Beginning and Intermediate Algebra - Wallace Math Courses ...

More documents

Recommendations

Info

$Solving Linear Equations - Distance, Rate and Time - Wallace Math ...$

$Inequalities - Compound Inequalities - Wallace Math Courses$

$Solving Linear Equations - Absolute Value - Wallace Math Courses$

9.11 Practice - Graphs of Quadratics Find the vertex <strong>and</strong> intercepts of the following quadratics. Use this information to graph the quadratic. 1) y = x 2 − 2x − 8 3) y = 2x 2 − 12x + 10 5) y = − 2x 2 + 12x − 18 7) y = − 3x 2 + 24x − 45 9) y = −x 2 + 4x +5 11) y = −x 2 + 6x − 5 13) y = − 2x 2 + 16x − 24 15) y = 3x 2 + 12x + 9 17) y = 5x 2 − 40x + 75 19) y = − 5x 2 − 60x − 175 384 2) y = x 2 − 2x − 3 4) y = 2x 2 − 12x + 16 6) y = − 2x 2 + 12x − 10 8) y = − 3x 2 + 12x − 9 10) y = −x 2 + 4x − 3 12) y = − 2x 2 + 16x − 30 14) y = 2x 2 +4x − 6 16) y = 5x 2 + 30x + 45 18) y = 5x 2 + 20x + 15 20) y = − 5x 2 + 20x − 15
Chapter 10 : Functions 10.1 Function Notation ..................................................................................386 10.2 Operations on Functions ........................................................................393 10.3 Inverse Functions ...................................................................................401 10.4 Exponential Functions ...........................................................................406 10.5 Logarithmic Functions ...........................................................................410 10.6 Application: Compound Interest ............................................................414 10.7 Trigonometric Functions ........................................................................420 10.8 Inverse Trigonometric Functions ............................................................428 385
Page 1 and 2:
Beginning and Intermediate Algebra
Page 3 and 4:
Special thanks to: My beautiful wif
Page 5 and 6:
Chapter 6: Factoring 6.1 Greatest C
Page 7 and 8:
0.1 Pre-Algebra - Integers Objectiv
Page 9 and 10:
Multiplication and division of inte
Page 11 and 12:
45) (4)( − 6) Find each quotient.
Page 13 and 14:
9 ÷ 3 3 = 21 ÷ 3 7 Our Soultion T
Page 15 and 16:
Example 21. 13 6 − 9 6 4 6 2 3 Sa
Page 17 and 18:
Find each quotient. 37) − 2 ÷ 7
Page 19 and 20:
the expression that is to be evalua
Page 21 and 22:
Solve. 1) − 6 · 4( − 1) 3) 3+(
Page 23 and 24:
It will be more common in our study
Page 25 and 26:
0.4 Practice - Properties of Algebr
Page 27 and 28:
Chapter 1 : Solving Linear Equation
Page 29 and 30:
Addition Problems To solve equation
Page 31 and 32:
8x = − 24 8 8 x = − 3 Division
Page 33 and 34:
1.2 Linear Equations - Two-Step Equ
Page 35 and 36:
− 1 − 1 Divide both sides by
Page 37 and 38:
1.3 Solving Linear Equations - Gene
Page 39 and 40:
Example 63. − 3x +9=6x − 27 Not
Page 41 and 42:
4[ − 2]+9=−15 +8(2) Finish mult
Page 43 and 44:
1.4 Solving Linear Equations - Frac
Page 45 and 46:
Example 72. � � 3 5 4 x + = 3 2
Page 47 and 48:
1.5 Solving Linear Equations - Form
Page 49 and 50:
Example 79. A = πr 2 +πrs for s S
Page 51 and 52:
1.5 Practice - Formulas Solve each
Page 53 and 54:
|x| = 5 Absolute value can be posit
Page 55 and 56:
Example 90. 7+|2x − 5| =4 Notice
Page 57 and 58:
1.7 Solving Linear Equations - Vari
Page 59 and 60:
Once we have found the constant of
Page 61 and 62:
1.7 Practice - Variation Write the
Page 63 and 64:
sure. If the pressure of a certain
Page 65 and 66:
Fifteen more than three times a num
Page 67 and 68:
When we started with our first, sec
Page 69 and 70:
1.8 Practice - Number and Geometry
Page 71 and 72:
30. The perimeter of a college bask
Page 73 and 74:
Our equation comes from the future
Page 75 and 76:
4x + 2=102 Solve the two − step e
Page 77 and 78:
years ago, the bronze plaque was on
Page 79 and 80:
1.10 Solving Linear Equations - Dis
Page 81 and 82:
Rate Time Distance Bob r + 2 3 Fred
Page 83 and 84:
2 =t Our solution fort, she catches
Page 85 and 86:
Find the distance he rode. 8. A man
Page 87 and 88:
The first plan is flying 25 mph slo
Page 89 and 90:
2.1 Graphing - Points and Lines Obj
Page 91 and 92:
E B D F G C A Our Solution The main
Page 93 and 94:
x y − 3 − 4 0 − 2 3 0 Our com
Page 95 and 96:
2.2 Graphing - Slope Objective: Fin
Page 97 and 98:
When mathematicians began working w
Page 99 and 100:
Example 131. Find the value of x be
Page 101 and 102:
9) 10) Find the slope of the line t
Page 103 and 104:
y = − 2 x + 3 Our Solution 3 Iden
Page 105 and 106:
2.3 Practice - Slope-Intercept Writ
Page 107 and 108:
2.4 Graphing - Point-Slope Form Obj
Page 109 and 110:
Find the equation of the line throu
Page 111 and 112:
Write the point-slope form of the e
Page 113 and 114:
m = 2 5 m = 2 5 Example 147. Slope
Page 115 and 116:
2.5 Practice - Parallel and Perpend
Page 117 and 118:
Chapter 3 : Inequalities 3.1 Solve
Page 119 and 120:
than 4. If we have an expression su
Page 121 and 122:
− 5 − 5 − 2x � 6 Divide bot
Page 123 and 124:
Solve each inequality, graph each s
Page 125 and 126:
As the graphs overlap, we take the
Page 127 and 128:
3.2 Practice - Compound Inequalitie
Page 129 and 130:
edition of a college algebra text!
Page 131 and 132:
It is important to remember as we a
Page 133 and 134:
Chapter 4 : Systems of Equations 4.
Page 135 and 136:
ested in the point that is a soluti
Page 137 and 138:
that parallel lines have the same s
Page 139 and 140:
4.2 Systems of Equations - Substitu
Page 141 and 142:
tion. This process is described and
Page 143 and 144:
World View Note: French mathematici
Page 145 and 146:
31) 2x + y = 2 3x + 7y = 14 33) x +
Page 147 and 148:
6x +9y = 6 New second equation −
Page 149 and 150:
Just as with graphing and substutio
Page 151 and 152:
4.4 Systems of Equations - Three Va
Page 153 and 154:
just the ordered pair (x, y). In th
Page 155 and 156:
15x − 12y +9z = − 12 5x − 4y
Page 157 and 158:
23) 3x + 3y − 2z = 13 6x + 2y −
Page 159 and 160:
are given to use. This means someti
Page 161 and 162:
− 0.5 − 0.5 c=17 We have c, num
Page 163 and 164:
− 0.06x − 0.06y = − 240 Add e
Page 165 and 166:
14) A bank contains 27 coins in dim
Page 167 and 168:
4.6 Systems of Equations - Mixture
Page 169 and 170:
Amount Part Total Start 40 3 120 Ad
Page 171 and 172:
4(30 −n)+2.5n=105 Substitute into
Page 173 and 174:
16) A certain grade of milk contain
Page 175 and 176:
175
Page 177 and 178:
5.1 Polynomials - Exponent Properti
Page 179 and 180:
A quicker method to arrive at the s
Page 181 and 182:
Example 210. Example 211. 7a 3 (2a
Page 183 and 184:
5.2 Polynomials - Negative Exponent
Page 185 and 186:
As we simplified our fraction we to
Page 187 and 188:
5.2 Practice - Negative Exponents S
Page 189 and 190:
Example 223. Convert 3.21 × 10 5 t
Page 191 and 192:
5.3 Practice - Scientific Notation
Page 193 and 194:
World View Note: Ada Lovelace in 18
Page 195 and 196:
21) (3+b 4 )+(7+2b + b 4 ) 22) (1+6
Page 197 and 198:
Just as we distribute a monomial th
Page 199 and 200:
Example 243. (2x − 5)(4x 2 − 7x
Page 201 and 202:
5.6 Polynomials - Multiply Special
Page 203 and 204:
Be very careful when we are squarin
Page 205 and 206:
5.7 Polynomials - Divide Polynomial
Page 207 and 208:
3. Change the sign of the terms and
Page 209 and 210:
Example 261. 2x 3 + 42 − 4x x + 3
Page 211 and 212:
Chapter 6 : Factoring 6.1 Greatest
Page 213 and 214:
ers using mental math, then we take
Page 215 and 216:
6.1 Practice - Greatest Common Fact
Page 217 and 218:
Example 273. 10ab + 15b + 4a+6 Spli
Page 219 and 220:
example the binomials are (a + b) a
Page 221 and 222:
6.3 Factoring - Trinomials where a
Page 223 and 224:
As the past few examples illustrate
Page 225 and 226:
6.3 Practice - Trinomials where a =
Page 227 and 228:
Example 296. 10x 2 − 27x +5 Multi
Page 229 and 230:
6.5 Factoring - Factoring Special P
Page 231 and 232:
Example 306. 4x 2 + 20xy + 25y 2 Mu
Page 233 and 234:
6.5 Practice - Factoring Special Pr
Page 235 and 236:
Example 313. Example 314. Example 3
Page 237 and 238:
6.7 Factoring - Solve by Factoring
Page 239 and 240:
0=(2x +3)(2x − 3) One factor must
Page 241 and 242:
6.7 Practice - Solve by Factoring S
Page 243 and 244:
7.1 Rational Expressions - Reduce R
Page 245 and 246:
However, if there is more than just
Page 247 and 248:
41) 8m+16 20m − 12 43) 2x2 − 10
Page 249 and 250:
Example 333. 25x2 24y4 · 9y8 55x7
Page 251 and 252:
Simplify each expression. 1) 8x2 9
Page 253 and 254:
7.3 Rational Expressions - Least Co
Page 255 and 256:
As the above example illustrates, w
Page 257 and 258:
7.4 Rational Expressions - Add & Su
Page 259 and 260:
13 12 Our Solution The same process
Page 261 and 262:
7.4 Practice - Add and Subtract Add
Page 263 and 264:
2(12) 1(12) − 3 4 5(12) 1(12) + 6
Page 265 and 266:
LCD =(x + 3)(x − 3) Multiply each
Page 267 and 268:
23) 25) 27) 29) x − 4+ 9 2x +3 x
Page 269 and 270:
(20)(9)=6x Multiply 180 = 6x Divide
Page 271 and 272:
3.5 6 The man hasashadow of 3.5 fee
Page 273 and 274:
33) Kali reduced the size of a pain
Page 275 and 276:
LCD will be more involved. We will
Page 277 and 278:
x=5 or − 2 Our Solution World Vie
Page 279 and 280:
7.8 Rational Expressions - Dimensio
Page 281 and 282:
� 435 1 �� 1 lbs = 16 435
Page 283 and 284:
To focus on the process of conversi
Page 285 and 286:
7.8 Practice - Dimensional Analysis
Page 287 and 288:
Chapter 8 : Radicals 8.1 Square Roo
Page 289 and 290:
√ process is being able to transl
Page 291 and 292:
Simplify. √ 1) 245 √ 3) 36 √
Page 293 and 294:
Example 384. 3√ 54 We are working
Page 295 and 296:
8.3 Radicals - Adding Radicals Obje
Page 297 and 298:
Simiplify 1) 2 5 √ + 2 5 √ + 2
Page 299 and 300:
√ √ √ √ 4 50 + 6 30 − 8 3
Page 301 and 302:
The previous example could have bee
Page 303 and 304:
8.5 Radicals - Rationalize Denomina
Page 305 and 306:
2x2 √ √ 10 − 6x 3x Our Soluti
Page 307 and 308:
Example 408. 2 5 √ − 3 7 √ 5
Page 309 and 310:
37) 5 2 √ + 3 √ 5+5 2 √ 38) 3
Page 311 and 312:
1 (3) 4 Evaluate exponent 1 81 Our
Page 313 and 314:
8.6 Practice - Rational Exponents W
Page 315 and 316:
Example 420. ab2 3√ a2 4√ b Rew
Page 317 and 318:
8.7 Practice - Radicals of Mixed In
Page 319 and 320:
Example 426. Example 427. i 35 Divi
Page 321 and 322:
√ Dividing with complex numbers a
Page 323 and 324:
Simplify. 1) 3 − ( − 8+4i) 3) (
Page 325 and 326:
Chapter 9 : Quadratics 9.1 Solving
Page 327 and 328:
Example 444. + 1 +1 Add1to both sid
Page 329 and 330:
2 − 2=0 Subtract 0=0 True! It wor
Page 331 and 332:
Solve. √ 1) 2x + 3 √ 3) 6x −
Page 333 and 334: x4 4√ = ± 4√ 16 Simplify roots
Page 335 and 336: 5√ 4x +1 = ± 3 Clear radical by
Page 337 and 338: 9.3 Quadratics - Complete the Squar
Page 339 and 340: x2 + 5 25 x+ 3 36 � x + 5 �2 6
Page 341 and 342: Example 464. − 7 3 � 3 3 + 3 3
Page 343 and 344: 9.4 Quadratics - Quadratic Formula
Page 345 and 346: x = Example 468. √ 30 ± 900 + 11
Page 347 and 348: 9.4 Practice - Quadratic Formula So
Page 349 and 350: 12x 2 − 17x + 6=0 Our Solution If
Page 351 and 352: 9.5 Practice - Build Quadratics fro
Page 353 and 354: Example 479. a −2 − a −1 −
Page 355 and 356: 12 = (x − 3) 2 or 13 =(x − 3) 2
Page 357 and 358: 9.7 Quadratics - Rectangles Objecti
Page 359 and 360: Example 486. 2 Our Solution The len
Page 361 and 362: 4(x 2 + 10x − 24) =0 Factor trino
Page 363 and 364: that require 24 square meters for p
Page 365 and 366: 1(12x) 3 + 1(12x) x 1 1 5 + = 3 x 1
Page 367 and 368: 6x +6(x − 1)=5x(x − 1) Reduce e
Page 369 and 370: 16) A sink can be filled from the f
Page 371 and 372: These simultaneous product equation
Page 373 and 374: 9.10 Quadratics - Revenue and Dista
Page 375 and 376: 96n(n − 2) 96n(n − 2) +4n(n −
Page 377 and 378: upstream, the current will pull aga
Page 379 and 380: 12) A pilot flying at a constant ra
Page 381 and 382: The above method to graph a parabol
Page 383: It is important to remember the gra
Page 387 and 388: Example 504. Which of the following
Page 389 and 390: 2x − 3 � 0 Set up an inequality
Page 391 and 392: Solve. 10.1 Practice - Function Not
Page 393 and 394: 10.2 Functions - Operations on Func
Page 395 and 396: (x − 5)(x +1) (x − 5) Divide ou
Page 397 and 398: We can also evaluate a composition
Page 399 and 400: 23) f(x) = x 2 − 5x g(x) = x + 5
Page 401 and 402: 10.3 Functions - Inverse Functions
Page 403 and 404: (3x +6)(3 − 4x) 3 − 4x (4x+8)(3
Page 405 and 406: 10.3 Practice - Inverse Functions S
Page 407 and 408: Example 530. 8 3x = 32 Rewrite 8 as
Page 409 and 410: 10.4 Practice - Exponential Functio
Page 411 and 412: log3x =7 Identify base, 3, answer,
Page 413 and 414: 10.5 Practice - Logarithmic Functio
Page 415 and 416: A = 25000(1.01625) 20 Evaluate expo
Page 417 and 418: The variable e is a constant simila
Page 419 and 420: j. All of the above compounded cont
Page 421 and 422: Using the diagram at right, find ea
Page 423 and 424: 10.7 Practice - Trigonometric Funct
Page 425 and 426: 21) 23) 25) 27) A B A 5 38 ◦ x x
Page 427 and 428: 37) 39) A A 37.1 ◦ C x x C 13.1 4
Page 429 and 430: θ 17 From angle θ the given sides
Page 431 and 432: function to find the missing angle
Page 433 and 434: Find the measure of each angle indi
Page 435 and 436:
27) 29) 14 A A θ C 15 7 C 14 θ B
Page 437 and 438:
437
Page 439 and 440:
7) 5 4 8) 4 3 9) 3 2 10) 8 3 11) 5
Page 441 and 442:
54) 60v − 7 55) − 3x + 8x 2 56)
Page 443 and 444:
45) 12 46) All real numbers 47) No
Page 445 and 446:
15) wx 3 = 1458 16) h = 1.5 j 17) a
Page 447 and 448:
1) B(4, − 3) C(1, 2) D( − 1, 4)
Page 449 and 450:
1) y = 2x +5 2) y = − 6x +4 3) y
Page 451 and 452:
23) x =4 24) y − 4 = 7 (x − 1)
Page 453 and 454:
25) 5�x
Page 455 and 456:
1) ( − 2, 4) 2) (2,4) 3) No solut
Page 457 and 458:
27) 56, 144 28) 1.5, 3.5 29) 30 30)
Page 459 and 460:
42) 1.2 × 10 6 5.4 1) 3 2) 7 3)
Page 461 and 462:
5) 2x 3 + 4x 2 + x 2 6) 5p3 4 +4p2
Page 463 and 464:
7) (b +8)(b + 4) 8) (b − 10)(b
Page 465 and 466:
11) n(n − 1) 12) (5x +3)(x − 5)
Page 467 and 468:
5) 3x2 2 6) 5p 2 7) 5m 8) 7 10 9) r
Page 469 and 470:
7) 8) 5 24r 7x + 3y x 2 y 2 9) 15t+
Page 471 and 472:
21) 0, 5 22) − 2, 5 3 23) 4,7 24)
Page 473 and 474:
42) − 18xz 4x3yz3 � 4 8.3 1) 6
Page 475 and 476:
16 3 √ + 4 5 √ 43 18) 19) 2 √
Page 477 and 478:
8.8 1) 11 − 4i 2) − 4i 3) − 3
Page 479 and 480:
√ √ 33) 4+i 39, 4 −i 39 34)
Page 481 and 482:
9) ± 2, ± 4 10) 2,3, − 1 ±i 3
Page 483 and 484:
1) 2) 3) 4) 5) 6) (-2,0) (0,-8) (-1
Page 485 and 486:
11) 100 12) − 74 13) 1 5 14) 27 1
Page 487 and 488:
10.5 1) 9 2 = 81 2) b −16 = a 3)
Page 489:
21) 51.3 ◦ 22) 45 ◦ 23) 56.4
show all

Beginning and Intermediate Algebra - Wallace Math Courses ...

Create successful ePaper yourself

Delete template?

Save as template?