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Algebra and Trigonometry, 2015a
Algebra and Trigonometry, 2015a
Algebra and Trigonometry, 2015a
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<strong>Algebra</strong> <strong>and</strong> <strong>Trigonometry</strong><br />
SENIOR CONTRIBUTING AUTHOR<br />
JAY ABRAMSON, ARIZONA STATE UNIVERSITY
<strong>Algebra</strong> <strong>and</strong> <strong>Trigonometry</strong> SENIOR CONTRIBUTING AUTHOR JAY ABRAMSON, ARIZONA STATE UNIVERSITY
- Page 4 and 5: About Our Team Senior Contributing
- Page 6: OpenStax Rice University 6100 Main
- Page 9: Brief Contents 1 Prerequisites 1 2
- Page 12 and 13: 4 Linear Functions 279 4.1 Linear F
- Page 14 and 15: 11 12 13 Systems of Equations and I
- Page 16 and 17: About Algebra and Trigonometry Writ
- Page 18 and 19: Section Exercises Each section of e
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38 CHAPTER 1 PREREQUISITES We know
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40 CHAPTER 1 PREREQUISITES 59. √
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42 CHAPTER 1 PREREQUISITES A polyno
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44 CHAPTER 1 PREREQUISITES How To
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46 CHAPTER 1 PREREQUISITES How To
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48 CHAPTER 1 PREREQUISITES 1.4 SECT
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50 CHAPTER 1 PREREQUISITES greatest
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52 CHAPTER 1 PREREQUISITES Example
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54 CHAPTER 1 PREREQUISITES We can u
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56 CHAPTER 1 PREREQUISITES 1.5 SECT
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58 CHAPTER 1 PREREQUISITES LEARNING
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60 CHAPTER 1 PREREQUISITES How To
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62 CHAPTER 1 PREREQUISITES Try It #
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64 CHAPTER 1 PREREQUISITES 1.6 SECT
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66 CHAPTER 1 PREREQUISITES CHAPTER
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68 CHAPTER 1 PREREQUISITES Key Conc
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70 CHAPTER 1 PREREQUISITES CHAPTER
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72 CHAPTER 1 PREREQUISITES CHAPTER
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74 CHAPTER 2 EQUATIONS AND INEQUALI
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76 CHAPTER 2 EQUATIONS AND INEQUALI
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158 CHAPTER 2 EQUATIONS AND INEQUAL
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160 CHAPTER 3 FUNCTIONS LEARNING OB
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162 CHAPTER 3 FUNCTIONS Percent gra
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164 CHAPTER 3 FUNCTIONS Table 4 def
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166 CHAPTER 3 FUNCTIONS Example 7 E
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168 CHAPTER 3 FUNCTIONS Evaluating
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170 CHAPTER 3 FUNCTIONS Try It #8 U
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172 CHAPTER 3 FUNCTIONS Example 14
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174 CHAPTER 3 FUNCTIONS we know the
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176 CHAPTER 3 FUNCTIONS 3.1 SECTION
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178 CHAPTER 3 FUNCTIONS 52. Given t
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180 CHAPTER 3 FUNCTIONS LEARNING OB
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182 CHAPTER 3 FUNCTIONS Example 2 F
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184 CHAPTER 3 FUNCTIONS To combine
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186 CHAPTER 3 FUNCTIONS Solution We
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188 CHAPTER 3 FUNCTIONS f (x) Domai
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190 CHAPTER 3 FUNCTIONS piecewise f
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192 CHAPTER 3 FUNCTIONS Now that we
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194 CHAPTER 3 FUNCTIONS 30. y 31. y
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196 CHAPTER 3 FUNCTIONS LEARNING OB
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198 CHAPTER 3 FUNCTIONS Solution At
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200 CHAPTER 3 FUNCTIONS Try It #3 F
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202 CHAPTER 3 FUNCTIONS Analysis No
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204 CHAPTER 3 FUNCTIONS Function In
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206 CHAPTER 3 FUNCTIONS 3.3 SECTION
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208 CHAPTER 3 FUNCTIONS For the fol
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210 CHAPTER 3 FUNCTIONS For two fun
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212 CHAPTER 3 FUNCTIONS Solution Le
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214 CHAPTER 3 FUNCTIONS How To… G
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216 CHAPTER 3 FUNCTIONS Try It #5 G
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218 CHAPTER 3 FUNCTIONS 3.4 SECTION
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220 CHAPTER 3 FUNCTIONS For the fol
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222 CHAPTER 3 FUNCTIONS LEARNING OB
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224 CHAPTER 3 FUNCTIONS Notice that
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226 CHAPTER 3 FUNCTIONS Analysis No
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228 CHAPTER 3 FUNCTIONS How To… G
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230 CHAPTER 3 FUNCTIONS reflections
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232 CHAPTER 3 FUNCTIONS Example 11
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234 CHAPTER 3 FUNCTIONS Analysis Co
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238 CHAPTER 3 FUNCTIONS Example 16
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240 CHAPTER 3 FUNCTIONS Performing
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242 CHAPTER 3 FUNCTIONS Next, we ho
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244 CHAPTER 3 FUNCTIONS NUMERIC 31.
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246 CHAPTER 3 FUNCTIONS For the fol
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248 CHAPTER 3 FUNCTIONS Graphing an
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250 CHAPTER 3 FUNCTIONS Q & A… Do
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252 CHAPTER 3 FUNCTIONS 3.6 SECTION
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254 CHAPTER 3 FUNCTIONS LEARNING OB
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256 CHAPTER 3 FUNCTIONS Example 1 I
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258 CHAPTER 3 FUNCTIONS domain and
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260 CHAPTER 3 FUNCTIONS Example 6 E
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262 CHAPTER 3 FUNCTIONS Try It #8 W
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264 CHAPTER 3 FUNCTIONS 3.7 SECTION
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266 CHAPTER 3 FUNCTIONS TECHNOLOGY
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268 CHAPTER 3 FUNCTIONS set-builder
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270 CHAPTER 3 FUNCTIONS A local mi
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272 CHAPTER 3 FUNCTIONS CHAPTER 3 R
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274 CHAPTER 3 FUNCTIONS 32. For the
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276 CHAPTER 3 FUNCTIONS INVERSE FUN
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278 CHAPTER 3 FUNCTIONS For the fol
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280 CHAPTER 4 LINEAR FUNCTIONS LEAR
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282 CHAPTER 4 LINEAR FUNCTIONS line
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284 CHAPTER 4 LINEAR FUNCTIONS x 2
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286 CHAPTER 4 LINEAR FUNCTIONS If w
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288 CHAPTER 4 LINEAR FUNCTIONS We c
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290 CHAPTER 4 LINEAR FUNCTIONS Try
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292 CHAPTER 4 LINEAR FUNCTIONS Q &
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294 CHAPTER 4 LINEAR FUNCTIONS y y
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296 CHAPTER 4 LINEAR FUNCTIONS Find
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298 CHAPTER 4 LINEAR FUNCTIONS hori
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300 CHAPTER 4 LINEAR FUNCTIONS Solu
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302 CHAPTER 4 LINEAR FUNCTIONS How
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304 CHAPTER 4 LINEAR FUNCTIONS 4.1
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306 CHAPTER 4 LINEAR FUNCTIONS 61.
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308 CHAPTER 4 LINEAR FUNCTIONS 111.
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310 CHAPTER 4 LINEAR FUNCTIONS Now
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312 CHAPTER 4 LINEAR FUNCTIONS 8100
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314 CHAPTER 4 LINEAR FUNCTIONS Usin
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316 CHAPTER 4 LINEAR FUNCTIONS Exam
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318 CHAPTER 4 LINEAR FUNCTIONS For
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320 CHAPTER 4 LINEAR FUNCTIONS REAL
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322 CHAPTER 4 LINEAR FUNCTIONS LEAR
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324 CHAPTER 4 LINEAR FUNCTIONS Reco
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326 CHAPTER 4 LINEAR FUNCTIONS How
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328 CHAPTER 4 LINEAR FUNCTIONS Exam
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330 CHAPTER 4 LINEAR FUNCTIONS GRAP
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332 CHAPTER 4 LINEAR FUNCTIONS 27.
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334 CHAPTER 4 LINEAR FUNCTIONS CHAP
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336 CHAPTER 4 LINEAR FUNCTIONS CHAP
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338 CHAPTER 4 LINEAR FUNCTIONS For
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340 CHAPTER 4 LINEAR FUNCTIONS CHAP
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342 CHAPTER 4 LINEAR FUNCTIONS 27.
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344 CHAPTER 5 POLYNOMIAL AND RATION
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346 CHAPTER 5 POLYNOMIAL AND RATION
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348 CHAPTER 5 POLYNOMIAL AND RATION
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464 CHAPTER 6 EXPONENTIAL AND LOGAR
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466 CHAPTER 6 EXPONENTIAL AND LOGAR
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576 CHAPTER 7 THE UNIT CIRCLE: SINE
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762 CHAPTER 10 FURTHER APPLICATIONS
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868 CHAPTER 10 FURTHER APPLICATIONS
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870 CHAPTER 10 FURTHER APPLICATIONS
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872 CHAPTER 10 FURTHER APPLICATIONS
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11 Systems of Equations and Inequal
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SYSTEMS OF LINEAR EQUA
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SECTION 11.1 SECTION EXERCISES 889
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SECTION 11.1 SECTION EXERCISES 891
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SECTION 11.2 SYSTEMS OF LINEAR EQUA
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SECTION 11.2 SYSTEMS OF LINEAR EQUA
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SECTION 11.2 SYSTEMS OF LINEAR EQUA
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11.2 SECTION EXERCISES VERBAL SECTI
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SECTION 11.2 SECTION EXERCISES 901
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SECTION 11.3 SYSTEMS OF NONLINEAR E
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SECTION 11.3 SYSTEMS OF NONLINEAR E
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SECTION 11.3 SYSTEMS OF NONLINEAR E
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SECTION 11.3 SYSTEMS OF NONLINEAR E
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SECTION 11.3 SECTION EXERCISES 911
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SECTION 11.4 PARTIAL FRACTIONS 913
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SECTION 11.4 PARTIAL FRACTIONS 915
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SECTION 11.4 PARTIAL FRACTIONS 917
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SECTION 11.4 PARTIAL FRACTIONS 919
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SECTION 11.4 SECTION EXERCISES 921
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SECTION 11.5 MATRICES AND MATRIX OP
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SECTION 11.5 MATRICES AND MATRIX OP
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SECTION 11.5 MATRICES AND MATRIX OP
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SECTION 11.5 MATRICES AND MATRIX OP
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SECTION 11.5 MATRICES AND MATRIX OP
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SECTION 11.5 SECTION EXERCISES 933
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SECTION 11.6 SOLVING SYSTEMS WITH G
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SECTION 11.6 SOLVING SYSTEMS WITH G
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SECTION 11.6 SOLVING SYSTEMS WITH G
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SECTION 11.6 SOLVING SYSTEMS WITH G
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SECTION 11.6 SOLVING SYSTEMS WITH G
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SECTION 11.6 SECTION EXERCISES 945
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SOLVING SYSTEMS WITH I
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SECTION 11.7 SECTION EXERCISES 959
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SECTION 11.8 SOLVING SYSTEMS WITH C
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SECTION 11.8 SOLVING SYSTEMS WITH C
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SECTION 11.8 SOLVING SYSTEMS WITH C
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SECTION 11.8 SOLVING SYSTEMS WITH C
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SECTION 11.8 SECTION EXERCISES 969
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SECTION 11.8 SECTION EXERCISES 971
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CHAPTER 11 REVIEW 973 system of lin
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CHAPTER 11 REVIEW 975 Many real-wo
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CHAPTER 11 REVIEW 977 SYSTEMS OF NO
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CHAPTER 11 PRACTICE TEST 979 CHAPTE
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12 Analytic Geometry a b Figure 1 (
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SECTION 12.1 THE ELLIPSE 983 equati
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SECTION 12.1 THE ELLIPSE 985 Writin
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SECTION 12.1 THE ELLIPSE 987 standa
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SECTION 12.1 THE ELLIPSE 989 How To
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SECTION 12.1 THE ELLIPSE 991 How To
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SECTION 12.1 THE ELLIPSE 993 Try It
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SECTION 12.1 SECTION EXERCISES 995
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SECTION 12.2 THE HYPERBOLA 997 LEAR
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SECTION 12.2 THE HYPERBOLA 999 If (
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SECTION 12.2 THE HYPERBOLA 1001 Exa
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SECTION 12.2 THE HYPERBOLA 1003 The
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SECTION 12.2 THE HYPERBOLA 1005 How
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SECTION 12.2 THE HYPERBOLA 1007 (y
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SECTION 12.2 THE HYPERBOLA 1009 Exa
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SECTION 12.2 SECTION EXERCISES 1011
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SECTION 12.2 SECTION EXERCISES 1013
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SECTION 12.3 THE PARABOLA 1015 Like
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SECTION 12.3 THE PARABOLA 1017 How
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SECTION 12.3 THE PARABOLA 1019 Try
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SECTION 12.3 THE PARABOLA 1021 Try
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SECTION 12.3 THE PARABOLA 1023 Try
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SECTION 12.3 SECTION EXERCISES 1025
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SECTION 12.4 ROTATION OF AXIS 1027
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SECTION 12.4 ROTATION OF AXIS 1029
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SECTION 12.4 ROTATION OF AXIS 1031
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SECTION 12.4 ROTATION OF AXIS 1033
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SECTION 12.4 ROTATION OF AXIS 1035
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SECTION 12.4 ROTATION OF AXIS 1037
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SECTION 12.4 SECTION EXERCISES 1039
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SECTION 12.5 CONIC SECTIONS IN POLA
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SECTION 12.5 CONIC SECTIONS IN POLA
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SECTION 12.5 CONIC SECTIONS IN POLA
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SECTION 12.5 CONIC SECTIONS IN POLA
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CHAPTER 12 REVIEW 1049 CHAPTER 12 R
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CHAPTER 12 REVIEW 1051 12.3 The Par
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CHAPTER 12 REVIEW 1053 For the foll
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13 Sequences, Probability and Count
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SECTION 13.1 SEQUENCES AND THEIR NO
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SECTION 13.1 SEQUENCES AND THEIR NO
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SECTION 13.1 SEQUENCES AND THEIR NO
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SECTION 13.1 SEQUENCES AND THEIR NO
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SECTION 13.1 SEQUENCES AND THEIR NO
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SECTION 13.1 SECTION EXERCISES 1067
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SECTION 13.2 ARITHMETIC SEQUENCES 1
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SECTION 13.2 ARITHMETIC SEQUENCES 1
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SECTION 13.2 ARITHMETIC SEQUENCES 1
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SECTION 13.2 ARITHMETIC SEQUENCES 1
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SECTION 13.2 SECTION EXERCISES 1077
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SECTION 13.3 GEOMETRIC SEQUENCES 10
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SECTION 13.3 GEOMETRIC SEQUENCES 10
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SECTION 13.3 GEOMETRIC SEQUENCES 10
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SECTION 13.3 SECTION EXERCISES 1085
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SECTION 13.4 SERIES AND THEIR NOTAT
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SECTION 13.4 SERIES AND THEIR NOTAT
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SECTION 13.4 SERIES AND THEIR NOTAT
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SECTION 13.4 SERIES AND THEIR NOTAT
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SECTION 13.4 SERIES AND THEIR NOTAT
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SECTION 13.4 SECTION EXERCISES 1097
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SECTION 13.4 SECTION EXERCISES 1099
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SECTION 13.5 COUNTING PRINCIPLES 11
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SECTION 13.5 COUNTING PRINCIPLES 11
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SECTION 13.5 COUNTING PRINCIPLES 11
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SECTION 13.5 COUNTING PRINCIPLES 11
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SECTION 13.5 SECTION EXERCISES 1109
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SECTION 13.6 BINOMIAL THEOREM 1111
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SECTION 13.6 BINOMIAL THEOREM 1113
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SECTION 13.6 SECTION EXERCISES 1115
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SECTION 13.7 PROBABILITY 1117 LEARN
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SECTION 13.7 PROBABILITY 1119 Try I
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SECTION 13.7 PROBABILITY 1121 Compl
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SECTION 13.7 PROBABILITY 1123 Becau
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SECTION 13.7 SECTION EXERCISES 1125
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CHAPTER 13 REVIEW 1127 recursive fo
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CHAPTER 13 REVIEW 1129 If the sum
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CHAPTER 13 REVIEW 1131 25. Use the
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CHAPTER 13 PRACTICE TEST 1133 CHAPT
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Proofs, Identities, and Toolkit Fun
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APPENDIX A-3 A3 Trigonometric Ident
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Try It Answers Chapter 1 Section 1.
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TRY IT ANSWERS B-3 2. A gravitation
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TRY IT ANSWERS B-5 Chapter 6 Sectio
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TRY IT ANSWERS B-7 8. 9. 10. 11. -
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TRY IT ANSWERS B-9 Section 10.6 1.
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TRY IT ANSWERS B-11 Section 12.5 Se
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C-2 ODD ANSWERS y + 5 5. _____ y +
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C-4 ODD ANSWERS 5. We start by find
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C-6 ODD ANSWERS 21. (−∞, 5) 23.
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C-8 ODD ANSWERS 77. The graph of f
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C-10 ODD ANSWERS 7. Yes 9. Yes 11.
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C-12 ODD ANSWERS 21. Domain: (−
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C-14 ODD ANSWERS 55. 2 positive, 2
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C-16 ODD ANSWERS 41. y = _ 3 x 2 4
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C-18 ODD ANSWERS 15. Domain: (−3,
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C-20 ODD ANSWERS Section 6.8 1. Log
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C-22 ODD ANSWERS 7. 9. 11. 13. 7. _
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C-24 ODD ANSWERS 17. Amplitude: 5;
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C-26 ODD ANSWERS 57. a. h(x) = 2 ta
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C-28 ODD ANSWERS 33. f (x) = 2 cos
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C-30 ODD ANSWERS 57. 59. cos(3x) +
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C-32 53. 55. r = 57. r = 2sin θ 61
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C-34 ODD ANSWERS Section 10.6 1. A
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C-36 ODD ANSWERS 43. 45. 47. 〈4,
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C-38 ODD ANSWERS 43. y 53. − ___
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C-40 ODD ANSWERS 27. y 29. y CHAPTE
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C-42 ODD ANSWERS 37. Vertex (3, 0)
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C-44 ODD ANSWERS 31. Vertex (−5,
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C-46 ODD ANSWERS 67. If a n = −42
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C-48 ODD ANSWERS C(20, 3)C(60, 17)
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D-2 INDEX exponential growth 464, 4
- Page 1220:
D-4 INDEX vertex form of a quadrati
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