Intermediate Algebra, 5th Edition

876 Pages·2008·17.91 MB·English

by  Ron Larson

Geometry
Formulas for Area (A), Perimeter (P), Circumference (C), and Volume (V)
Square Rectangle
A(cid:2)s2 A(cid:2)lw w
s
P(cid:2)4s P(cid:2)2l(cid:4)2w
l
s
Triangle Circle
A(cid:2)1bh a h c A(cid:2)(cid:3)r2 r
2
C(cid:2)2(cid:3)r
P(cid:2)a(cid:4)b(cid:4)c
b
Trapezoid b1 Parallelogram
A(cid:2)bh
1 h h a
A(cid:2)2h(cid:2)b1(cid:4)b2(cid:3) P(cid:2)2a(cid:4)2b
b
2 b
Cube Rectangular Solid
h
V(cid:2)s3 s V(cid:2)lwh
l
s w
s
Circular Cylinder r Sphere
4
V(cid:2)(cid:3)r2h h V(cid:2)3(cid:3)r3 r
Special Triangles Pythagorean Theorem
Equilateral Triangle Isosceles Triangle a2(cid:4)b2(cid:2)c2
c
a
a a
a a
a b b
Right Triangle
Similar Triangles
Hypotenuse ad(cid:2)be (cid:2)cf c a f d
Legs b e
Common Formulas Basic Rules of Algebra
Distance Commutative Property of Addition
d(cid:2)distance traveled
d(cid:2)rt t(cid:2)time a(cid:4)b(cid:2)b(cid:4)a
r(cid:2)rate
Commutative Property of Multiplication
Temperature ab(cid:2)ba
F(cid:2)degrees Fahrenheit
F(cid:2)9C(cid:4)32 C(cid:2)degrees Celsius Associative Property of Addition
5
(cid:2)a(cid:4)b(cid:3)(cid:4)c(cid:2)a(cid:4)(cid:2)b(cid:4)c(cid:3)
Simple Interest
I(cid:2)interest
I(cid:2)Prt P(cid:2)principal Associative Property of Multiplication
r(cid:2)annual interest rate (cid:2)ab(cid:3)c(cid:2)a(cid:2)bc(cid:3)
t(cid:2)time in years
Left Distributive Property
Compound Interest A(cid:2)balance a(cid:2)b(cid:4)c(cid:3)(cid:2)ab(cid:4)ac
A(cid:2)P(cid:4)1(cid:4) r(cid:5)nt P(cid:2)principal Right Distributive Property
n r(cid:2)annual interest rate
n(cid:2)compoundings per year (cid:2)a(cid:4)b(cid:3)c(cid:2)ac(cid:4)bc
t(cid:2)time in years
Additive Identity Property
Coordinate Plane: Midpoint Formula a(cid:4)0(cid:2)0(cid:4)a(cid:2)a
Mjoiindipnogi n(cid:2)xt 1o, fy l1i(cid:3)naen sde g(cid:2)xm2e, nyt2(cid:3) (cid:4)x1(cid:4)2 x2, y1(cid:4)2 y2(cid:5) Multaip(cid:6)li1ca(cid:2)tiv1e(cid:6) Idae(cid:2)ntaity Property
Coordinate Plane: Distance Formula
Additive Inverse Property
d(cid:2)distance between d(cid:2)(cid:6)(cid:2)x (cid:7)x (cid:3)2(cid:4)(cid:2)y (cid:7)y (cid:3)2
points (cid:2)x , y (cid:3)and (cid:2)x , y (cid:3) 2 1 2 1 a(cid:4)(cid:2)(cid:7)a(cid:3)(cid:2)0
1 1 2 2
Multiplicative Inverse Property
Quadratic Formula
a(cid:6)1(cid:2)1, a(cid:5)0
a
Solutions of ax2(cid:4)bx(cid:4)c(cid:2)0
(cid:7)b ± (cid:6)b2(cid:7)4ac Properties of Equality
x(cid:2)
2a
Addition Property of Equality
Rules of Exponents
If a(cid:2)b,then a(cid:4)c(cid:2)b(cid:4)c.
(cid:2)Assume a(cid:5)0and b(cid:5)0.(cid:3)
Multiplication Property of Equality
a0(cid:2)1 am(cid:6)an(cid:2)am(cid:4)n
If a(cid:2)b,then ac(cid:2)bc.
(cid:2)ab(cid:3)m(cid:2)am(cid:6)bm (cid:2)am(cid:3)n(cid:2)amn
Cancellation Property of Addition
am (cid:4)a(cid:5)m am If a(cid:4)c(cid:2)b(cid:4)c,then a(cid:2)b.
(cid:2)am(cid:7)n (cid:2)
an b bm
Cancellation Property of Multiplication
1 (cid:4)a(cid:5)(cid:7)n bn
a(cid:7)n(cid:2) (cid:2) If ac(cid:2)bc,and c(cid:5)0,then a(cid:2)b.
an b an
Zero Factor Property
If ab(cid:2)0,then a(cid:2)0or b(cid:2)0.
Intermediate Algebra
F I F T H E D I T I O N
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Intermediate Algebra
F I F T H E D I T I O N
Ron Larson
The Pennsylvania State University
The Behrend College
With the assistance of
Kimberly Nolting
Hillsborough Community College
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Intermediate Algebra, Fifth Edition © 2010 Brooks/Cole, Cengage Learning
Ron Larson
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Printed in the United States of America
1 2 3 4 5 6 7 12 11 10 09 08
Contents
A Word from the Author (Preface) ix
Features xi
Study Skills in Action xxii
1
Fundamentals of Algebra 1
1.1 The Real Number System 2
1.2 Operations with Real Numbers 11
1.3 Properties of Real Numbers 23
Mid-Chapter Quiz 31
1.4 Algebraic Expressions 32
1.5 Constructing Algebraic Expressions 41
What Did You Learn? (Chapter Summary) 50
Review Exercises 52 Chapter Test 55
Study Skills in Action 56
2
Linear Equations and Inequalities 57
2.1 Linear Equations 58
2.2 Linear Equations and Problem Solving 69
2.3 Business and Scientific Problems 80
Mid-Chapter Quiz 93
2.4 Linear Inequalities 94
2.5 Absolute Value Equations and Inequalities 107
What Did You Learn? (Chapter Summary) 116
Review Exercises 118 Chapter Test 123
Study Skills in Action 124
3
Graphs and Functions 125
3.1 The Rectangular Coordinate System 126
3.2 Graphs of Equations 140
3.3 Slope and Graphs of Linear Equations 149
3.4 Equations of Lines 162
Mid-Chapter Quiz 173
3.5 Graphs of Linear Inequalities 174
3.6 Relations and Functions 183
3.7 Graphs of Functions 197
What Did You Learn? (Chapter Summary) 208
Review Exercises 210 Chapter Test 215
v
vi Contents
Study Skills in Action 216
4
Systems of Equations and Inequalities 217
4.1 Systems of Equations 218
4.2 Linear Systems in Two Variables 231
4.3 Linear Systems in Three Variables 241
Mid-Chapter Quiz 253
4.4 Matrices and Linear Systems 254
4.5 Determinants and Linear Systems 267
4.6 Systems of Linear Inequalities 279
What Did You Learn? (Chapter Summary) 288
Review Exercises 290 Chapter Test 294
Cumulative Test: Chapters 1–4 295
Study Skills in Action 296
5
Polynomials and Factoring 297
5.1 Integer Exponents and Scientific Notation 298
5.2 Adding and Subtracting Polynomials 308
5.3 Multiplying Polynomials 318
Mid-Chapter Quiz 327
5.4 Factoring by Grouping and Special Forms 328
5.5 Factoring Trinomials 338
5.6 Solving Polynomial Equations by Factoring 350
What Did You Learn? (Chapter Summary) 360
Review Exercises 362 Chapter Test 367
Study Skills in Action 368
6
Rational Expressions, Equations, and
Functions 369
6.1 Rational Expressions and Functions 370
6.2 Multiplying and Dividing Rational Expressions 382
6.3 Adding and Subtracting Rational Expressions 391
6.4 Complex Fractions 400
Mid-Chapter Quiz 408
6.5 Dividing Polynomials and Synthetic Division 409
6.6 Solving Rational Equations 419
6.7 Applications and Variation 427
What Did You Learn? (Chapter Summary) 440
Review Exercises 442 Chapter Test 447
Contents vii
Study Skills in Action 448
7
Radicals and Complex Numbers 449
7.1 Radicals and Rational Exponents 450
7.2 Simplifying Radical Expressions 461
7.3 Adding and Subtracting Radical Expressions 468
Mid-Chapter Quiz 474
7.4 Multiplying and Dividing Radical Expressions 475
7.5 Radical Equations and Applications 483
7.6 Complex Numbers 493
What Did You Learn? (Chapter Summary) 502
Review Exercises 504 Chapter Test 507
Cumulative Test: Chapters 5–7 508
Study Skills in Action 510
8
Quadratic Equations, Functions, and
Inequalities 511
8.1 Solving Quadratic Equations: Factoring and Special Forms 512
8.2 Completing the Square 521
8.3 The Quadratic Formula 529
Mid-Chapter Quiz 538
8.4 Graphs of Quadratic Functions 539
8.5 Applications of Quadratic Equations 549
8.6 Quadratic and Rational Inequalities 560
What Did You Learn? (Chapter Summary) 570
Review Exercises 572 Chapter Test 575
Study Skills in Action 576
9
Exponential and Logarithmic Functions 577
9.1 Exponential Functions 578
9.2 Composite and Inverse Functions 591
9.3 Logarithmic Functions 605
Mid-Chapter Quiz 616
9.4 Properties of Logarithms 617
9.5 Solving Exponential and Logarithmic Equations 625
9.6 Applications 635
What Did You Learn? (Chapter Summary) 646
Review Exercises 648 Chapter Test 653