16y2=144.Graph 16x2+25y2=400.Find the equation of the ellipse shown.Find the equation of the ellipse shown.Graph: ( x+3)24+( y5)216=1.Graph: ( x1)225+( y+3)216=1.Graph ( x5)29+( y+4)24=1 by translation.Graph ( x+6)216+( y+2)225=1 by transaction.(a) Write the equation 6x2+4y2+12x32y+34=0 in standard form and (b) graph.(a) Write the equation 4x2+y216x6y+9=0 in standard form and (b) graph.A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 20 Au and the furthest is approximately 30 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below, use the graph to write an equation for the elliptical orbit of the planet.A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 20 AU and the furthest is approximately 50 AU The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the Orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the planet.In the following exercises, graph each ellipse. 99. x24+y225=1In the following exercises, graph each ellipse. 100. x29+y225=1In the following exercises, graph each ellipse. 101. x225+y236=1In the following exercises, graph each ellipse. 102. x216+y236=1In the following exercises, graph each ellipse. 103. x236+y216=1In the following exercises, graph each ellipse. 104. x225+y29=1In the following exercises, graph each ellipse. 105. x2+y24=1In the following exercises, graph each ellipse. 106. x29+y2=1In the following exercises, graph each ellipse. 107. 4x2+25y2=100In the following exercises, graph each ellipse. 108. 16x2+9y2=144In the following exercises, graph each ellipse. 109. 16x2+36y2=576In the following exercises, graph each ellipse. 110. 9x2+25y2=225In the following exercises, find the equation of the ellipse shown in the graph.In the following exercises, find the equation of the ellipse shown in the graph.In the following exercises, find the equation of the ellipse shown in the graph.In the following exercises, find the equation of the ellipse shown in the graph.In the following exercises, graph each ellipse. 115. ( x+1)24+( y+6)225=1In the following exercises, graph each ellipse. 116. ( x3)225+( y+2)29=1In the following exercises, graph each ellipse. 117. ( x+4)24+( y2)29=1In the following exercises, graph each ellipse. 118. ( x4)29+( y1)216=1In the following exercises, graph each ellipse. 119. ( x3)24+( y7)225=1In the following exercises, graph each ellipse. 120. ( x+6)216+( y+5)24=1In the following exercises, graph each ellipse. 121. ( x5)29+( y+4)225=1In the following exercises, graph each ellipse. 122. ( x+5)236+( y3)216=1In the following exercises, (a) write the equation in standard form and (b) graph. 123. 25x2+9y2100x54y44=0In the following exercises, (a) write the equation in standard form and (b) graph. 124. 4x2+25y2+8x+100y+4=0In the following exercises, (a) write the equation in standard form and (b) graph. 125. 4x2+25y224x64=0In the following exercises, (a) write the equation in standard form and (b) graph. 126. 9x2+4y2+56y+160=0In the following exercises, graph the equation. 127. x=2(y1)2+2In the following exercises, graph the equation. 128. x2+y2=49In the following exercises, graph the equation. 129. (x+5)2+(y+2)2=4In the following exercises, graph the equation. 130. y=x2+8x15In the following exercises, graph the equation. 131. ( x+3)216+( y+1)24=1In the following exercises, graph the equation. 132. (x2)2+(y3)2=9In the following exercises, graph the equation. 133. x225+y236=1In the following exercises, graph the equation. 134. x=4(y+1)24In the following exercises, graph the equation. 135. x2+y2=64In the following exercises, graph the equation. 136. x29+y225=1In the following exercises, graph the equation. 137. y=6x2+2x1In the following exercises, graph the equation. 138. ( x2)29+( y+3)225=1A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 10 AU and the furthest is approximately 30 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the planet.A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 10 AU and the furthest is approximately 70 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the planet.A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 15 AU and the furthest is approximately 85 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 15 AU and the furthest is approximately 95 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.In your own words, define an ellipse and write the equation of an ellipse centered at the origin in standard form. Draw a sketch of the ellipse labeling the center, vertices and major and minor axes.Explain in your own words how to get the axes from the equation in standard form.Compare and contrast the graphs of the equations x24+y29=1 and x29+y24=1.Explain in your own words, the difference between a vertex and a focus of the ellipse.Graph x216y24=1.x29y216=1.Graph 4y225x2=100.Graph 25y29x2=225.Graph ( x3)225( y1)29=1.Graph ( x2)24( y2)29=1.Graph ( y+3)216( x+2)29=1.Graph ( y+2)29( x+2)29=1.Write the equation in standard form and (b) graph 9x216y2+18x+64y199=0.Write the equation in standard form and (b) graph 16x225y2+96x50y281=0.Identify the graph of each equation as a circle, a parabola, ellipse, or hyperbola. (a) x2+y28x6y=0 (b) 4x2+25y2=100 (c) y=6x2+2x1 (d) 16y29x2=144Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola. (a) 16x2+9y2=144 (b) y=2x2+4x+6 (c) x2+y2+2x+6y+9=0 (d) 4x216y2=64In the following exercises, graph. 147. x29y24=1In the following exercises, graph. 148. x225y29=1In the following exercises, graph. 149. x216y225=1In the following exercises, graph. 150. x29y236=1In the following exercises, graph. 151. y225x24=1In the following exercises, graph. 152. y236x216=1In the following exercises, graph. 153. 16y29x2=144In the following exercises, graph. 154. 25y29x2=225In the following exercises, graph. 155. 4y29x2=36In the following exercises, graph. 156. 16y225x2=400In the following exercises, graph. 157. 4x216y2=64AIn the following exercises, graph. 158. 9x24y2=36In the following exercises, graph. 159. ( x1)216( y3)24=1In the following exercises, graph. 160. ( x2)24( y3)216=1In the following exercises, graph. 161. ( y4)29( x2)225=1In the following exercises, graph. 162. ( y1)225( x4)216=1LIn the following exercises, graph. 163. ( y+4)225( x+1)236=1In the following exercises, graph. 164. ( y+1)216( x+1)24=1In the following exercises, graph. 165. ( y4)216( x+1)225=1In the following exercises, graph. 166. ( y+3)216( x3)236=1In the following exercises, graph. 167. ( x3)225( y+2)29=1In the following exercises, graph. 168. ( x+2)24( y1)29=1In the following exercises, (a) write the equation in standard form and (b) graph. 169. 9x24y218x+8y31=0In the following exercises, (a) write the equation in standard form and (b) graph. 170. 16x24y2+64x24y36=0In the following exercises, (a) write the equation in standard form and (b) graph. 171. y2x24y+2x6=0In the following exercises, (a) write the equation in standard form and (b) graph. 172. 4y216x224y+96x172=0In the following exercises, (a) write the equation in standard form and (b) graph. 173. 9y2x2+18y4x4=0In the following exercises, identify the type of graph. 174. (a) x=y22y+3 (b) 9y2x2+18y4x4=0 (c) 9x2+25y2=225 (d) x2+y24x+10y7=0In the following exercises, identify the type of graph. 175. (a) x=2y212y16 (b) x2+y2=9 (c) 16x24y2+64x24y36=0 (d) 16x2+36y2=576In the following exercises, graph each equation. 176. ( y3)29( x+2)216=1In the following exercises, graph each equation. 177. x2+y24x+10y7=0In the following exercises, graph each equation. 178. y=(x1)2+2In the following exercises, graph each equation. 179. x29+y225=1In the following exercises, graph each equation. 180. (x+2)2+(y5)2=4In the following exercises, graph each equation. 181. y2x24y+2x6=0In the following exercises, graph each equation. 182. x=y22y+3In the following exercises, graph each equation. 183. 16x2+9y2=144In your own words, define a hyperbola and write the equation of a hyperbola centered at the origin in standard form. Draw a sketch of the hyperbola labeling the center, vertices, and asymptotes.Explain in your own words how to create and use the rectangle that helps graph a hyperbola.Compare and contrast the graphs of the equations x24y29=1 and y29x24=1.Explain in your own words, how to distinguish the equation of an ellipse with the equation of a hyperbola.Solve the system by graphing: {x+y=4y=x2+2.Solve the system by graphing: {xy=1y=x2+3.Solve the system by graphing: {x=6 (x3 )2+ (y1 )2=9.LSolve the system by graphing: {y=4 (x2 )2+ (y+3 )2=4.Solve the system by using substitution: {x2+9y2=9y=13x3.Solve the system by using substitution: {4x2+y2=4y=x+2.Solve the system by using substitution: {x2y=0y=2x3.Solve the system by using substitution: {y2x=0y=3x2.Solve the system by elimination: {x2+y2=9x2y=9.Solve the system by elimination: {x2+y2=1x+y2=1.Solve the system by elimination: {x2+y2=25x2y2=7.Solve the system by elimination: {x2+y2=4x2y2=4.The difference of the squares of two numbers is -20. The sum of the numbers is 10. Findthe numbers.The difference of the squares of two numbers is 35. The sum of the numbers is -1. Find the numbers.Edgar purchased a small 20" TV for his garage. The size of a TV is measured on the diagonal of the screen. The Screen also has an area of 192 Square inches. What are the length and Width of the TV screen?The Harper family purchased a small microwave for their family room. The diagonal of the door measures 15 inches. The door also has an area of 108 square inches. What are the length and width of the microwave door?In the following exercises, solve the system of equations by using graphing. 188. {y=2x+2y=x2+2In the following exercises, solve the system of equations by using graphing. 189. {y=6x4y=2x2In the following exercises, solve the system of equations by using graphing. 190. { x+y=2 x= y 2In the following exercises, solve the system of equations by using graphing. 191. {xy=2x=y2In the following exercises, solve the system of equations by using graphing. 192. {y=32x+3y=x2+2In the following exercises, solve the system of equations by using graphing. 193. {y=x1y=x2+1In the following exercises, solve the system of equations by using graphing. 194. {x=2x2+y2=4In the following exercises, solve the system of equations by using graphing. 195.{y=4x2+y=16In the following exercises, solve the system of equations by using graphing. 196. {x=2 (x+2 )2+ (y+3 )2=16In the following exercises, solve the system of equations by using graphing. 197. {y=1 (x2 )2+ (y4 )2=25In the following exercises, solve the system of equations by using graphing. 198. {y=2x+4y=x+1In the following exercises, solve the system of equations by using graphing. 199. {y=12x+2y=x2In the following exercises, solve the system of equations by using substitution. 200. {x2+4y2=4y=12x1In the following exercises, solve the system of equations by using substitution. 201. {9x2+y2=9y=3x+3In the following exercises, solve the system of equations by using substitution. 202. {9x2+y2=9y=x+3In the following exercises, solve the system of equations by using substitution. 203. {9x2+y2=36x=2In the following exercises, solve the system of equations by using substitution. 204. {4x2+y2=4y=4In the following exercises, solve the system of equations by using substitution. 205. {x2+y2=169x=12In the following exercises, solve the system of equations by using substitution. 206. {3x2y=0y=2x1In the following exercises, solve the system of equations by using substitution. 207. {2y2x=0y=x+1In the following exercises, solve the system of equations by using substitution. 208. {y=x2+3y=x+3In the following exercises, solve the system of equations by using substitution. 209. {y=x24y=x4In the following exercises, solve the system of equations by using substitution. 210. {x2+y2=25xy=1In the following exercises, solve the system of equations by using substitution. 211. {x2+y2=252x+y=10In the following exercises, solve the system of equations by using elimination. 212. {x2+y2=16x22y=8In the following exercises, solve the system of equations by using elimination. 213. {x2+y2=16x2y=4In the following exercises, solve the system of equations by using elimination. 214. {x2+y2=4x22y=1In the following exercises, solve the system of equations by using elimination. 215. {x2+y2=4x2y=2In the following exercises, solve the system of equations by using elimination. 216.{x2+y2=9x2y=3In the following exercises, solve the system of equations by using elimination. 217. {x2+y2=4y2x=2In the following exercises, solve the system of equations by using elimination. 218. {x2+y2=252x23y2=5In the following exercises, solve the system of equations by using elimination. 219. {x2+y2=20x2y2=12In the following exercises, solve the system of equations by using elimination. 220. {x2+y2=13x2y2=5In the following exercises, solve the system of equations by using elimination. 221. {x2+y2=16x2y2=16In the following exercises, solve the system of equations by using elimination. 222. {4x2+9y2=362x29y2=18In the following exercises, solve the system of equations by using elimination. 223. {x2y2=32x2+y2=6In the following exercises, solve the system of equations by using elimination. 224. {4x2y2=44x2+y2=4In the following exercises, solve the system of equations by using elimination. 255. {x2y2=53x2+2y2=30In the following exercises, solve the system of equations by using elimination. 226. {x2y2=1x22y=4In the following exercises, solve the system of equations by using elimination. 227. {2x2+y2=11x2+3y2=28In the following exercises, solve the problem using a system of equations. 228. The sum of two numbers is 6and the product is 8. Find the numbers.In the following exercises, solve the problem using a system of equations. 229. The sum of two numbers is 11 and the product is 42. Find the numbers.In the following exercises, solve the problem using a system of equations. 230. The sum of the squares of two numbers is 65. The difference of the number is 3. Find the numbers.In the following exercises, solve the problem using a system of equations. 231. The sum of the squares of two numbers is 113. The difference of the number is I. Find the numbers.In the following exercises, solve the problem using a system of equations. 232. The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.In the following exercises, solve the problem using a system of equations. 233. The difference of the squares of two numbers is 20. The difference of the square of the first number and twice the square of the second number is 4. Find the numbers.In the following exercises, solve the problem using a system of equations. 234. The perimeter of a rectangle is 32 inches and its area is 63 square inches. Find the length and width of the rectangle.In the following exercises, solve the problem using a system of equations. 235. The perimeter of a rectangle is 52 cm and its area is 165cm2.Find the length and width of the rectangle.In the following exercises, solve the problem using a system of equations. 236. Dion purchased a new microwave. The diagonal of the door measures 17 inches. The door also has an area of 120 square inches. What are the length and width of the microwave door?In the following exercises, solve the problem using a system of equations. 237. Jules purchased a microwave for his kitchen. The diagonal of the front of the microwave measures 26 inches. The front also has an area of 240 square inches. What are the length and width of the microwave?In the following exercises, solve the problem using a system of equations. 238. Roman found a widescreen TV on sale, but isn't sure if it will fit his entertainment center. The TV is 60". The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of 1728 square inches. His entertainment center has an insert for the TV with a length of 50 inches and width of 40 inches. What are the length and width of the TV screen and will it fit Roman's entertainment center?In the following exercises, solve the problem using a system of equations. 239. Donnette found a widescreen TV at a garage sale, but isn't sure if it will fit her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of 1200 square inches. Her entertainment center has an insert for the TV with a length of 38 inches and width of 27 inches. What are the length and width of the TV screen and will it fit Donnette's entertainment center?In your own words, explain the advantages and disadvantages of solving a system of equations by graphing.Explain in your own words how to solve a system of equations using substitution.Explain in your own words how to solve a system of equations using elimination.A circle and a parabola can intersect in ways that would result in 0, 1, 2, 3, or 4 solutions. Draw a sketch of each of the possibilities.In the following exercises, find the distance between the points. Round to the nearest tenth if needed. 244. (5,1) and (1,4)In the following exercises, find the distance between the points. Round to the nearest tenth if needed. 245. (2,5) and (1,5)In the following exercises, find the distance between the points. Round to the nearest tenth if needed. 246. (8,2) and (7,3)In the following exercises, find the distance between the points. Round to the nearest tenth if needed. 247. (1,4) and (5,5)In the following exercises, find the midpoint of the line segments whose endpoints are given. 248. (2,6) and (4,2)In the following exercises, find the midpoint of the line segments whose endpoints are given. 249. (3,7) and (5,1)In the following exercises, find the midpoint of the line segments whose endpoints are given. 250. (8,10) and (9,5)In the following exercises, find the midpoint of the line segments whose endpoints are given. 251. (3,2) and (6,9)In the following exercises, write the standard form of the equation of the circle with the given information. 252. radius is 15 and center is (0,0)In the following exercises, write the standard form of the equation of the circle with the given information. 253. radius is 7 and center is (0,0)In the following exercises, write the standard form of the equation of the circle with the given information. 254. radius is 9 and center is (3,5)In the following exercises, write the standard form of the equation of the circle with the given information. 255. radius is 7 and center is (2,5)In the following exercises, write the standard form of the equation of the circle with the given information. 256. center is (3,6) and a point on the circle is (3,2)In the following exercises, write the standard form of the equation of the circle with the given information. 257. center is (2,2) and a point on the circle is (4,4)In the following exercises, (a) find the center and radius, then (b) graph each circle. 258. 2x2+2y2=450In the following exercises, (a) find the center and radius, then (b) graph each circle. 259. 3x2+3y2=432In the following exercises, (a) find the center and radius, then (b) graph each circle. 260. (x+3)2+(y5)2=81In the following exercises, (a) find the center and radius, then (b) graph each circle. 261. (x+2)2+(y+5)2=49In the following exercises, (a) find the center and radius, then (b) graph each circle. 262. x2+y26x12y19=0In the following exercises, (a) find the center and radius, then (b) graph each circle. 263. x2+y24y60=0In the following exercises, graph each equation by using its properties. 264. y=x2+4x3In the following exercises, graph each equation by using its properties. 265. y=2x2+10x+7In the following exercises, graph each equation by using its properties. 266. y=6x2+12x1In the following exercises, graph each equation by using its properties. 267. y=x2+10xIn the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 268. y=x2+4x+7In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 269. y=2x24x2In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 270. y=3x218x29In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 271. y=x2+12x35In the following exercises, graph each equation by using its properties. 272. x=2y2In the following exercises, graph each equation by using its properties. 273. x=2y2+4y+6In the following exercises, graph each equation by using its properties. 274. x=y2+2y4In the following exercises, graph each equation by using its properties. 275. x=3y2In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 276. x=4y2+8yIn the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 277. x=y2+4y+5In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 278. x=y26y7In the following exercises, (a) write the equation in standard form, then (b) use properties of the standard form to graph the equation. 279. x=2y2+4yIn the following exercises, create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in standard form. 280.In the following exercises, create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in standard form. 281.]In the following exercises, graph each ellipse. 282. x236+y225=1In the following exercises, graph each ellipse. 283. x24+y281=1In the following exercises, graph each ellipse. 285. 9x2+y2=9In the following exercises, graph each ellipse. 285. 9x2+y2=9In the following exercises, find the equation of the ellipse shown in the graph. 286.In the following exercises, find the equation of the ellipse shown in the graph. 287.In the following exercises, graph each ellipse. 288. ( x1)225+( y6)24=1In the following exercises, graph each ellipse. 289. ( x+4)216+( y+1)29=1In the following exercises, graph each ellipse. 290. ( x5)216+( y+3)236=1In the following exercises, graph each ellipse. 291. ( x+3)29+( y2)225=1In the following exercises, (a) write the equation in standard form and (b) graph. 292. x2+y2+12x+40y+120=0In the following exercises, (a) write the equation in standard form and (b) graph. 293. 25x2+4y2150x56y+321=0In the following exercises, (a) write the equation in standard form and (b) graph. 294. 25x2+4y2+150x+125=0In the following exercises, (a) write the equation in standard form and (b) graph. 295. 4x2+9y2126x+405=0In the following exercises, write the equation of the ellipse described. 296. A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 10 AU and the furthest is approximately 90 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.In the following exercises, graph. 297. x225y29=1In the following exercises, graph. 298. y249x216=1In the following exercises, graph. 299. 9y216x2=144In the following exercises, graph. 300. 16x24y2=64In the following exercises, graph. 301. ( x+1)24( y+1)29=1]In the following exercises, graph. 302. ( x2 ) 2 4 ( y3 ) 2 16 =1In the following exercises, graph. 303. ( y+2)29( x+1)29=1In the following exercises, graph. 304. ( y1)225( x2)29=1In the following exercises, (a) write the equation in standard form and (b) graph. 305. 4x216y2+8x+96y204=0In the following exercises, (a) write the equation in standard form and (b) graph. 306. 16x24y264x24y36=0In the following exercises, (a) write the equation in standard form and (b) graph. 307. 4y216x2+32x8y76=0In the following exercises, (a) write the equation in standard form and (b) graph. 308. 36y216x296x+216y396=0In the following exercises, identify the type of graph. 309. (a) 16y29x236x96y36=0 (b) x2+y24x+10y7=0 (c) y=x22x+3 (d) 25x2+9y2=225In the following exercises, identify the type of graph. 310. (a) x2+y2+4x10y+25=0 (b) y2x24y+2x6=0 (c) x=y22y+3 (d) 16x2+9y2=144In the following exercises, solve the system of equations by using graphing. 311. {3 x 2y=0y=2x1In the following exercises, solve the system of equations by using graphing. 312. {y= x 24y=x4In the following exercises, solve the system of equations by using graphing. 313. { x 2+ y 2=169x=12In the following exercises, solve the system of equations by using graphing. 314. { x 2+ y 2=25y=5In the following exercises, solve the system of equations by using substitution. 315. {y= x 2+3y=2x+2In the following exercises, solve the system of equations by using substitution. 316. { x 2+ y 2=4xy=5In the following exercises, solve the system of equations by using substitution. 317. {9 x 2+4 y 2=36yx=5In the following exercises, solve the system of equations by using substitution. 318. { x 2+4 y 2=42xy=1In the following exercises, solve the system of equations by using elimination. 319. { x 2+ y 2=16 x 22 y 2=0In the following exercises, solve the system of equations by using elimination. 320. { x 2 y 2=52 x 23 y 2=30In the following exercises, solve the system of equations by using elimination. 321. {4 x 2+9 y 2=363 y 24x=12In the following exercises, solve the system of equations by using elimination. 322. { x 2+ y 2=14 x 2 y 2=16In the following exercises, solve the problem using a system of equations. 323. The sum of the squares of two numbers is 25. The difference of the numbers is 1. Find the numbers.In the following exercises, solve the problem using a system of equations. 324. The difference of the squares of two numbers is 45. The difference of the square of the first number and twice the square of the second number is 9. Find the numbers.In the following exercises, solve the problem using a system of equations. 325. The perimeter of a rectangle is 58 meters and its area is 210 square meters. Find the length and width of the rectangle.In the following exercises, solve the problem using a system of equations. 326. Colton purchased a larger microwave for his kitchen. The diagonal of the front of the microwave measures 34 inches. The front also has an area of 480 square inches. What are the length and width of the microwave?In the following exercises, find the distance between the points and the midpoint of the line segment with the given endpoints. Round to the nearest tenth as needed. 327. (4,3) and (10,11)In the following exercises, find the distance between the points and the midpoint of the line segment with the given endpoints. Round to the nearest tenth as needed. 328. (6,8) and (5,3)In the following exercises, write the standard form of the equation of the circle with the given information. 329. radius is 11 and center is (0,0)In the following exercises, write the standard form of the equation of the circle with the given information. 330. radius is 12 and center is (10,2)In the following exercises, write the standard form of the equation of the circle with the given information. 331. center is (2,3) and a point on the circle is (2,3)In the following exercises, write the standard form of the equation of the circle with the given information. 332. Find the equation of the ellipse shown in the graph.In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 333. 4x2+49y2=196In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 334. y=3(x2)22In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 335. 3x2+3y2=27In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 336. y2100x236=1In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 337. x216+y281=1In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 338. x=2y2+10y+7In the following exercises, (a) identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and (b) graph the equation. 339. 64x29y2=576In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 340. 25x2+64y2+200x256y944=0In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 341. x2+y2+10x+6y+30=0In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 342. x=y2+2y4In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 343. 9x225y236x50y214=0In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 344. y=x2+6x+8In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 345. Solve the nonlinear system of equations by graphing: {3 y 2x=0y=2x1.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 346. Solve the nonlinear system of equations using substitution: { x 2+ y 2=7y=x=4.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 347. Solve the nonlinear system of equations using elimination: { x 2+9 y 2=92 x 29 y 2=18.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 348. Create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in y=ax2+bx+c form.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 349. A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 20 AU and the furthest is approximately 70 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 350. The sum of two numbers is 22 and the product is -240. Find the numbers.In the following exercises, (a) identify the type of graph equation as a circle, parabola, ellipse, or hyperbola, (b) write the equation in standard form, and (c) graph the equation. 351. For her birthday, Olive's grandparents bought her a new widescreen TV. Before opening it she wants to make sure it will fit her entertainment center. The TV is 55". The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of 1452 square inches. Her entertainment center has an insert for the TV with a length of 50 inches and width of 40 inches. What are the length and width of the TV screen and will it fit Olive's entertainment center?