Beginning Algebra With Applications,9780395969793

Beginning Algebra With Applications

by ; ;
ISBN13: 9780395969793
ISBN10: 0395969794
Format: Hardcover
Pub. Date: 1999-10-01
Publisher(s): Cengage Learning
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Table of Contents

Preface ix
Index of Applications xviii
Real Numbers
1(48)
Introduction to Integers
3(7)
Order relations
3(2)
Opposites and absolute value
5(5)
Operations with Integers
10(12)
Add integers
10(1)
Subtract integers
11(1)
Multiply integers
12(2)
Divide integers
14(1)
Application problems
15(7)
Rational Numbers
22(12)
Write rational numbers as decimals
22(1)
Convert among percents, fractions, and decimals
23(2)
Add and subtract rational numbers
25(2)
Multiply and divide rational numbers
27(7)
Exponents and the Order of Operations Agreement
34(15)
Exponential expressions
34(1)
The Order of Operations Agreement
35(5)
Focus on Problem Solving: Inductive Reasoning
40(1)
Projects and Group Activities: Calculators
41(1)
Moving Averages
42(1)
WWW.fedstats.gov
42(1)
Chapter Summary
42(2)
Chapter Review Exercises
44(3)
Chapter Test
47(2)
Variable Expressions
49(36)
Evaluating Variable Expressions
51(6)
Evaluate variable expressions
51(6)
Simplifying Variable Expressions
57(10)
The Properties of the Real Numbers
57(2)
Simplify variable expressions using the Properties of Addition
59(2)
Simplify variable expressions using the Properties of Multiplication
61(1)
Simplify variable expression using the Distributive Property
62(1)
Simplify general variable expressions
62(5)
Translating Verbal Expressions into Variable Expressions
67(18)
Translate a verbal expression into a variable expression given the variable
67(2)
Translate a verbal expression into a variable expression by assigning the variable
69(1)
Translate a verbal expression into a variable expression and then simplify the resulting expression
69(1)
Translate application problems
70(7)
Focus on Problem Solving: From Concrete to Abstract
77(2)
Projects And Group Activities: Investigation into Operations with Even and Odd Integers
79(1)
Applications of Patterns in Mathematics
79(1)
Chapter Summary
80(1)
Chapter Review Exercises
81(2)
Chapter Test
83(1)
Cumulative Review Exercises
84(1)
Solving Equations and Inequalities
85(48)
Introduction to Equations
87(14)
Determine Whether a given number is a solution of an equation
87(1)
Solve equations of the form x + a = b
89(1)
Solve equations of the form ax = b
90(2)
Application problems: the basic percent equation
92(9)
General Equations
101(14)
Solve equations of the form ax + b = c
101(3)
Solve equations of the form ax + b = cx + d
104(1)
Solve equations containing parentheses
105(1)
Application problems
106(9)
Inequalities
115(18)
Solve inequalities using the Addition Property of Inequalities
115(2)
Solve inequalities using the Multiplication Property of Inequalities
117(2)
Solve general inequalities
119(6)
Focus on Problem Solving: Graphing Data
125(1)
Project and Group Activities: Measurements as Approximations
126(1)
Chapter Summary
127(1)
Chapter Review Exercises
128(2)
Chapter Test
130(1)
Cumulative Review Exercises
131(2)
Solving Equations and inequalities: Applications
133(74)
Translating Sentences into Equations
135(6)
Translate a sentence into an equation and solve
135(1)
Application problems
135(6)
Integer, Coin, and Stamp Problems
141(8)
Consecutive integer problems
141(2)
Coin and stamp problems
143(6)
Geometry Problems
149(14)
Perimeter problems
149(2)
Problems involving angles formed by intersecting lines
151(4)
Problems involving the angles of a triangle
155(8)
Markup and Discount Problems
163(6)
Markup problems
163(2)
Discount problems
165(4)
Investment Problems
169(6)
Investment problems
169(6)
Mixture Problems
175(9)
Value mixture problems
175(2)
Percent mixture problems
177(7)
Uniform Motion Problems
184(6)
Uniform motion problems
184(6)
Inequalities
190(17)
Applications of inequalities
190(5)
Focus on Problem Solving: Trial-and-Error Approach to Problem Solving
195(1)
Diagramming Problems
196(1)
Projects and Group Activities: Nielsen Ratings
197(1)
Changes in Percent Concentration
198(1)
Chapter Summary
199(2)
Chapter Review Exercises
201(3)
Chapter Test
204(1)
Cumulative Review Exercises
205(2)
Linear Equations and Inequalities
207(68)
The Rectangular Coordinate System
209(7)
Graph points in a rectangular coordinate system
209(2)
Scatter diagrams
211(5)
Graphs of Straight Lines
216(14)
Determine solutions of linear equations in two variables
216(2)
Graph equations of the form y = mx + b
218(2)
Graph equations of the form Ax + By = C
220(10)
Slopes of Straight Lines
230(9)
Find the slope of a straight line
230(4)
Graph a line using the slope and y-intercept
234(5)
Equations of Straight Lines
239(5)
Find the equation of a line using the equation y = mx + b
239(1)
Find the equation of a line using the point-slope formula
240(4)
Functions
244(12)
Introduction to functions
244(3)
Graphs of linear functions
247(9)
Graphing Linear Inequalities
256(19)
Graph inequalities in two variable
256(5)
Focus on Problem Solving: Counterexamples
261(1)
Projects and Group Activities: Graphing Linear Equations with a Graphing Utility
262(1)
Graphs of Motion
263(1)
Chapter Summary
264(2)
Chapter Review Exercises
266(3)
Chapter Test
269(3)
Cumulative Review Exercises
272(3)
Systems of Linear Equations
275(38)
Solving Systems of Linear Equations by Graphing
277(6)
Solve systems of linear equations by graphing
277(6)
Solving Systems of Linear Equations by the Substitution Method
283(5)
Solve systems of linear equations by the substitution method
283(5)
Solving Systems of Linear Equations by the Addition Method
288(5)
Solve systems of linear equations by the addition method
288(5)
Application Problems in Two Variables
293(20)
Rate-of-wind and water-current problems
293(2)
Application problems
295(6)
Focus on Problem Solving: Using a Table and Searching for a Pattern
301(1)
Projects and Group Activities: Find a Pattern
302(1)
Solving a system of Equations with a Scientific Calculator
302(1)
Solving a System of Equations with a Graphing Calculator
302(3)
Chapter Summary
305(2)
Chapter Review Exercises
307(2)
Chapter Test
309(1)
Cumulative Review Exercises
310(3)
Polynomials
313(40)
Addition and Subtraction of Polynomials
315(4)
Add polynomials
315(1)
Subtract polynomials
316(3)
Multiplication of Monomials
319(4)
Multiply monomials
319(1)
Simplify powers of monomials
320(3)
Multiplication of Polynomials
323(9)
Multiply a polynomial by a monomial
323(1)
Multiply two polynomials
324(1)
Multiply two binomials
324(1)
Multiply binomials that have special products
325(2)
Application problems
327(5)
Division of Polynomials
332(21)
Integer exponents
332(3)
Scientific notation
335(2)
Divide a polynomial by a monomial
337(1)
Divide polynomials
338(6)
Focus on Problem Solving: Dimensional Analysis
344(2)
Projects and Group Activities: Pascal's Triangle
346(1)
Properties of Polynomials
347(1)
Chapter Summary
347(1)
Chapter Review Exercises
348(2)
Chapter Test
350(1)
Cumulative Review Exercises
351(2)
Factoring
353(46)
Common Factors
355(5)
Factor a monomial from a polynomial
355(1)
Factor by grouping
356(4)
Factoring Polynomials of the Form x2 + bx + c
360(6)
Factor trinomials of the form x2 + bx + c
360(3)
Factor completely
363(3)
Factoring Polynomials of the Form ax2 + bx + c
366(9)
Factor trinomials of the form ax2 + bx + c using trial factors
366(4)
Factor trinomials of the form ax2 + bx + c by grouping
370(5)
Special Factoring
375(7)
Factor the difference of two squares and perfect-square trinomials
375(3)
Factor completely
378(4)
Solving Equations
382(17)
Solve equations by factoring
382(1)
Application problems
383(6)
Focus on Problem solving: Making a Table
389(1)
The Trial-and-Error Method
389(2)
Projects and Group Activities: Prime and Composite Numbers
391(1)
Search the World Wide Web
392(1)
Chapter Summary
393(1)
Chapter Review Exercises
394(2)
Chapter Test
396(1)
Cumulative Review Exercises
397(2)
Algebraic Fractions
399(62)
Multiplication and Division of Algebraic Fractions
401(7)
Simplify algebraic fractions
401(1)
Multiply algebraic fractions
402(2)
Divide algebraic fractions
404(4)
Expressing Fractions in Terms of the Least Common Multiple (LCM)
408(5)
Find the least common multiple (LCM) of two or more polynomials
408(1)
Express two fractions in terms of the LCM of their denominators
409(4)
Addition and Subtraction of Algebraic Fractions
413(6)
Add and subtract algebraic fractions with the same denominator
413(1)
Add and subtract algebraic fractions with different denominators
414(5)
Complex Fractions
419(4)
Simplify complex fractions
419(4)
Equations Containing Fractions
423(14)
Solve equations containing fractions
423(2)
Solve proportions
425(1)
Applications of proportions
426(1)
Problems involving similar triangles
427(10)
Literal Equations
437(4)
Solve a literal equation for one of the variables
437(4)
Application problems
441(20)
Work problems
441(1)
Uniform motion problems
442(7)
Focus on Problem Solving: Negations and If...then...Sentences
449(2)
Calculators
451(1)
Projects and Group Activities: Intensity of Illumination
451(2)
Chapter Summary
453(2)
Chapter Review Exercises
455(2)
Chapter Test
457(1)
Cumulative Review Exercises
458(3)
Radical Expressions
461(40)
Introduction to Radical Expressions
463(6)
Simplify numerical radical expression
463(2)
Simplify variable radical expressions
465(4)
Addition and Subtraction of Radical Expressions
469(3)
Add and subtract radical expressions
469(3)
Multiplication and Division of Radical Expressions
472(6)
Multiply radical expressions
472(2)
Divide radical expressions
474(4)
Solving Equations Containing Radical Expressions
478(23)
Solve equations containing one or more radical expressions
478(3)
Application problems
481(7)
Focus on Problems Solving: Deductive Reasoning
488(1)
Projects and Group Activities: Mean and Standard Deviation
489(3)
Distance to the Horizon
492(1)
Expressway On-Ramp Curves
493(1)
Chapter Summary
493(2)
Chapter Review Exercises
495(2)
Chapter Test
497(1)
Cumulative Review Exercises
498(3)
Quadratic Equations
501(44)
Solving Quadratic Equations by Factoring or by Taking Square Roots
503(7)
Solve quadratic equations by factoring
503(2)
Solve quadratic equations by taking square roots
505(5)
Solving Quadratic Equations by Completing the Square
510(6)
Solve quadratic equations by completing the square
510(6)
Solving Quadratic Equations by using the Quadratic Formula
516(5)
Solve quadratic equations by using the quadratic formula
516(5)
Graphing Quadratic Equations in Two Variables
521(6)
Graph a quadratic equation of the form y = ax2 + bx + c
521(6)
Application Problems
527(18)
Application problems
527(6)
Focus on Problem Solving: Algebraic Manipulation and Graphing Techniques
533(1)
Projects and Group Activities: Graphical Solutions of Quadratic Equations
534(1)
Iterative Calculations
535(1)
Geometric Construction of Completing the Square
535(1)
Chapter Summary
536(2)
Chapter Review Exercises
538(3)
Chapter Test
541(1)
Cumulative Review Exercises
542(3)
Final Exam 545(4)
Appendix: Guidelines for Using Graphing Calculators 549
Solutions to Problems S1
Answers to the Odd-Numbered Exercises A1
Glossary G1
Index I1

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