OverviewWhen preparing to write this text, the authors solicited feedback from the marketabout what types of pedagogical tools would better help students to understand andretain the key beginning algebra concepts, in addition to what content should beupdated or expanded. Increasing the number of applications and integrating themthroughout the sections was one of the most prevalent responses. Based on thisfeedback, the authors focused on these themes as they revised the text.
In terms of pedagogical tools, this worktext seeks to provide carefully detailedexplanations and accessible pedagogy to introduce beginning algebra concepts to the students. The authors use a three-pronged approach to present the materialand encourage critical thinking skills. The areas used to create the framework arecommunication, pattern recognition, and problem solving. Items such as Math Anxietyboxes, Check Yourself exercises, and Activities represent this approach and theunderlying philosophy of mastering math through practice. A new feature is ReadingYour Text—these quick exercises presented at the end of each section quiz students’vocabulary knowledge and help strengthen their communication skills.
Market research has reinforced the importance of the exercise sets to the students’ability to process the content. To that end, the exercise sets in this edition have beenexpanded, organized, and clearly labeled (as previously outlined). Vocational andprofessional-technical exercises have been added throughout. In addition, exerciseswith fractions, decimals, and negative numbers have been added as appropriate.Repeated exposure to this consistent structure should help advance the students’skills in relating to mathematics.
FeaturesA number of features have contributed to the previous success of the Hutchisontexts. All of these features are also included in this text, and help reinforce the
authors’ philosophy of masteringmath through practice. Eachfeature was thoroughly discussedby the authors and review panelsduring the development of thetext. More than ever, we areconfident that the entire learningpackage is of value to yourstudents and to you as aninstructor. We will describe each ofthe key features of our package.
preface
> Make the Connection—Chapter-OpeningVignettes
The chapter-opening vignettes weresubstantially revised to provide studentsinteresting, relevant scenarios thatwill capture their attention and engage themin the upcoming material. Furthermore,exercises and Activities related to theOpening Vignette were added or updated ineach chapter. These exercises are markedwith a special icon.
Graphs are used to discern patterns thatmay be difficult to see when looking at a listof numbers or other kinds of data. The wordgraph comes from Latin and Greek rootsand means “to draw a picture.” A graph inmathematics is a picture of a relationshipbetween variables. Graphs are used inevery field in which numbers are used.
In the field of pediatric medicine therehas been controversy about the use ofhuman growth hormone to help childrenwhose growth has been impeded by healthproblems. The reason for the controversy isthat many doctors are giving this expensivedrug therapy to children who are simplyshorter than average or shorter than theirparents want them to be. The determina-tion of which children are healthy but smallin stature and which children have healthdefects that keep them from growing is anissue that has been vigorously argued inmedical research.
Measures used to distinguish betweenthe two groups include blood tests and ageand height measurements. These meas-urements are graphed and monitored overseveral years to gauge the child’s rate ofgrowth. If this rate of growth slows to below4.5 centimeters per year, this indicates thatthere may be a problem. The graph canalso indicate whether the child’s size iswithin a range considered normal at eachage of the child’s life.
Activities are included in each chapter.The Activities promote active learning byrequiring students to find, interpret, andmanipulate real-world data. Each Activityrelates to the chapter-opening vignette,providing cohesiveness to the chapter.Students can complete the Activities on theirown, but these are best solved in smallgroups.
Each activity in this text is designed to either enhance your understanding of the top-ics of the preceding chapter, provide you with a mathematical extension of those top-ics, or both. The activities can be undertaken by one student, but they are better suitedfor small group projects. Occasionally, it is only through discussion that differentfacets of the activity become apparent. For material related to this activity, visit the textwebsite at www.mhhe.com/streeter.
The graphing calculator is a tool that can be used to help you solve many differentkinds of problems. This activity will walk you through several features of the TI-83Plus. By the time you complete this activity, you will be able to graph equations,change the viewing window to better accommodate a graph, and look at a table ofvalues that represents some of the solutions for an equation. The first portion of this ac-tivity will demonstrate how you can create the graph of an equation. The features de-scribed here can be found on most graphing calculators. See your calculator manual tolearn how to get your particular calculator model to perform this activity.
Menus and Graphing
1. To graph the equation y � 2x � 3 on a graphing calculator, follow these steps.
(a) Press the key.
(b) Type 2x + 3 at the Y1 prompt. (This represents the first equation. Youcan type up to 10 separate equa-tions.) Use the key forthe variable.
(c) Press the key to see the graph.
(d) Press the key to displaythe equation. Once you haveselected the key, youcan use the left and right arrowsof the calculator to move thecursor along the line. Experimentwith this movement. Look at thecoordinates at the bottom of thedisplay screen as you move alongthe line.
TRACE
TRACE
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X, T, �, n
Y �
>Make the Connection
chapter
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Be sure the window is thestandard window to see thesame graph displayed.
> Check YourselfExercises
Check Yourself exercises have been thehallmark of the Hutchison series; they aredesigned to actively involve studentsthroughout the learning process. Everyexample is followed by an exercise thatencourages students to solve a problemsimilar to the one just presented andcheck/practice what they have just learned.Answers are provided at the end of thesection for immediate feedback.
(a) 5 � 9 � 9 � 5
This is an application of the commutative property of addition.
(b) 5 � 9 � 9 � 5
This is an application of the commutative property of multiplication.
Example 1 Identifying the Commutative Properties
< Objective 1 >
c
Check Yourself 1
Identify the property being applied.
(a) 7 � 3 � 3 � 7 (b) 7 � 3 � 3 � 7
Overcoming Math Anxiety
Hint #5Working TogetherHow many of your classmates do you know? Whether you are by naturegregarious or shy, you have much to gain by getting to know your classmates.
1. It is important to have someone to call when you miss class or are unclearon an assignment.
2. Working with another person is almost always beneficial to both people. Ifyou don’t understand something, it helps to have someone to ask about it.If you do understand something, nothing cements that understanding morethan explaining the idea to another person.
3. Sometimes we need to commiserate. If an assignment is particularlyfrustrating, it is reassuring to find that it is also frustrating for other students.
4. Have you ever thought you had the right answer, but it doesn’t match theanswer in the text? Frequently the answers are equivalent, but that’s notalways easy to see. A different perspective can help you see that.Occasionally there is an error in a textbook (here we are talking about othertextbooks). In such cases it is wonderfully reassuring to find that someoneelse has the same answer you do.
c> Overcoming Math
Anxiety Boxes
Overcoming Math Anxiety boxes are locatedwithin the first few chapters. Thesesuggestions are designed to be timely anduseful. They are similar to the suggestionsmost instructors make in class, but havingthem in the text provides anotheropportunity to impact the student.
The new Reading Your Text feature is a setof quick exercises presented at the end ofeach section to quiz students’ vocabularyknowledge. These exercises are designed toencourage careful reading of the text. Ifstudents do not understand the vocabulary,they cannot communicate effectively. TheReading Your Text exercises address thevocabulary issue with which many studentsstruggle in learning and understandingmathematics. Answers to these exercisesare provided at the end of the book.
> End-of-SectionExercises
The comprehensive End-of-SectionExercises have been reorganized to moreclearly identify the different types ofexercises being presented. This structurehighlights the progression in level and typeof exercise for each section. This will notonly provide clarity for the student, but willalso make it easier for the instructor todetermine the exercises for theirassignments. The application exercises thatare now integrated into every section are acrucial component of this organization.
> Getting ReadyExercises
Starting with Chapter 1, each section endswith a set of Getting Ready Exercises. Theseshort exercises are designed to help studentsprepare for material in the next section of thetext. If the students have any difficulty withthese exercises, a section for review isreferenced in brackets.
> Summary andSummary Exercises
The comprehensive Summary at the end ofeach chapter enables students to reviewimportant concepts. The Summary Exercisesprovide an opportunity for the student topractice these important concepts. Theanswers to odd-numbered exercises areprovided in the answers appendix.
The following fill-in-the-blank exercises are designed to ensure that you understand some of the key vocabulary used in this section.
SECTION 1.2
(a) When two negative numbers are added, the sign of the sum is.
(b) The sum of two numbers with different signs is given the sign of thenumber with the larger value.
(c) is called the additive identity.
(d) When subtracting negative numbers, change the minus to a plus and replace the second number with its .
77. BUSINESS AND FINANCE On her vacation in Europe, Jovita’s expenses for foodand lodging were $60 less than twice as much as her airfare. If she spent$2,400 in all, what was her airfare?
78. BUSINESS AND FINANCE Rachel earns $6,000 less than twice as much as Tom.If their two incomes total $48,000, how much does each earn?
79. STATISTICS There are 99 students registered in three sections of algebra. Thereare twice as many students in the 10 A.M. section as the 8 A.M. section and 7more students at 12 P.M. than at 8 A.M. How many students are in each section?
80. BUSINESS AND FINANCE The Randolphs used 12 more gal of fuel oil in Octoberthan in September and twice as much oil in November as in September. If theyused 132 gal for the 3 months, how much was used during each month?
81. MECHANICAL ENGINEERING A motor’s horsepower (hp) is approximated by theequation
in which T is the torque of the motor and (rpm) is its revolutions per minute.Find the rpm required to produce 240 hp in a motor that produces
380 foot-pounds of torque (nearest hundredth).
82. MECHANICAL ENGINEERING In a planetary gear, the size and number of teethmust satisfy the equation
Calculate the number of teeth y needed ifand
83. ELECTRICAL ENGINEERING Power dissipation, in watts, is given by the quotientof the square of the voltage and the resistance.
(a) Express the given relationship with a formula.
(b) Determine the power dissipation when 13.2 volts pass through a 220-resistor (nearest thousandth).
84. INFORMATION TECHNOLOGY The total distance around a circular ring networkin a metropolitan area is 100 mi. What is the diameter of the ring network(three decimal places)?
85. ALLIED HEALTH A patient enters treatment with an abdominal tumor weighing32 g. Each day, chemotherapy reduces the size of the tumor by 2.33 g. There-fore, a formula to describe the mass m of the tumor after t days of treatment is
(a) How much does the tumor weigh after one week of treatment?
(b) When will the tumor weigh less than 10 g?
(c) How many days of chemotherapy are required to eliminate the tumor?
What number do you end up with? Compare your answer with everyoneelse’s. Does everyone have the same answer? Make sure that everyonefollowed the directions accurately. How do you explain the results? Algebramakes the explanation clear. Work together to do the problem again, using avariable for the number. Make up another series of computations that yields“surprising results.”
1. Yes 3. No 5. No 7. No 9. No 11. No 13. Yes15. Yes 17. Yes 19. No 21. Yes 23. Linear equation25. Expression 27. An equation that is not linear 29. Linear equation31. 2 33. �4 35. �2 37. �7 39. 6 41. 443. �12 45. �3 47. 5 49. 2 51. 12 53. 225
Make the Connection—exercise,activity, and chapter opener relate toeach other
Check Yourself—exercise tied topreceding example
Calculator—example can be done usinga calculator
Video—exercise has a video that walksthrough the solution
Caution—points out potential troublespots
> Margin Notes andRecall Notes
Margin notes throughout the text aredesigned to help students focus onimportant topics and techniques, whileRecall notes give references to previouslylearned material.
> Learning Objectives
Learning Objectives are clearly identified foreach section. Annotations for the Objectivesappear next to examples, showing whena particular objective is about to bedeveloped. References are also includedwithin the exercise sets to help studentsquickly identify examples related to topicswhere they need more practice.
> Self-Tests
Self-Tests appear in each chapter to providestudents with an opportunity to check theirprogress and to review important concepts,as well as provide confidence and guidancein preparing for in-class tests or exams. Theanswers to the Self-Test exercises aregiven at the end of the book. Sectionreferences are given with the answers tohelp the student.
Systems of Linear Equations:Solving by Graphing
< 8.1 Objectives > 1 > Solve a consistent system of linear equations by graphing
2 > Solve an inconsistent system of linear equations by graphing
3 > Solve a dependent system of linear equations by graphing
The purpose of this self-test is to help you check your progress and to reviewfor the next in-class exam. Allow yourself about an hour to take this test. At theend of that hour check your answers against those given in the back of thetext. Section references accompany the answers. If you missed any questions,go back to those sections and reread the examples until you master theconcepts.
Solve each of the following systems by graphing. If a unique solution does not exist,state whether the system is inconsistent or dependent.
1. x � y � 5 2. x � 2y � 8
x � y � 3 x � y � 2
3. x � 3y � 3 4. 4x � y � 4
x � 3y � 6 x � 2y � �6
Solve each of the following systems by addition. If a unique solution does not exist,state whether the system is inconsistent or dependent.
5. x � y � 5 6. x � 2y � 8 7. 3x � y � 6
x � y � 3 x � y � 2 �3x � 2y � 3
8. 3x � 2y � 11 9. 3x � 6y � 12 10. 4x � y � 2
5x � 2y � 15 x � 2y � 4 8x � 3y � 9
11. 2x � 5y � 2 12. x � 3y � 6
3x � 4y � 26 3x � 9y � 9
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> Videos > C A U T I O N
NOTE
This definition tells us thata composite number hasfactors other than 1 and itself.
Content Changes• In Chapter 0, more complex order-of-operations examples and exercises
are now included. The coverage of mixed numbers has also expanded. Inaddition, the review of material on percent has been revised, and the summarytable has expanded to include a more complete list of words signifyingarithmetic operations.
• In Chapter 1, more complex order-of-operations content is included and thereis now more material involving negative numbers. Coverage of the median andsummation notation has been removed.
• In Chapter 2, the algorithm for solving linear equations has been clarified and isused consistently throughout. The discussion of the mean has been removed.
• In Chapter 3, the properties of exponents are now named. Examples withnegative coefficients are included, and material is included to provide a moregradual development of evaluating expressions. The exposition for scientificnotation with regard to small numbers is improved, and the section on specialproducts has been incorporated into the section on multiplying polynomials.
• In Chapter 4, factoring by grouping is incorporated into the first section. The ac-method is now part of Section 4.3, while factoring cubes is now in Section 4.5.
• Chapter 5 contains examples simplifying expressions using the GCF. Complexradical expressions are now covered before equations.
• In Chapter 6, some of the exercises have been revised to increase the numberof non-integer results.
• Chapter 7 has additional examples on the discussion of slope. It includes moreon graphing of boundary lines.
• In Chapter 8, a discussion demonstrating that either equation may be used inthe substitution method is included. The discussion of the system of linearinequalities now includes new examples and some revised examples.
> Cumulative Reviews
Cumulative Reviews are included startingwith Chapter 2, following the Self-Tests.These reviews help students build onpreviously covered material and give theman opportunity to reinforce the skillsnecessary in preparing for midterm and finalexams. These reviews assist students withthe retention of knowledge throughout thecourse. The answers to these exercises arealso given at the end of the book, along withsection references.
> Graph Paper Card
A Graph Paper card is bound into the backof the book. This perforated card can betorn out and copied as needed by thestudents. An electronic version of the card isavailable through the book’s website in theInformation Center.
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The following exercises are presented to help you review concepts from earlierchapters. This is meant as a review and not as a comprehensive exam. The an-swers are presented in the back of the text. Section references accompany theanswers. If you have difficulty with any of these exercises, be certain to at leastread through the summary related to those sections.
Simplify the following expressions.
1. 8x2y3 � 5x3y � 5x2y3 � 3x3y
2. (4x2 � 2x � 7) � (�3x2 � 4x � 5)
Evaluate each expression when x � 2, y � �1, and z � �4.
