Hsiang-Ping Huang math1010fall2008-3€¦ · Hsiang-Ping Huang math1010fall2008-3 ... Usually you...

Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 1 WebWork Demo is due : 09/02/2008 at 05:00pm MDT.The link

¡a href=” http://www.math.utah.edu/*/”¿ http://www.math.utah.edu/*/ ¡/a¿for the course contains the syllabus, grading policy and other information.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, youcan if you wish enter elementary expressions such as 23 instead of 8.

Here’s the list of the functions which WeBWorK understands.You can use the Feedback button on each problem page to send e-mails to the professors.

1. (1 pt) 1010Library/set1 WebWork Demo/m1p165.pgEnter here the expression 1

a + 1b .

Enter here the expression 1a+b .

Correct Answers:• 1/a+1/b• 1/(a+b)

2. (1 pt) 1010Library/set1 WebWork Demo/s1.p29.pg

For each of the WeBWorK phrases below enter a T (true)if the two given phrases describe the same algebraic expressionand a F (false) otherwise. One way you can decide whether thephrases are equivalent is to substitute specific values for a, b,etc. If you get two different results the two phrases are certainlynot equivalent. If you get the same values there is small chancethis happened accidentally for just that choice of particular val-ues. In any case, pay close attention to when these phrases areequivalent and when they are not, it will help you tremendouslywith future WeBWorK assignments.

a+b2 (a+b)2

a2 +b2 (a+b)2

a∗b∗ c a∗ (b∗ c)

a/b/c a/(b/c)

Correct Answers:• F• F• T• F

3. (1 pt) 1010Library/set1 WebWork Demo/s1p1.pgThis first question is just an exercise in entering answers intoWeBWorK. It also gives you an opportunity to experiment withentering different arithmetic and algebraic expressions intoWeBWorK and seeing what WeBWorK really thinks you are do-ing (as opposed to what you believe it should think).

Notice the buttons on this page and try them out before movingto the next problem. Use the ”Back” Button on your browser toget back here when needed.

”Prob. List” gets you back to the list of all problems in this set.

”Next” gets you to the next question in this set.

”Submit Answer” submits your answer as you might expect, butthere may be other ways to do so. Specifically, in this problem,there is only one question. In that case you can submit youranswer by typing it into the answer window and then pressing”Return” (or ”Enter”) on your keyboard. But even in this case,you can also type the answer and click on the ”submit” button.There is no harm in submitting an answer even if you are notquite sure that it’s correct, since if it is not you have an unlim-ited number of additional tries. On the other hand, it is usuallymore efficient to print your own private problems set, work outthe answers in a quiet environment like your home, and then sitdown in front of a computer and enter your answers. If someare wrong you can try to fix them right at the computer, or youmay want to go back and work on them quietly elsewhere beforereturning to the computer.

Pressing on the ”Preview Answer” Button makes WeBWorKdisplay what it thinks you entered in the answer window. Afterusing ”Preview” you can modify your answer and use a ”Pre-view Again” button.

”images” denotes the ordinary display mode on your worksta-tion.

”Logout” terminates this WeBWorK session for you. You canof course log back in and continue.

”Feedback” enables you to send a message to your instructor,and the WeBWorK assistants. If you use this way of sending

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e-mail the recipients receive information about your WeBWorKstate, in addition to your actual message.

The ”Help” Button transports you to an official WeBWorK helppage that has a more information than this first problem.

”Problem Sets” transports you back to the page where you canselect a certain problem set. When you do this particular prob-lem in this first set, there is only one set, but eventually therewill be 13 of them.

For all problems in this course you will be able to see the An-swers to the problems after the due date . Go to a problem,click on ”show correct answers”, and then click on ”submit an-swer”. You can also download and print a hard copy with theanswers showing. These answers are the precise strings againstwhich WeBWorK compares your answer. If the answer is analgebraic expression your answer needs to be equivalent to theWeBWorK answer, but it may be in a different form. For ex-ample if WeBWorK thinks the answer is 2 ∗ a, it is OK for youto type a + a instead. If WeBWorK expects a numerical an-swer then you can usually enter it as an arithmetic expression(like 1/7 instead of .142857), and usually WeBWorK will ex-pect your answer to be within one tenth of one percent of whatit thinks the answer is.

Most of the problems (including this one) in this course willalso have solutions attached that you can see after the due dateby clicking on ”show solutions” followed by ”submit answers”.The solutions are text typed by your instructor that gives moreinformation than the ”answers”, and in particular often explainshow the answers can be obtained.

Now for the meat of this problem. Notice that the answer win-dow is extra large so you can try the things suggested above.

Type the number 3 here:.

Try entering other expressions and use the preview buttonto see what WeBWorK thinks you entered. Return to thisproblem to try out things when you get stuck somewhereelse.

Here are some good examples to try. Check them all out usingthe Preview button. (In later questions on this set you will getto use what you learn here.) Never mind that you may have al-ready answered the correct answer 3. Once you get credit for ananswer it won’t be taken away by trying other answers.

a/2b versus a/2/b versus a/(2b)

a/b+c versus a/(b+c)

a+b**2 versus (a+b)**2

sqrt a+b versus sqrt(a+b)

4/3 pi r**2 versus (4/3) pi r**2 (In other words, if you are notsure use parentheses freely.)

Note: WeBWorK will not usually let you enter algebraic ex-pressions when the answer is a number, and it will only let youuse certain variables when the answer is in fact an algebraic ex-pression. So the above window, and the opportunity for exper-imentation that it offers is unique. Make good use of it!

Presumably this has been your first encounter with WeBWorK.Come back here to try things out and to refresh your memory ifyou get stuck somewhere down the line.

Correct Answers:

• 3

4. (1 pt) 1010Library/set1 WebWork Demo/s1p2.pgThe purpose of this exercise is to illustrate further the use of thebuttons on this page and to show you the most common way inwhich WeBWorK processes partially correct problems. Try en-tering incorrect answers in the answer fields below, to see whathappens. (This time WeBWorK will reject algebraic expressionssince I told it to expect a numerical answer.)

Type the number 4 here: .

Type the number 5 here: .

Correct Answers:

• 4• 5

5. (1 pt) 1010Library/set1 WebWork Demo/s1p3.pg

In the first few problems, now that you are familiar with thebasic mechanics of WeBWorK, you will be asked to evaluatesome arithmetic expressions and enter the answer as a numberinto WeBWorK. You may of course use a calculator. In laterproblems you will be able to enter the answer as an arithmeticexpression, but at present your answer must be a number suchas 4, -4, or 17.5.

Evaluate the expression2(7 + 6) = . (Remember that by conventiona missing arithmetic operator means multiplication .)

Correct Answers:

• 26


Evaluate the expression7(7−8) = .

2

Correct Answers:

• -7


Evaluate the expression8/(8+2) = .Enter your answer as a decimal number listing at least 4 decimaldigits. (WeBWorK will reject your answer if it differs by morethan one tenth of 1 percent from what it thinks the answer is.)

Correct Answers:

• 0.8


Evaluate the expression18− (3−2) = .

Correct Answers:

• 17


Evaluate the expression6− (4−7) = .

Correct Answers:

• 9

10. (1 pt) 1010Library/set1 WebWork Demo/s1p8.pgThis problem illustrates the standard rules of arithmetic prece-dence:

Multiplication and Division precede Subtraction and Addition.Among operations with the same level of precedence, evalua-tion proceeds from left to right.However, expressions in parentheses are evaluated first.

Evaluate the expression6×5−4×2 =

Evaluate the expression6× (5−4)×2 =

Evaluate the expression6× (5−4×2) =

Correct Answers:

• 22• 12• -18

11. (1 pt) 1010Library/set1 WebWork Demo/s1p9.pgThis problem provides more illustrations of the use of parenthe-ses.

Evaluate the expression8−8−5−6 =

Evaluate the expression8− (8−5)−6 =

Evaluate the expression8− (8−5−6) =

Evaluate the expression8− (8− (5−6)) =

Correct Answers:• -11• -1• 11• -1

12. (1 pt) 1010Library/set1 WebWork Demo/s1p10.pgThe key idea in Algebra is to use variables in addition to num-bers. Sometimes we need to replace variables with specificnumbers. That’s called evaluating an algebraic expression.For example, if a = 2 then 3a = 6, and we say that we evaluatedthe expression 3a at a = 2. We’ll do this sort of thing all semes-ter long, and in this problem you get your first experience withevaluating algebraic expressions. Again, the emphasis in theseexercises is on understanding the rules of arithmetic precedence.

Let a = 10, b = 3, c = 13.Then a−b/c =and (a−b)/c =As usual, enter your answers as decimal numbers with at

least 4 digits.Correct Answers:

• 9.76923076923077• 0.538461538461538

13. (1 pt) 1010Library/set1 WebWork Demo/s1p11.pgLet r = 7.

Then 4/π∗ r =and 4/(π∗ r) =Correct Answers:

• 8.91267681314614• 0.181891363533595

14. (1 pt) 1010Library/set1 WebWork Demo/s1p12.pgLet a = 3, b = 4, c = 6, d = 9.

Then a−b/c−d = ,

(a−b)/(c−d) = ,a− (b/c−d) = , anda−b/(c−d) = .

3

Correct Answers:

• -6.66666666666667• 0.333333333333333• 11.3333333333333• 4.33333333333333

15. (1 pt) 1010Library/set1 WebWork Demo/s1p13.pgThe next three problems are like the preceding three, except thatyou need to get all answers correct before WeBWorK will giveyou credit. This will be true for many problems in this class.The purpose of insisting on all answers being correct is to en-courage you to think about the whole context of the problemrather than the individual pieces.

Let a = 2.7, b = 3.7, c = 5.9.Then a−b/c =and (a−b)/c =Correct Answers:

• 2.0728813559322• -0.169491525423729

16. (1 pt) 1010Library/set1 WebWork Demo/s1p14.pgLet r = 4.7.

Then 4/π∗ r =and 4/(π∗ r) =Correct Answers:

• 5.98422586025527• 0.270902030794715

17. (1 pt) 1010Library/set1 WebWork Demo/s1p15.pgLet a = 3.7, b = 5.1, c = 6.5, d = 7.5.

Thena−b/c−d = ,

(a−b)/(c−d) = ,a− (b/c−d) = , anda−b/(c−d) = .

Correct Answers:

• -4.58461538461539• 1.4• 10.4153846153846• 8.8

18. (1 pt) 1010Library/set1 WebWork Demo/s1p16.pgIn this and the following problems you will practice en-tering algebraic expressions into WeBWorK. Remember theRules of Arithmetic Precedence and use parentheses to makeyour meaning clear. Most of the difficulties students have withWeBWorK are due to not appreciating the precise rules that gov-ern the interpretation of what you enter. This is not just a matterof WeBWorK understanding what you are trying to say, Therules are used universally all over the world. Appreciating andapplying them properly is also crucial, for example, in computerprogramming. Make sure you understand what’s going in theseproblems. If you enter a wrong expression use the Preview But-ton to see what WeBWorK thinks you have entered.

We start simply. Enter here the expression a+b.Correct Answers:

• a+b

19. (1 pt) 1010Library/set1 WebWork Demo/s1p17.pgEnter here the expression

a+12+b

Enter here the expression

a+bc+d

If WeBWorK rejects your answer use the preview button tosee what it thinks you are trying to tell it.

Correct Answers:

• (a+1)/(2+b)• (a+b)/(c+d)


11a + 1

b


a+b+11+ 1

a+b

Correct Answers:

• 1/(1/a+1/b)• (a+b+1)/(1+1/(a+b))


Enter here the expressionab + c

def + g

h.

Correct Answers:

• (a/b+c/d)/(e/f+g/h)


The square x2 of a number x simply means the product of xwith itself. For example, 32 = 3∗3 = 9. You can enter a numbersuch as 32 as 3**2 . (An expression such as 32 or x2 is calleda power . We will learn a great deal more about powers duringthis semester.)

Enter here the expression x2

The square root√

x of a number x is a number whose squareequals x. For example

√25 = 5 since 52 = 5∗5 = 25.

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To enter square roots you can use the function sqrt . Forexample, to enter the square root of 2 you can type sqrt (2).

Enter here the expression√

aCorrect Answers:

• x**2• sqrt{a}


√a+b

Enter here the expressiona√

a+bEnter here the expression

a+b√a+b

Correct Answers:

• sqrt(a+b)• a/sqrt(a+b)• (a+b)/sqrt(a+b)


Enter here the expression√x2 + y2


x√

x2 + y2

Enter here the expressionx+ y√x2 + y2

Correct Answers:

• sqrt(x**2+y**2)• x*sqrt(x**2+y**2)• (x+y)/sqrt(x**2+y**2)



−b+√

b2−4ac2a

Note: this is an expression that gives the solution of a quadraticequation by the quadratic formula . We will learn much moreabout it later in the semester.

Correct Answers:

• (-b+sqrt(b**2-4*a*c))/(2a)

26. (1 pt) 1010Library/set1 WebWork Demo/s1p24.pgConsider the following expressions:

A = a+bc

and

B =a+b

cFor each of the WeBWorK phrases below write A if they de-

fine A and B if they define B.

You need to get all answers correct before obtaining credit.

a+b/c (This is the standard way to enter A, so enter A).

(a+b)/c (This is the standard way to enter B, so enter B).

((a+b)/c)

a+(b/c)

(a+(b/c))

Correct Answers:

• A• B• B• A• A

27. (1 pt) 1010Library/set1 WebWork Demo/s1p25.pgConsider again the formula for the solution of a quadratic equa-tion:

x =−b+

√b2−4ac

2aFor each of the WeBWorK phrases below enter a T (true) if

the phrase describes x, correctly, and a F (false) otherwise.


-b+sqrt(b**2-4*a*c)/2a

(-b+sqrt(b**2-4*a*c))/2a

(-b+sqrt(b**2-4*a*c))/(2a)

Correct Answers:

• F• F

5

• T

28. (1 pt) 1010Library/set1 WebWork Demo/s1p26.pgMore of the same.

(-b+sqrt(b**2-(4*a*c)))/(2a)

(-b+(sqrt(b**2-4*a*c)))/(2a)

((-b+sqrt(b**2-4*a*c))/(2a))

(-b+(sqrt(b**2-4*a*c))/(2a))

(-b+sqrt(b*b-(4*a*c)))/(2a)

Correct Answers:

• T• T• T• F• T


For each of the WeBWorK phrases below enter a T (true) ifthe two given phrases describe the same algebraic expressionand an F (false) otherwise. One way you can decide whether thephrases are equivalent is to substitute specific values for a, b,etc. If you get two different results the two phrases are certainlynot equivalent. If you get the same values there is small chancethis happened accidentally for just that choice of particular val-ues. In any case, pay close attention to when these phrases areequivalent and when they are not, it will help you tremendouslywith future WeBWorK assignments.

a+b b+a

a+b+ c a+(b+ c)

a−b− c a− (b− c)

Correct Answers:

• T• T• F


More of the same.

a+b2 (a+b)2

a2 +b2 (a+b)2

a∗b∗ c a∗ (b∗ c)

a/b/c a/(b/c)

Correct Answers:• F• F• T• F


In mathematics, lower and upper case letters mean differentthings. The letter a is not the same as the letter A. Keep that inmind when answering the questions below, using T or F as inthe preceding questions.

a a

a A

a+A A+a

Correct Answers:• T• F• T


Much of this course will center around the manipulation ofalgebraic expressions, often with the goal of solving an equa-tion. This exercise is the first step in this direction. Again, indi-cated with T or F if the two expressions are equivalent.

a∗ (b+ c) a∗b+a∗ c

1/(a+b) 1/a+1/b

1/a/a 1/(a∗a)

Correct Answers:• T• F• T


The reason why Mathematics is required for so many sub-jects is that it can be used to solve problems outside of mathe-matics, the dreaded word problems . There will be many wordproblems in this class, usually leading to a mathematical prob-lem of the kind we are discussing at the time. Students don’tlike word problems because they involve the extra layer of con-verting the word problem to a math problem. But keep in mind

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that math classes are the only kind of classes you take wheresome problems are not word problems!

This first word problem of this course can be solved by derivingand solving an equation, but it can also be solved essentially byguessing and modifying the answer until it fits, without any al-gebraic manipulation. We will revisit it in the future in a morecomplicated setting.

You buy a pot and its lid for a total of $ 11. The sales per-son tells you that the pot by itself costs $ 10 more than the lid.The price of the pot is $ and the price of the lid is $

.Correct Answers:

• 10.5• 0.5

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

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Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 1 is due : 09/05/2008 at 05:00pm MDT.

1. (1 pt) math1010fall2006-1/set2/e1 1.pgThe purpose of this last and lengthy problem is to help you pre-pare for the first exam.

Work through the list below and make sure you understandthe described items and can answer questions related to them.

Fractions. You need to be able to add, multiply, subtract, and di-vide fractions. Moreover, you need to be able to recognize com-mon factors in numerator and denominator, and cancel them. Itdoes not hurt to practice, so here we go:27 + 4

21 = / .27 −

421 = / .

27 ×

421 = / .

27 ÷

421 = / .

Here is a more complicated fraction problem:43−

12

25 + 1

3= / .

Language. Understand the language related to the four ba-sic arithmetic operations. Don’t use embarrassingly juvenilewords like “timesing” and “minussing”. Use the proper terms”multiplying” and ”subtracting”. Understand the words add,multiply, subtract, divide, sum, difference, product, quotient,factor, multiple, divisor, dividend. Also understand and knowthe names of the rules of arithmetic: the commutative and asso-ciative laws of addition and multiplication, and the distributivelaw. Use the Glossary and have someone quiz you if you are notsure. Know what kind of numbers (natural numbers, integers,rational numbers, real numbers) there are.

The Distributive Law. Understand how to apply the Distribu-tive Law to simplify algebraic expressions.

Precedence. Understand the conventions of arithmetic prece-dence. There are a large number of problems like this on set1. Multiplication and division come before addition and sub-traction. If there are several operations of the same level ofprecedence we work from left to right. However, anything inparentheses is evaluated first. Addition and subtraction have thesame level of precedence, and so do multiplication and division.You can also use superfluous parentheses to make your meaningclear if you are not sure.

Know how to compute absolute values of arithmetic expres-sions.

Correct Answers:

• 10• 21• 2• 21• 8• 147• 3• 2• 25• 22

2. (1 pt) math1010fall2006-1/set2/prob.pg

The expression

105 −

32

125 + 4

7

can be written as a fractionab

where the integers a and b have no factor in common, and b ispositive.

Enter a= and b=Correct Answers:

• 35• 208

3. (1 pt) math1010fall2006-1/set2/s2p11.pg

The expression 12 ×

23 ×

34 ×

45 ×

56 ×

67 is a fraction a

b where b ispositive, and a and b have no common factors.


• 1• 7

4. (1 pt) uumathLibrary/math1010fall2006-1/set2/s2p12.pgIf you are unfamiliar with the terminology in this and the nextproblem learn about it here.

The greatest common factor (GCF) of 14 and 21 is and theirleast common multiple (LCM) is The GCF of 12 and 42 is

and their least common multiple (LCM) is The GCF of3 and 5 is and their least common multiple (LCM) is

Correct Answers:1

• 7• 42• 6• 84• 1• 15

5. (1 pt) uumathLibrary/math1010fall2006-1/set2/s2p13.pg

The least common multiple of 1,2,3,4 is .The least common multiple of 1,2,3,4,5 is .The least common multiple of 1,2,3,4,5,6 is .The least common multiple of 1,2,3,4,5,6,7 is .

Correct Answers:

• 12• 60• 60• 420


Let xy be a fraction (reduced to lowest terms) that satisfies

12

+xy

=56.

Then x= and y=If this problem gives you pause check here for a generalprinciple of problem solving

Correct Answers:

• 1• 3


Let xy be a fraction (reduced to lowest terms) that satisfies

37× x

y=

65.

Then x= and y=Correct Answers:

• 14• 5


The expression 12 ÷

23 ÷

34 ÷

45 ÷

56 ÷

67 is a fraction a

b where b ispositive, and a and b have no common factors.


• 7• 4

9. (1 pt) uumathLibrary/math1010fall2006-1/set2/s2p17.pgList all the factors of 60 in increasing sequence. (If you enter acorrect factor in the wrong place of the sequence WeBWork willconsider it wrong.)

, , , , , , , , , , , .Correct Answers:

• 1• 2• 3• 4• 5• 6• 10• 12• 15• 20• 30• 60

10. (1 pt) Library/Rochester/setAlgebra03Expressions/Test1 11-12.pgGiven

P = 5b3−6b−2,

Q = b2 +7b+4,

R = b3 +7

Then P+Q = b3+ b2+ b+

and R(P+Q) = b6+ b5+ b4+ b3+ b2+b+

Correct Answers:

• 5• 1• 1• 2• 5• 1• 1• 37• 7• 7• 14

11. (1 pt) Library/Rochester/setAlgebra03Expressions/lhp3 58.pgThe expression (3x+7)2 equals x2+ x+

Correct Answers:

• 9• 42• 49

2

12. (1 pt) Library/Rochester/setAlgebra03Expressions/lhp3 26.pgThe expression 5(5x2−8x+9)− (3x2 +6x−3) equals

x2+ x+

Correct Answers:

• 22• -46• 48

13. (1 pt) Fifth Library/set2/4wp.pgA cash register contains only five dollar and ten dollar bills. Itcontains twice as many five’s as ten’s and the total amount ofmoney in the cash register is 640 dollars. How many ten’s arein the cash register?

Correct Answers:

• 32

14. (1 pt) uumathLibrary/math1010fall2006-1/set3/s3p14.pgEnter the appropriate symbol <, =, or > below.1. 3 −1

2. −2 −1

3. x x+1

4. x2 |x|2

5. 3(x+1) 3x+3

6. −1 |x|

Correct Answers:

• >• <• <• =• =• <

15. (1 pt) uumathLibrary/math1010fall2006-1/set3/s3p19.pgMatch the phrases given below with the letters labeling the al-gebraic expression.You must get all of the answers correct to receive credit.

1. The sum of x and 82. The sum of x and 2, all squared3. The difference of x and x2 divided by the sum of x and

x2

4. The product of the sum of x and 2 and the sum of x2 and2

5. The quotient of x and the sum of x and 8A. (x+2)(x2 +2)

B. xx+8

C. x−x2

x+x2

D. x+8E. (x+2)2

Correct Answers:

• D• E• C• A• B

16. (1 pt) math1010fall2006-1/set3/s3p20.pgMatch the phrases given below with the letters labeling the al-gebraic expression. You may have to simplify your expressionto recognize it as the correct one.You must get all of the answers correct to receive credit.

1. The sum of x and x+42. The square of x+43. The difference of x and x+44. The quotient of x and x+45. The product of x and x+4

A. xx+4

B. 2x+4C. −4D. x2 +8x+16E. x2 +4x

Correct Answers:

• B• D• C• A• E

17. (1 pt) uumathLibrary/math1010fall2006-1/set3/s3p21.pgIndicate whether the following statements are True (T) or False(F).

1. -17 is an integer2. π is a real number3. 2 is a real number4.√

49 is a rational number5. 0 is a natural number6. 3

2 is an integer7.√

3 is a rational numberCorrect Answers:

• T• T• T• T• F• F• F

3


1. The difference of two integers is always an integer.2. The difference of two integers is always a natural num-

ber.3. The quotient of two integers is always an integer (pro-

vided the denominator is non-zero).4. The quotient of two integers is always a rational num-

ber (provided the denominator is non-zero).5. The sum of two integers is always an integer.6. The product of two integers is always an integer.7. The ratio of two integers is always positive

Correct Answers:

• T• F• F• T• T• T• F


1. The ratio of two real numbers is never zero.2. The sum of two real numbers is always a real number.3. The difference of two real numbers is always an irra-

tional number.4. The product of two real numbers is always a real num-

ber.5. The quotient of two real numbers is always a rational

number (provided the denominator is non-zero).6. The difference of two real numbers is always a real

number.7. The quotient of two real numbers is always a real num-

ber (provided the denominator is non-zero).Correct Answers:

• F• T• F• T• F• T• T


4

Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 2 is due : 09/12/2008 at 05:00pm MDT.The link http://www.math.utah.edu/*/ for the course contains the syllabus, grading policy and other information.The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making

some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.



1. (1 pt) First Library/set4/s3p35.pgThe expression (x−6)(x2 +6x+2)equals Ax3 +Bx2 +Cx+Dwhere A equals:and B equals:and C equals:and D equals:

Correct Answers:

• 1• 0• -34• -12

2. (1 pt) First Library/set4/s4p1.pg

The solution of the equation 7x = 4is x = .You may enter your answer as a decimal number or as a frac-tion. I recommend that in problems like this you use fractionsrather than decimal approximations. You don’t have to figureout your approximation, and you don’t have to worry about justhow accurately you should approximate the answer.

Correct Answers:

• 0.571428571428571


The solution of the equation 7x+8 = 7is x = .

Correct Answers:

• -0.142857142857143


The solution of the equation 5x+9 = 10x+12is x = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• -0.6


The solution of the equation 4y+11 = 9y+16is y = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• -1


You are probably used to solving problems where the coeffi-cients are specific numbers. However, in many problems thecoefficients are variables themselves, and the answer dependson those variables. As you go on in mathematics, the role ofspecific numbers will keep decreasing, and the role of generalcoefficients (or parameters) will increase. The next couple ofproblems are our first foray into this new area.

The solution of the equation ax+b = cis x = .(Your answer will of course be in terms of a, b, and c. You mayassume that a is non-zero.)

Correct Answers:

• (c-b)/a


The solution of the equation ax+b = cx+dis x = .(Your answer will of course be in terms of a, b, c, and d. Youmay assume that a does not equal c.)

Correct Answers:

• (d-b)/(a-c)

8. (1 pt) set4/s4p7.pg

The solution of the equation

x2 +8x+11 = x2 +7x+11

is x = .Correct Answers:

1

• 0

9. (1 pt) set4/s4p9.pg


(x−6)(x−5) = (x+3)(x+9)

is x = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• 0.130434782608696

10. (1 pt) set4/s4p11.pg


1x−4

=1

2x+9

is x = .Correct Answers:

• -13

11. (1 pt) set4/s4p15.pg


xx−4

=x−7x+7

is x = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• 1.55555555555556

12. (1 pt) set4/s4p17.pgIndicate with T (true) if the equations below are linear, and F(false) if they are not.

1. 3x+4 = 5x−42. x2 + x = 43. 3x+4 = 174. x2 = 1

Correct Answers:

• T• F• T• F

13. (1 pt) set4/s4p20.pgFor the following equations, enter U if the equation has a uniquesolution, N if it has no solution, and I if it has infinitely manysolutions. You need to get all answers correct before obtainingcredit.

1.6x+3 = 7

2.7x+6 = 7x+3

3. 16x+3 = 1

3x+7

4. 16x+3 = 2

6x+3

5. (x+6)(x+3) = x2 +9x+18

6.2(6x+3) = 12x+6

Correct Answers:

• U• N• U• N• I• I

14. (1 pt) set4/s4p26 e.pg

This problem is just like the pot and lid problem on homework1.

You buy a house including the land it sits on for $ 175000. Thereal estate agent tells you that the land costs $ 23000 more thanthe house.

The price of the house is $ and the price of theland is $ .

Correct Answers:

• 76000• 99000

15. (1 pt) set4/s4p30.pg

The last two problems are examples of ”simple Hindu Alge-bra”, quoted on page 528 of ”The Story of Civilization”, v.1., byWill Durant, Simon and Schuster, 1935. The problems are ap-proximately 1,800 years old. (Mental pursuits by women were

2

discouraged at that time. You ponder the significance of ficti-tiously directing the questions at women. Durant does not com-ment on this issue.)

Out of a swarm of bees one fifth part settled on a Kadamba blos-som; one third on a Silihindra flower; three times the differenceof those numbers flew to the bloom of a Kutaja. One bee, whichremained, hovered about in the air. Tell me, charming woman,the number of bees .

Correct Answers:• 15

16. (1 pt) set4/s4p31.pgHere is the other problem from ”The Story of Civilization”:

Eight rubies, ten emeralds, and a hundred pearls, which are inthy ear-ring, my beloved, were purchased by me for thee at anequal amount; and the sum of the prices of the three sort of gemswas three less than half a hundred; tell me the price of each, aus-picious woman.Enter the price of one pearl , the price of one emerald

, and the the price of one ruby .Correct Answers:

• 2• 20• 25


3


The WebCT’s page for the course contains the syllabus, grading policy and other information.


Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors. However, if you do use that option, thentry to be as specific as you can as to what is giving you problems. ”I don’t get it”, ”This is terrible” are not questions and there isnothing I can do about it. However, telling me what you attempted and why you think you’re correct and what you think should bedone in the problem can help me understand your thinking and possibly enable me to offer some assistance.

1. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling-/sw3 2 28.pgA change purse contains an equal number of pennies, nickels,and dimes. The total value of the coins is 144 cents. How manycoins of each type does the purse contain?

Number of pennies :

Correct Answers:

• 9

2. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling-/ur ab 6 1.pgA student has scores of 77.5, 79, and 81 on his first three tests.He needs an average of at least 80 to earn a grade of B. What isthe minimum score that the student needs on the fourth test toensure a B?Note: The answer need not be an integer.

Correct Answers:

• 82.5

3. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling-/sw3 2 57.pgWilma drove at an average speed of 50 mi/h from her homein City A to visit her sister in City B. She stayed in City B 25hours, and on the trip back averaged 50 mi/h. She returnedhome 43 hours after leaving. How many miles is City A fromCity B

Your answer is :

Correct Answers:

• 450

4. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling/lh1-3 46.pgYour weekly paycheck is 30 percent less than your coworker’s.Your two paychecks total 730. Find the amount of each pay-check.

Your coworker’s is : and yours is .

Correct Answers:

• 429.411764705882• 300.588235294118

5. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling-/srw1 6 20.pgAfter robbing a bank in Dodge City, a robber gallops off at 12mi/h. 20 minutes later, the marshall leaves to pursue the robberat 15 mi/h. How long (in hours) does it take the marshall tocatch up to the robber?

Correct Answers:

• 1.33333333333333

6. (1 pt) Library/Rochester/setAlgebra09LinearEqnsModeling-/sw3 2 9.pgThe distance (in miles) traveled when driving at a certain speeds for 31 hours, then driving 14 miles/hour faster for anotherhour. Express the distance in terms of s.

Your answer is :

Correct Answers:

• (31+1)*s+14

1

7. (1 pt) Library/ASU-topics/setSolveEquations/zhu10.pgJohn wants to get to the bus stop, the bus stop is across a grassypark, 2000 feet west and 600 feet north of his starting position.John can walk west along the edge of the park on the sidewalkat a speed of 6 ft/sec and 4 ft/sec through the grass. How farshould he walk on the sidewalk before veering off onto the grassif he wishes to get to the bus stop in exactly 7 min 30 sec?

Answer:

Correct Answers:

• 1200, 1680


Consider the inequality

3x+7 < 2

By subtracting 7 on both sides and dividing by 3 we see thatthis inequality is equivalent to

x <−53.

The first few problems in this set are similar. In the aboveexample you would enter < and − 5

3 as your answers.

In the actual first problem of this set consider the inequality

6x+9 < 9

Below insert the appropriate symbol < or > and the appropriatenumber such that the two inequalities are equivalent.x (insert symbol) (insert number)

As usual I recommend that you enter non-integer answers asfractions rather than decimal expressions.

Correct Answers:

• <• 0



−8x+7 < 1


Correct Answers:

• >• 0.75



8x+3 > 13x+6


Correct Answers:• <• -0.6



11x+1 < 6x+6


Correct Answers:• <• 1

12. (1 pt) math1010fall2006-1/set5/s5p5 e.pg

To solve the next few problems you need to understand thedefinition and properties of absolute value.

The equation|4x−7|= 5

has two solutions. Enter the smaller here and thelarger here

Correct Answers:• 0.5• 3


The equation|8x−9|= |3x+8|


Correct Answers:• 0.0909090909090909• 3.4


The equation|4x−5|= |9x+2|


Correct Answers:• -1.4• 0.230769230769231

2


The equation|x−1|+ |x−2|= 3.

has two solutions.

Enter the smaller hereand the larger hereCorrect Answers:

• 0• 3

16. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p43.pgYou are going to drive 480 miles today at an average speed of60 miles per hour. Thus you are going to drive for a total ofhours. The diameter of the wheels on your car (including tires)is 25 inches. Thus each wheel is going to turn a total oftimes today.

Correct Answers:• 8• 387227.75356324


3





1. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/srw1 2 33.pgEvaluate the expression 72 +74.

[NOTE: Your answer cannot be an algebraic expression. ]

Correct Answers:

• 2450

2. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 25.pgThe expression

(2y4)4

2y2

equals cye wherethe coefficient c is , the exponent e of y is .

Correct Answers:

• 8• 14

3. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/srw1 2 2.pgEvaluate the expression −23.

[NOTE: Your answer cannot be an algebraic expression. ]Correct Answers:

• -8

4. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 47b.pgEvaluate the expression |−63|.

Correct Answers:

• 63

5. (1 pt) Library/Rochester/setAlgebra01RealNumbers/srw1 1 8.pgEvaluate the expression 3(−4)(2−4−2(3)).

(Your answer cannot be an algebraic expression. )

Correct Answers:

• 96

6. (1 pt) Library/Rochester/setAlgebra01RealNumbers/srw1 8 67.pgEvaluate the expression |186−329|.

Correct Answers:

• 143

7. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 11.pgUse properties of real numbers to write the expression

−92(4x−20y)

in the form ofA · x+B · y.

The number A = and the number B = .Correct Answers:

• -18• 90

8. (1 pt) Library/Rochester/setAlgebra01RealNumbers/srw1 8 73.pg

Evaluate the expression|199−284||−23|

. Give you answer in deci-

mal notation correct to three decimal places or give your answeras a fraction.

[NOTE: Your answer can be an algebraic expression.Make sure to include all necessary (, ). ]

Correct Answers:

• 3.69565217391304

1

9. (1 pt) Library/Rochester/setAlgebra01RealNumbers/srw1 1 21-28.pgMatch the statements defined below with the letters labelingtheir equivalent expressions.You must get all of the answers correct to receive credit.

1. x is less than -72. x is any real number3. The distance from x to -7 is less than or equal to 14. x is less than or equal to -75. x is greater than -7

A. x≤−7B. −∞ < x < ∞

C. −7 < xD. x <−7E. |x+7| ≤ 1

Correct Answers:

• D• B• E• A• C

10. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 50a.pgEvaluate the expression

|4−|−44|| .

Your answer isCorrect Answers:

• 40

11. (1 pt) Library/Rochester/setAlgebra01RealNumbers/srw1 8 1.pgMatch the statements defined below with the letters labelingtheir equivalent expressions.You must get all of the answers correct to receive credit.

1. |x−5| ≤ 72. |x−5|< 73. |x−5|< ∞

4. |x−5| ≥ 75. |x−5|> 7

A. x ∈ (−∞,−2)∪ (12,∞)B. x ∈ (−2,12)C. x ∈ (−∞,∞)D. x ∈ [−2,12]E. x ∈ (−∞,−2]∪ [12,∞)

Correct Answers:

• D• B• C• E• A

12. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 49a.pgEvaluate the expression

||−28|− |−13|| .

Correct Answers:

• 15

13. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 18.pgEnter a T or an F in each answer space below to indicate whetherthe corresponding statement is true or false.You must get all of the answers correct to receive credit.Your answer for the following statement is

1112

<1314

Your answer for the following statement is

−2021

<−2122

Correct Answers:

• T• F

14. (1 pt) Library/Rochester/setAlgebra01RealNumbers/ur ab 8 2.pgThe interval described in set-builder notation by the inequality|5x−15|< 40 has interval notation (a,b)fora =andb =

Correct Answers:

• -5• 11

15. (1 pt) Library/Rochester/setAlgebra01RealNumbers-/ur ab 10 1.pgMatch each interval below with set-builder notation for the sameinterval.

1. [4,∞)2. (−∞,4]3. (4,8)4. (−∞,4)5. [4,8]A. {x|x≤ 4}B. {x|4≤ x≤ 8}C. {x|4 < x < 8}D. {x|4≤ x}E. {x|x < 4}

Correct Answers:2

• D• A• C• E• B

16. (1 pt) Library/Rochester/setAlgebra01RealNumbers/lhp1 31-34.pgSketch the following sets on a piece of paper and write them ininterval notation. Enter the interval in the answer box. You mayuse ”infinity” for ∞ and ”-infinity” for −∞. For example, youmay write (-infinity, 5] for the interval (−∞,5].

12≤ x≤ 1511 < x≤ 169 < x < 139≤ x < 14Correct Answers:

• [12,15]• (11,16]• (9,13)• [9,14)

17. (1 pt) Library/Rochester/setAlgebra01RealNumbers/sw1 2 15b.pgAdd the fractions, and reduce your answer.(

8÷ 810

)− 8

10

The reduced answer is /Correct Answers:

• 46• 5

18. (1 pt) Library/Rochester/setAlgebra01RealNumbers/ur ab 8 1.pgEvaluate the expression |− (11−200)|.

Correct Answers:

• 189

19. (1 pt) Library/Rochester/setAlgebra05RationalExpressions-/lhp5 60.pg

Simplify the expression1

x+5− 1

x+7and give your answer in the form of

f (x)g(x)

.

Your answer for the function f (x) is :Your answer for the function g(x) is :

Correct Answers:

• 7-5• (x+5)*(x+7)

20. (1 pt) Library/Rochester/setAlgebra05RationalExpressions-/srw1 4 55-59.pgEnter a T or an F in each answer space below to indicate whetherthe corresponding equation is true or false. An equation is trueony if it is true for all values of the variables. Disregard valuesthat make denominators 0.

You must get all of the answers correct to receive credit.

1.14+a

14= 1+

a14

2.x

x+ y=

11+ y

3.x+14y+14

=xy

4.7

7− c= 1− 7

cCorrect Answers:

• T• F• F• F

21. (1 pt) Library/ma117DB/set1b/srw1 6 21.pgA plumber and his assistant work together to replace the pipesin an old house. The plumber charges 45 dollars per hour for hisown labor and 25 dollars for his assistant’s labor. The plumberworks twice as long as his assistant on this job, and the laborcharge on the final bill is 575. How long did the plumber workon this job?

Your answer is hours.

Correct Answers:

• 10

22. (1 pt) Library/ma117DB/set1b/srw1 6 1.pgExpress the sum of 5 consecutive integers in terms of the firstinteger n of them.

Your answer is :

Correct Answers:

• 5*n+(5*(5-1))/2

23. (1 pt) Library/ma117DB/set1b/srw1 6 23.pgSeven years ago, I was eleven times as old as my daughter. NowI am four times as old as she is.My age is .

Correct Answers:

• 40

3

24. (1 pt) Library/ma117DB/set1b/srw1 5 7.pgSolve the equation 9x−6 = 3x+1 algebraically.

x =

Correct Answers:

• 1.16666666666667

25. (1 pt) Library/ma117DB/set1b/srw1 5 15.pgSolve the equation 2(y+1)− y = 4(10− y) algebraically.

y =

Correct Answers:

• 7.6

26. (1 pt) Library/ma112DB/set2/sw1 6 74.pgSolve the equation P = 2l +2w for w.Your answer is :Note: The answer is case sensitive!!!

Correct Answers:

• (P-2*l)/2

27. (1 pt) Library/ma112DB/set2/sw1 6 13.pgSolve the equation 1

4 y−10 = 110 y.

y =

Correct Answers:

• 66.6666666666667

28. (1 pt) Library/Rochester/setAlgebra13Inequalities/srw1 7 73.pgA car rental company offers two plans for renting a car.Plan A: 30 dollars per day and 15 cents per milePlan B: 50 dollars per day with free unlimited mileageFor what range of miles will plan B save you money?

Your answer is that the mileage must be greater than .

Correct Answers:

• 133.333333333333

29. (1 pt) Library/Rochester/setAlgebra13Inequalities/srw1 7 61.pgSolve the following inequality. Write the answer ininterval notation.

|2x−10| ≤ 15

Answer:Correct Answers:

• [-2.5,12.5]

30. (1 pt) Library/ma117DB/set2/srw1 7 13.pgThe solution of the linear inequality 3x+17≤ 6x+9is [ , ).If your answer is −∞, enter -infinity; if your answer is ∞,enter infinity.

Correct Answers:• 2.66666666666667• infinity

31. (1 pt) Library/ma117DB/set2/srw1 7 9.pgThe solution of the linear inequality 8− x≥ 10is ( , ].If your answer is −∞, enter -infinity; if your answer is ∞,enter infinity.

Correct Answers:• -infinity• -2


4|x+7|−4 < 4


• (-7-8/4, -7+8/4)


(x−1)(x−16) > 0


• (-infinity,1) U (16,infinity)


4






1. (1 pt) First Library/set5/s5p10.pgThree numbers may be the lengths of the side of a triangle if thelargest side is shorter than the sum of the two smaller. Indicateas true (T) of false (F), whether the following triples of numbersmay be the length of the sides of a triangle.


3,4,5

1,2,4

3,3,5

17,17,17

2,17,18

Hint: This question is about inequalities. It has nothing to dowith the Pythagorean Theorem.

Correct Answers:

• T• F• T• T• T

2. (1 pt) set5/s5p11 e.pgI recommend that instead of decimal numbers you enter an ex-pression using sqrt() to indicate a square root. For example in-stead of 1.4142 you would enter sqrt(2).

The distance between the points (9,8) and (6,3) is.

The distance between the points (4,6) and (8,5) is.

The distance between the points (−4,8) and (5,1) is.

The distance between the points (−1,−1) and (−4,−8) is.

Hint: Don’t try to memorize a formula. Draw a picture show-ing the two points in a rectangular coordinate system and applythe Pythagorean Theorem.

Correct Answers:

• 5.8309518948453• 4.12310562561766• 11.4017542509914• 7.61577310586391

3. (1 pt) First Library/set5/s5p12.pgEach of the following phrases describes a point in the Cartesian(rectangular) coordinate system. Enter the coordinates x and yof the point.

The point is located 5 units to the left of the y axis and 2 unitsabove the x axis.x= and y=The point is located 10 units to the right of the y axis and 4 unitsbelow the x axis.x= and y=The coordinates of the point have equal absolute value, the pointis in the second quadrant, and the distance of the point from theorigin is 2.x= and y=Hint: use ”sqrt(z)” to denote the square root of a number z.The point is the origin.x= and y=The point is on the positive x axis 10 units from the origin.x= and y=Hint: If you get stuck draw a picture.

Correct Answers:1

• -5• 2• 10• -4• -1.4142135623731• 1.4142135623731• 0• 0• 10• 0

4. (1 pt) First Library/set5/s5p21.pgLet F denote a certain temperature in degrees Fahrenheit, and Cthe same temperature in degrees Celsius. Then you can convertbetween F and C by the formula

F = 32+95

C.

Suppose the temperature is 17 degrees Celsius.

Enter here the corresponding temperature in degreesFahrenheit.Hint: Substitute the value of C in the given formula.

Correct Answers:

• 62.6


Suppose the temperature is 39 degrees Fahrenheit.

Enter here the corresponding temperature in degreesCelsius.Hint: Substitute the value of F in the formula given in the pre-ceding problem and solve for C.

Correct Answers:

• 3.88888888888889

6. (1 pt) First Library/set5/s5p23.pgThere is a temperature for which the numerical values of degreesFahrenheit and degrees Celsius are equal. Enter that numericalvalue here

.Hint: Set up an equation and solve it. The answer is going to becold.

Correct Answers:

• -40


You are working on a new temperature scale that will unifythe earth. After some thought you decide to call it the Hsiang-Ping Huang-universal-scale. Let F denote the temperaturein degrees Fahrenheit, and let X denote your new temperaturescale. You want it to be such that if F = 0 then X = 11 and ifF = 100 then X = 142. You also want X to be such that if youplot X against F you obtain a straight line. (This is described as”linear interpolation” in the textbook.) You obtain the formula

X = mF +bwhere m =and b =

Hint: Think of this problem as one of finding the slope-interceptform of a straight line in the (F,X) plane given two points on theline.

Correct Answers:

• (142-11)/100• 11

8. (1 pt) First Library/set5/s5p25/prob.pgMatch the functions with their graphs.

1. F(x) = x + 12. F(x) = x - 13. F(x) = -x + 14. F(x) = -x - 1

A B C D

(Click on image for a larger view )Hint: Draw the graphs of the functions.

Correct Answers:

• D• A• B• C


1. F(x) = 2x + 12. F(x) = x + 23. F(x) = 2x - 14. F(x) = x - 2

A B C D


Correct Answers:

• B• C• A• D

2

10. (1 pt) First Library/set5/s5p27/prob.pgMatch the equations with their graphs.

1. 2y-2x-2=02. 2y-2x-4=03. y+x-1 = 04. y+x+1=0

A B C D

(Click on image for a larger view )Hint: Draw the graphs of the equations.

Correct Answers:

• A• B• C• D


1. F(x) = x**22. F(x) = (x-1)**23. F(x) = x**2-14. F(x) = (x+1)**2

A B C D


Correct Answers:

• C• B• A• D

12. (1 pt) First Library/set5/s5p29/prob.pgMatch the equations with their graphs.

1. x**2+y**2 = 12. (x-1)**2+y**2=13. x**2+(y-1)**2=14. (x-1)**2+(y-1)**2=1

A B C D

(Click on image for a larger view )Hint: Think of the definition of a circle and the distance formula.

Correct Answers:

• A• D• B• C

13. (1 pt) First Library/set5/s5p30.pgFor the next few problems you need to understand what it meansto evaluate a function. You simply replace the value of the vari-able with the number at which you evaluate the function. Forexample, the answer to the first question below is 23 since

23 = 9∗2+5.

Let the function f be defined by

f (x) = 9x+5.

Then f (2) = and f (3) =Correct Answers:

• 23• 32



f (x) =−9x−9.

Then f (−6) = and f (−5) =Correct Answers:

• 45• 36



f (x) = 2x+8.

Then f (7)+ f (2) = and f (7)− f (2) =Correct Answers:

• 34• 10



f (x) = 5x+2.

Then f (7)× f (9) = and f (7)/ f (9) =Correct Answers:

• 1739• 0.787234042553192

3



f (x) = 5x+6.

Then f (2)+ f (9) = and f (2+9) =Correct Answers:

• 67• 61



f (x) = 3x+7.

Then f (2)× f (4) = and f (2×4) =Correct Answers:

• 247• 31



f (x) = 3x+2.

Then f (x+1) = and f (x−1) =Hint: For the first question, take the definition of f (x), replace xwith (x+1), and simplify.

Correct Answers:• 3*(x+1)+2• 3*(x-1)+2



f (x) = 2x+5.

Then f ( f (6)) = and f ( f (7)) =Hint: As always, first figure out what’s inside the parentheses.

Correct Answers:• 39• 43

21. (1 pt) First Library/set5/s5p38.pgThe next few problems are exercises in identifying the (natural)domain of a function. The concept of a function is very generalbut for our purposes the inputs and outputs of a function are realnumbers. The domain is the set of real numbers at which thefunction can be evaluated, and the range is the set of all possibleoutputs. To determine the domain ask yourself at what pointsthe function can NOT be evaluated. Usually this is because of anundefined operation, which practically speaking means dividingby zero, or extracting the square root of a negative number.


f (x) =7x+59x+8

.

The domain of f contains all real numbers x except x =

Hint: Never divide by zero.Correct Answers:

• -0.888888888888889



f (x) =√

2x+2.

Then x is in the domain of f provided x≥

Hint: There is no real number that is the square root of a nega-tive real number.

Correct Answers:

• -1



f (x) =√−3x+5.

Then x is in the domain of f provided x≤

Hint: There is no real number that is the square root of a nega-tive real number.

Correct Answers:

• 1.66666666666667

24. (1 pt) First Library/set5/s5p42.pgSome equations involving x and y define y as a function of x,and others do not. For example, if x + y = 1 we can solve for yand obtain y = 1− x and we can then think of y = f (x) = 1− x.On the other hand, if we have the equation x = y2 then y is not afucntion of x since for a given non-negative value of x the valueof y could equal the positive or the negative square root of x. In-dicate by True (T) or False (F). whether the following equationsdefine y as a function of x. You may assume that 0≤ x≤ 1.

1. |y|− x = 02. y−|x|= 03. y2 + x2 = 14. y+ x2 = 15. 2x+1y+8 = 06. x+ y = 17. y2 + x = 1

Correct Answers:

• F• T• F• T• T• T• F

4


5





1. (1 pt) math1010fall2006-1/set5/s5p3-1.pg


4x+7 > 13x+4

Below insert the appropriate symbol < or > and the appropriatenumber such that the two inequalities are equivalent.x (insert symbol) (insert number)Hint: Move the x’s all to one side.

Correct Answers:

• <• 0.333333333333333



5x+5 < 2x+8

Below insert the appropriate symbol < or > and the appropriatenumber such that the two inequalities are equivalent.x (insert symbol) (insert number)Hint: This is much like the preceding problem.

Correct Answers:

• <• 1


The equation

|2x−7|= |3x+3|

has two solutions. Enter the smaller here and thelarger hereHint: Remember that there are two possibilities for each of theabsolute values and check this page.

Correct Answers:

• -10• 0.8

4. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p13.pgThe slope of the line through the points (8,2) and (9,9) is

.The slope of the line through the points (6,2) and (5,3) is

.The slope of the line through the points (−4,6) and (5,5) is

.The slope of the line through the points (−3,−1) and

(−5,−9) is .

Hint: The slope of a line is the ratio of rise and run. Draw apicture if necessary.

Correct Answers:

• 7• -1• -0.111111111111111• 4


The line defined by the equation y = 3x + 2 has the x-intercept

and the y-intercept .The line defined by the equation y = 3.5x− 5.5 has the x-interceptand the y-intercept .Hint: The x intercept is the x coordinate of the point where theline intersects the x axis. Similarly, the y intercept is the y coor-dinate of the point where the line intersects the y axis. Draw thegraph of the line if necessary.

Correct Answers:

• -0.666666666666667• 2• 1.57142857142857• -5.5


The equation9x+8y+7 = 0

has the x-intercept and the y-intercept .It defines a straight line of slope

1

The line defined by the equation

5.5x+4.3y+3.1 = 0

has the x-intercept and the y-intercept .Its slope isThe line defined by the equation

−3.2x+4.4y−6.6 = 0

has the x-intercept and the y-intercept .Its slope isHint: See the hints for the preceding problems on graphs ofstraight lines for a definition of the terms involved.

Correct Answers:

• -0.777777777777778• -0.875• -1.125• -0.563636363636364• -0.72093023255814• -1.27906976744186• -2.0625• 1.5• 0.727272727272727

7. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p16.pgFor the lines defined by the following equations indicate with a”V” if they are vertical, an ”H” if they are horizontal, and an ”S”(for slanted) if they are neither vertical nor horizontal.

3x+4y+5 = 04y+5 = 03x+5 = 0x = 1y = 1y = x

Hint: Draw the graphs of these lines.Correct Answers:

• S• H• V• V• H• S

8. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p17.pgFor the pairs of lines defined by the following equations indicatewith an ”I” if they are identical, a ”P” if they are distinct but par-allel, an ”N” (for ”normal”) if they are perpendicular, and a ”G”(for ”general”) if they are neither parallel nor perpendicular.

3x+4y+5 = 0 and 6x+8y+10 = 0.3x+4y+5 = 0 and 3x+4y+7 = 0.3x+4y+5 = 0 and 3x+5y+7 = 0.−4x+3y+5 = 0 and 3x+4y+7 = 0.

Correct Answers:

• I• P• G

• N

9. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p18.pgFor the pairs of lines defined by the following equations indicatewith an ”I” if they are identical, a ”P” if they are distinct but par-allel, an ”N” (for ”normal”) if they are perpendicular, and a ”G”(for ”general”) if they are neither parallel nor perpendicular.

3x+4y+5 = 0 and y =− 34 x− 5

4 .x =

√2 and y = π.

y = x+1 and 3x+5y+7 = 0.y =− 3

4 x and 3x+4y+7 = 0.Correct Answers:

• I• N• G• P


The slope-intercept equation of the line through the points(12,9) and (9,2) isy = mx+b

where m = and b = .Hint: Compute the slope first and then use one of the points tocompute the y-intercept.

Correct Answers:

• 2.33333333333333• -19


The slope-intercept equation of the line through the points(6.1,−5.3) and (−5.5,3.7) isy = mx+b

where m = and b = .Hint: This is exactly like the preceding problem.

Correct Answers:

• -0.775862068965517• -0.567241379310345

12. (1 pt) uumathLibrary/math1010fall2006-1/set5/s5p44.pgSuppose you are given a function y = f (x), and you considershifting and reflecting the graph of f . Indicate whether the fol-lowing statements are true (T) of false (F).

The graph of g(x) = f (x) + 1 is obtained by shifting thegraph of f up one unit.

The graph of g(x) = f (x)− 1 is obtained by shifting thegraph of f down one unit.

The graph of g(x) = f (x− 1) is obtained by shifting thegraph of f right one unit.

The graph of g(x) = f (x + 1) is obtained by shifting thegraph of f left one unit.

The graph of g(x) = f (−x) is obtained by reflecting thegraph of f in the y axis.

2

The graph of g(x) = − f (x) is obtained by reflecting thegraph of f in the x axis.

Correct Answers:• T• T• T• T• T• T

13. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p24.pgThe next few questions will reinforce your mas-tery of the Cartesian Coordinate System and ofequations of straight lines.

The equation of the line through the point (−1,2) with slope− 1

2 can be written asy = x + .The line has the x-intercept .Hint: The slope-intercept form of a line with slope m and y-intercept b is

y = mx+b.Correct Answers:

• -0.5• 1.5• 3

14. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p25.pgThe line through the point (−1,2) and perpendicular to the linedefined by

y =x3

+1

has the slopem = .It can be written asy = x− .Hint: Two lines are perpendicular if their slopes are negativereciprocals of each other.

Correct Answers:• -3• -3• 1

15. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p26.pgThe line defined by

y =x2

+1

and the line defined by

y =−2x−1

intersect in the point ( , ).Hint: The point of intersection satisfies both equations. Equatethe right sides and solve for x.

Correct Answers:• -0.8• 0.6

16. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p27.pgThe distance between two points is obtained by thePythagorean Theorem. The distance of a point P from a lineL is the shortest distance between that point and a point on theline. Geometrically, you can obtain it by drawing a line throughP perpendicularly to L. It will intersect L in a point Q whichis the point on L closest to P. Once you have Q you simplycompute the distance between P and Q.

The point (0,1) has the distance , from the line definedby

y =−2x−1

Hint: The point (0,1) lies on the other line discussed in the pre-vious problem, and the two lines are perpendicular.

Correct Answers:• 0.894427190999916

17. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p28.pgThe line defined by

y =− x3

+1

and the line defined by

y = 3x−1

intersect in the point ( , ).Hint: This problem is like Problem 26.

Correct Answers:• 0.6• 0.8

18. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p29.pgThe point (1,2) has the distance from the line definedby

y =− x3

+1.

Hint: The point (1,2) lies on the line y = 3x− 1 which is per-pendicular to the given line. You computed the intersection ofthe two lines in the previous problem.


19. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p30.pgThe point (−3,4) has the distance

from the line defined by

y =−2x+2

Hint: This is like the preceding two problems combined. Youwill need to do quite a few calculations. To help you check asyou go along I recommend you draw a picture and keep check-ing your algebra against the picture. You could also do the nextproblem first and then simply use the formula you obtain there.(However, the purpose of including this problem is to help yougear up for the next one.)

3

Correct Answers:

• 1.78885438199983

20. (1 pt) uumathLibrary/math1010fall2006-1/set5/s6p31.pgThis question is the capstone of the previous few problems. Inthe last question you had to do quite a few calculations. If youwere to compute frequently the distance of a point from a line itwould be handy to have a formula into which you plug the co-ordinates of the point and the equation of the line. At the end ofthis problem you will obtain such a formula. To help you alongyou can use WeBWorK to check your intermediate answers.

Let P be the point (p,q) and L the line y = mx + b. It isnot necessary, but if you like you may assume that P lies be-low the line L. All your answers below should be algebraicexpressions in terms of m, b, p and q. The slope of L is

. The slope of a line perpendicular to Lis . The line through P perpendicular to Lcan be written as y = sx + c where s isand c is: . That line intersects L inthe point Q = (u,v), where u is: andv is: . The distance of P and Q is

. The expression you enter here may bequite messy. However, if it is correct it can be simplified intoa very concise and meaningful form. Make sure you check thesolution of this problem when the set closes.

Hint: If you are bewildered by all the symbols ask yourself whatthey mean in the special case of the preceding problem, andcompare your calculations for this problem with the numericalcalculations you did earlier.

Correct Answers:

• m• -1/m• -1/m• q+p/m• (m*(q+p/m - b))/(1+m*m)• m*(m*(q+p/m - b))/(1+m*m) + b• (m*p+b-q)/sqrt((1+m**2))

21. (1 pt) Library/Rochester/setAlgebra15Functions/srw2 1 44.pgThe domain of the function

19x2 +10

isWrite the answer in interval notation.Note: If the answer includes more than one interval write theintervals separated by the union symbol, U. If needed enter −∞

as - infinity and ∞ as infinity .Correct Answers:

• (-infinity,infinity)

22. (1 pt) Library/Rochester/setAlgebra15Functions/s0 1 11.pgThe domain of the function f (x) =

√5x+47 consists of one or

more of the following intervals: (−∞,A] and [A,∞).Find AFor each interval, answer YES or NO to whether the interval isincluded in the solution.(−∞,A)(A,∞)

Correct Answers:

• -9.4• no• yes

23. (1 pt) Library/Rochester/setAlgebra15Functions/ur fn 1 4.pg

Find the domain of the function f (x) =

√5−5x2+5x

. What is the

greatest value of x in the domain?

Greatest Value=

Correct Answers:

• 1

24. (1 pt) Library/Rochester/setAlgebra15Functions/p8.pgFind domain and range of the function

14√

x−7

Domain:Range:Write the answer in interval notation.Note: If the answer includes more than one interval write theintervals separated by the union symbol, U. If needed enter −∞


• [0,infinity)• [-7,infinity)

25. (1 pt) Library/Rochester/setAlgebra15Functions/p7.pgThe domain of the function

x+10x2−144

isWrite the answer in interval notation.Note: If the answer includes more than one interval write theintervals separated by the union symbol, U. If needed enter −∞


• (-infinity,-12) U (-12,12) U (12,infinity)

4

26. (1 pt) Library/Rochester/setAlgebra15Functions/nc1s1p1.pgFind the domain of this function:

4√−4−4x

(which reads the 4th root of −4−4x ).The function is defined on the interval from to

.Use INF for infinity or -INF for minus infinity.

Now find the domain of this function:5√−4−4x

(which reads the 5th root of −4−4x ).The function is defined on the interval from to

.Correct Answers:

• -INF• -1• -INF• INF

27. (1 pt) Library/ASU-topics/setFunctions/di7.pgThe domain of the function

f (x) =√

11+ x4− x

is .

Note: Write your answer in interval notation. If the answerincludes more than one interval write the intervals separated bythe union symbol, U. If the answer involves −∞, input -infinity; if the answer involves ∞, input infinity .

Correct Answers:

• [-11,4) U (4,infinity)


5






1. (1 pt) ASU-topics/setFunctions/p3.pgThe domain of the function

g(x) =√

x(x−2)

isNote: Write the answer in interval notation. If the answer in-cludes more than one interval write the intervals separated bythe ”union” symbol, U. If needed enter −∞ as - infinity and ∞

as infinity .

Correct Answers:• (-infinity,0] U [2,infinity)

2. (1 pt) ASU-topics/setFunctions/srw2 2 7.pgClick on the graph to view the enlarged graphConsider the function given in the following graph.{image(”c2s2p7.gif”)}

What is its domain?What is its range?Note: Write the answer in interval notation.

Correct Answers:• [-3,3]• [-1,2]

3. (1 pt) Rochester/setAlgebra07PointsCircles/equidist on axis.pgFind the point (x,y) on the x-axis that is equidistant from thepoints (−3,8) and (10,−9).

x =y =

Correct Answers:• 4.15384615384615• 0

4. (1 pt) Rochester/setAlgebra07PointsCircles/equidist off axis hard.pgFind the point (x,y) on the line y = −3x + 3 that is equidistantfrom the points (1,5) and (2,−4).

x =y =

Correct Answers:

• 0.857142857142857• 0.428571428571429

5. (1 pt) Rochester/setGeometry2Lines/ur geo 2 2.pgThe line through (−5,6) and (6,−10) also goes through thepoint (t,−4) fort =

Correct Answers:

• 1.875

6. (1 pt) Rochester/setAlgebra14Lines/lh2-1 7.pgFind an equation y = mx+b for the line whose graph is sketched

1

The slope m equals .The y-intercept b equals .

Correct Answers:

• 0• 4

7. (1 pt) ASU-topics/setLinearModels/beth1.pgA manufacturer pays its assembly line workers $11.17 per hour.In addition, workers receive a piece work rate of $0.84 per unitproduced. Write a linear equation for the hourly wages W interms of the number of units x produced per hour.

linear equation: W =What is the hourly wage for Mike, who produces 10 units in

one hour?Mike’s wage =

Correct Answers:

• 0.84*x + 11.17• 19.57

8. (1 pt) Rochester/setAlgebra32EqnSystems/beth2sys2var.pgUse the method of elimination to solve the system

−3x−2y=−2,2x+3y= 3.

Answer:

Note: If there is more than one point, type the points as acomma separated list (e.g.: (1,2),(3,4)). If the system has nosolutions, enter None .

Correct Answers:

• (0,1)

9. (1 pt) Rochester/setAlgebra32EqnSystems/linearsystem 2 2.pgSolve the following system of equations. If there are no solu-tions, type ”No Solution” for both x and y. If there are infinitelymany solutions, type ”x” for x, and an expression in terms of xfor y.

−1x+3y = 22x−3y = 8

x = .y = .


10. (1 pt) Rochester/setAlgebra32EqnSystems/sw7 2 19.pgSolve the system

6x+4y =−24,9x+6y =−36.

If the system has infinitely many solutions, express your answerin the form x = x and y as a function of xYour answer isx =y =

Correct Answers:• x• (-24-6*x)/4

11. (1 pt) Rochester/setAlgebra32EqnSystems/beth4sys2var.pgSolve the system

2x−6y =−13,−3x+9y = 18.

Your answer isIf there is more than one point, type the points separated by acomma (e.g.: (1,2),(3,4)).If the system has no solutions, type none in the answer blank.

Correct Answers:• none

12. (1 pt) ASU-topics/set119LinearSystems/ez3by3.pg

Solve the system x+2y= 1−3y− z=−2

x−3z= 2

Give the coordinates of the solution below.

x =

2

y =

z =Correct Answers:

• -1• 1• -1

13. (1 pt) ASU-topics/set119LinearSystems/p17.pgSolve the system using substitution{

x−2y = 19x−19y=−5

x =

y =Correct Answers:

• 29• 14

14. (1 pt) ASU-topics/set119LinearSystems/p25.pg

For each system, determine whether it has a unique solution(in this case, find the solution), infinitely many solutions, or nosolutions.

1. {9x−6y=0

−3x−3y=0• A. No solutions• B. Unique solution: x = +3, y = 9• C. Infinitely many solutions• D. Unique solution: x = 3, y =−6• E. Unique solution: x = 0, y = 0• F. None of the above

2. {−1x+3y= 8

2x−6y=−16• A. Unique solution: x = 8, y =−16• B. Unique solution: x = 0, y = 0• C. Unique solution:x = 8

−1 , y = 0• D. No solutions• E. Infinitely many solutions• F. None of the above

3. {5x+10y=−453x −7y= 77

• A. No solutions• B. Unique solution: x =−8, y = 7• C. Unique solution: x = 0, y = 0• D. Unique solution: x = 7, y =−8• E. Infinitely many solutions• F. None of the above

4. {4x+3y= 3

−8x−6y=−5• A. Unique solution: x = 0, y = 0

• B. Infinitely many solutions• C. No solutions• D. Unique solution: x =−5, y = 3• E. Unique solution: x = 3, y =−5• F. None of the above

Correct Answers:

• E• E• D• C

15. (1 pt) ASU-topics/set119LinearSystems/p15.pgUse the method of elimination to solve the system

4x− y =−5,−x−3y =−2.

Your answer isIf there is more than one point, type the points separated by acomma (i.e.: (1,2),(3,4)).If the system has no solutions, type none in the answer blank.

Correct Answers:

• (-1,1)

16. (1 pt) ASU-topics/set119LinearSystems/p30.pgSusan places $6300 in three investments at rates of 5%, 6% and9% per annum, respectively. The total income after one year is$ 470.00 . If the amount placed in the third investment is $1500more than the amount placed in the second, find the amount ofeach investment.Your answer is:Amount at 5% equals: $Amount at 6% equals: $Amount at 9% equals: $

Correct Answers:

• 1000• 1900• 3400

17. (1 pt) ASU-topics/set119LinearSystems/p11.pgThe admission fee at an amusement park is $ 1.50 for childrenand $ 4.00 for adults. On a certain day, 288 people entered thepark, and the admission fees collected totaled $832 . How manychildren and how many adults were admitted?

Your answer is:Number of children equalsNumber of adults equals

Correct Answers:

• 128• 160

3

18. (1 pt) ASU-topics/set119LinearSystems/p1.pgSolve the system using the substitution or elimination method{

5x+2y = 57x+3y = 7

How many solutions are there to this system?

• A. None• B. Exactly 1• C. Exactly 2• D. Exactly 3• E. Infinitely many• F. None of the above

If there is one solution, give its coordinates in the answer spacesbelow.

If there are infinitely many solutions, enter x in the answerblank for x and enter a formula for y in terms of x in the answerblank for y.

If there are no solutions, leave the answer blanks for x and yempty.

x =

y =Correct Answers:

• B• 1• 0

19. (1 pt) ASU-topics/set119LinearSystems/p6.pgSolve the system using the substitution or elimination method{

2x−6y = 14,−3x+9y =−21.

How many solutions are there to this system?

• A. None• B. Exactly 1• C. Exactly 2• D. Exactly 3• E. Infinitely many• F. None of the above

If there is one solution, give its coordinates in the answer spacesbelow.

If there are infinitely many solutions, enter x in the answerblank for x and enter a formula for y in terms of x in the answerblank for y.

If there are no solutions, leave the answer blanks for x and yempty.

x =

y =Correct Answers:

• E• x• (2*x-14)/6

20. (1 pt) ASU-topics/set119LinearSystems/p29.pgSolve the system

x+4y = 1,3x+12y = 3.

If the system has infinitely many solutions, express your answerin the form x = x and y as a function of xYour answer isx =y =

Correct Answers:

• x• (1-x)/4

21. (1 pt) ASU-topics/setSystems2Variables/jj4.pgTwo solutions of salt water contain 0.07% and 0.17% salt re-spectively. A lab technician wants to make 1 liter of solutionwhich contains 0.11% salt. How much of each solution shouldshe use?

Amount of 0.07% solution = milliliters

Amount of 0.17% solution = millilitersCorrect Answers:

• 1000*(0.17-0.11)/(0.17-0.07)• 1000*(0.11-0.07)/(0.17-0.07)

22. (1 pt) ASU-topics/setSystems2Variables/decs.pgSolve the linear system{

0.6x+0.5y = −2.2

−0.5x+0.5y = 0

If there are infinitely many solutions, enter x for x and writey as a function of x in the answer blank for y. If there are nosolutions, enter None for x.

If there is only one solution, just enter the values for x andy.

x =

y =Correct Answers:

4

• -2• -2

23. (1 pt) Rochester/setAlgebra09LinearEqnsModeling/lh1-3 32.pgThis exercise concerns with modeling with linear equations.

One positive number is one-fifth of another number. The differ-ence between the two numbers is 84, find the numbers.

The two numbers in increasing order are andCorrect Answers:

• 21• 105

24. (1 pt) Rochester/setAlgebra09LinearEqnsModeling/sw3 2 17.pgThe oldest child in a family of four children is twice as old asthe yougest. The two middle children are 13 and 16 years old.If the average age of the children is 14, how old is the youngestchild?

Your answer is :

Correct Answers:

• 9


5






1. (1 pt) First Library/set7/s7p7.pgNote that in general (a+b)2 doe not equal a2 +b2.

Evaluate the following arithmetic expressions and enter them asan integer(3+2)2− (32 +22) = .

(9+5)2− (92 +52) = .Correct Answers:

• 12• 90

2. (1 pt) First Library/set7/s7p32.pgA 10-foot plank is used to brace a basement wall during con-struction of a home. The plank is nailed to the wall 6 feet abovethe floor. The slope of the plank is .Hint: Draw a picture. You also need to understand the conceptof the slope of a straight line.

Correct Answers:

• 0.75

3. (1 pt) set7/s12p15/Prob.pgConsider the absolute value function f (x) = |x| whose graph is

given in the first Figure in this problem.

You can describe this function to WeBWorK by entering abs(x)here: . (Go ahead, try it right now.)

1

Consider the function whose graph is given in this Figure:

Let’s call that function g(x) = . (Enter an algebraicexpression involving the absolute value function abs.)

Hint: Ask what happens to the vertex of the graph.Correct Answers:

• abs(x)• 2+abs(x-1)

4. (1 pt) First Library/set7/s12p16.pgThis is similar to the preceding problem. Consider the functionwhose graph is given in this Figure:

Let’s call that function g(x) = . (Enter an algebraicexpression involving the absolute value function abs.)

Hint: Ask what happens to the vertex of the graph of f (x) = |x|Correct Answers:

• -1+abs(x+2)

5. (1 pt) First Library/set8/s9p1.pgLet the polynomial p be defined by

p(x) = 2x3−3x2 +4x−5

Thenp(1) = ,p(2) = , andp(−1) = .

Correct Answers:

• -2• 7• -14


p(x) =−4x3−2x2 +3x−9.

The degree of p is ,its leading coefficient is ,and its constant term is ,

Correct Answers:

• 3• -4• -9


p(x) =−6x3−2x2 +3x.


Correct Answers:

• 3• -6• 0


p(x) = (x−6)(x−5).

The degree of p is , its leading coefficient is , and its con-stant term is ,Hint: Apply the distributive law to convert the polynomial tostandard form.

Correct Answers:

• 2• 1• 30

2


p(x) = (9x−8)(8x+9).

The degree of p is ,its leading coefficient is ,and its constant term is ,Hint: Apply the distributive law to convert the polynomial tostandard form.

Correct Answers:

• 2• 72• -72


p(x) = (x−4)(x−5).

Then p(x) = x2 − x + ,Hint: Apply the Distributive Law.

Correct Answers:

• 1• 9• 20


p(x) = (x−6)(x−7).

Then p(x) = x2 − x + ,Hint: Apply the Distributive Law.

Correct Answers:

• 1• 13• 42


p(x) = (x−2)(x−3)(x−5).

Then p(x) = x3 − x2 + x − ,Hint: Apply the Distributive Law twice.

Correct Answers:

• 1• 10• 31• 30


p(x) = (x+3)(x−5)(x−7).

Then p(x) = x3 + x2 + x + ,Note: some of the coefficients may be negative.Hint: Apply the Distributive Law twice.

Correct Answers:

• 1• -9• -1• 105

14. (1 pt) First Library/set8/s9p15.pgThis problem is like the preceding one, except you have to getall answers right before receiving credit. Let the polynomial pbe defined by

p(x) = (x+2)(x+5)(x−7).

Then p(x) = x3 + x2 + x + ,Note: some of the coefficients may be negative.Hint: Apply the Distributive Law twice.

Correct Answers:

• 1• 0• -39• -70


p(x) = (3x2−6x+8)(11x2 +12x−15).

Thenp(x) = x4 + x3 + x2 + x + ,Note: some of the coefficients may be negative.Hint: Apply the Distributive Law.

Correct Answers:

• 33• -30• -29• 186• -120


p(x) = (x−1)(x2 + x+1).

Thenp(x) = x3 + x2 + x +Note: some of the coefficients may be negative.Hint: Once again, apply the Distributive Law.

Correct Answers:

• 1• 0• 0• -1

3


p(x) = x3−2x2 +3x+4.

Then p(x+1) = x3 + x2 + x + ,Hint: The notation p(x + 1) means ”replace x with x + 1 in thedefinition of p.

Correct Answers:• 1• 1• 2• 6

18. (1 pt) First Library/set8/s9p20.pgThis is like the preceding problem except that you must get allanswers right before receiving credit. Let the polynomial p bedefined by

p(x) = x3−2x2 +3x+4Then p(x−1) = x3 − x2 + x − ,Hint: The notation p(x− 1) means ”replace x with x− 1 in thedefinition of p.

Correct Answers:• 1• 5• 10• 2

19. (1 pt) First Library/set8/s9p22.pgThis may be a little more challenging, but you do not need toexpand this polynomial to standard form! Let the polyno-mial p be defined by

p(x) = (x+2)17.


Correct Answers:• 17• 1• 131072

20. (1 pt) First Library/set8/s9p23.pgIndicate with true (T) or false (F) whether the following func-tions are polynomials.

f (x) = x+2.

f (x) =√

2.f (x) =

√x.

f (x) = |x|.f (x) = 1

x .

f (x) = (x+1)200000.

f (x) =√

1+ x2.Hint: You need to understand the definition of the wordpolynomial.

Correct Answers:• T

• T• F• F• F• T• F

21. (1 pt) set8/s9p24.pgMatch the verbal descriptions with the given polynomials. Youneed to use all polynomials and all descriptions. Recall thatpolynomials of degrees 0, 1, 2, 3, 4, 5, are called constant, lin-ear, quadratic, cubic, quartic, and quintic, respectively. Also re-call the definitions of the terms monomial, binomial, trinomial,given here. and in the textbook.

You must get all of the answers correct to receive credit.

1. The square of a cubic polynomial2. A trinomial3. A cubic polynomial4. A quartic binomial5. A quintic monomial.A. x4−2x3

B. x2 +2x+1C. (x3 +1)2

D. x3 +3x2 +3x+1E. πx5

Hint: Check here for the relevant definitions.l.Correct Answers:

• C• B• D• A• E

22. (1 pt) First Library/set8/s9p25.pgThis is much like the preceding problem. You may have to ma-nipulate the algebraic expressions defining the polynomials torecognize the correct match.You must get all of the answers correct to receive credit.

1. A quintic monomial.2. A quartic binomial3. A trinomial4. A cubic polynomial5. The square of a cubic polynomialA. (x+1)3

B. x6 +2x3 +1C. x3(x−2)D. πx5

E. (x+1)2

Hint: Try to reduce the expressions in this problem to those youconsidered in the preceding problem.

4

Correct Answers:

• D• C• E• A• B

23. (1 pt) First Library/set8/s9p26.pgThink about the following statements and indicate whether theyare true (T) of false (F).


The product of 2 linear polynomials is quadratic.

The sum of two cubic polynomials cannot have a degreegreater than 3.

The sum of two cubic polynomials may have a degree lessthan 3.

The sum of a cubic and a quartic polynomial may have adegree different from 4.

The product of two monomials is a monomial.

The product of two binomials is a binomial.

Hint: Look at an example. Try to prove the statement wrong byfinding an example where it does not hold.

Correct Answers:

• T• T• T• F• T• F

24. (1 pt) First Library/set8/s9p27.pgThink about the following statements and indicate whether theyare true (T) of false (F).


The graph of a linear polynomial is a straight line.

The degree of a trinomial is at least 2.

The product of two polynomials is always a polynomial.

The quotient of two polynomials is always a polynomial.

The sum of two polynomials is always a polynomial.

The difference of two polynomials is always a polynomial.

Hint: Look at an example. Try to prove the statement wrong byfinding g an example where it does not hold.

Correct Answers:

• T• T• T• F• T• T

25. (1 pt) First Library/set8/s9p28.pgSuppose you multiply a polynomial of degree m with a polyno-mial of degree n. The result is a polynomial of degreeHint: Look at a simple example and generalize boldly.

Correct Answers:

• m+n

26. (1 pt) First Library/set8/s9p29.pgSuppose you add a polynomial of degree m to a polynomial ofdegree n where m > n. Then the result is a polynomial of degree

Hint: Look at a simple example and generalize.Correct Answers:

• m

27. (1 pt) First Library/set8/s9p30.pgSuppose you subtract a polynomial of degree m from a polyno-mial of degree n where m > n. Then the result is a polynomialof degreeHint: Compare with the preceding problem.

Correct Answers:

• m

28. (1 pt) First Library/set8/s9p31.pgThe obelisk in the movie 2001 has the shape of a rectangularbox with lengths x, 4x, and 9x, where x is a parameter.The volume V of the obelisk is a polynomial expression in x ofdegree and leading coefficient .In fact, V = (enter an expression in x).Hint: The volume of a brick shaped object equals length timeswidth times height.

Correct Answers:

• 3• 36• 36*x*x*x

5

29. (1 pt) First Library/set8/s9p32.pgThe area A of that same obelisk is a polynomial expression in xof degree and leading coefficient .In fact, A = (enter an expression in x).Hint: Compute the area of each face and add those areas.

Correct Answers:• 2• 98• 98*x*x

30. (1 pt) First Library/set8/s9p33.pgHere is a small challenge for your entertainment and gratifi-cation. For any natural number n, let f (n) denote the sum ofthe numbers from 1 to n. Thus f (1) = 1, f (2) = 1 + 2 = 3,f (3) = 1 + 2 + 3 = 6, f (100) = 1 + 2 + 3 + . . .+ 100 = 5050,etc.It turns out that f is a polynomial of degree 2 in n. Figure outthe coefficients of f :

f (n) = n2 + n + ,There is a story about Carl Friedrich Gauss (1777-1855) whomay have been the most outstanding mathematician in humanhistory. According to the story, when Gauss was seven yearsold, his teacher at one stage was unhappy with the class and asa punishment he asked them to compute f (100). Gauss’ classmates started writing the numbers from 1 to 100 on their paper,and adding those numbers. Gauss stared at the ceiling and thenwrote the single number 5050 on the sheet and handed it in. Youaren’t Gauss, but you also aren’t seven years old, so maybe youcan figure out what he was thinking!Hint: Think about how to do this in your head for large valuesof n.

Correct Answers:

• 0.5• 0.5• 0


6

Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 9 is due : 11/14/2008 at 05:00pm MST.






p(x) = 2x3−3x2 +4x−5

Thenp(1) = ,p(2) = , andp(−1) = .

Correct Answers:

• -2• 7• -14


p(x) =−6x3−2x2 +3x−5.


Correct Answers:

• 3• -6• -5


p(x) =−6x3−2x2 +3x.


Correct Answers:

• 3• -6• 0

4. (1 pt) First Library/set9/s11p1.pgSimplify the expression 15x+21

9x+15 = ( )/( ).Hint: Look for an integer factor that’s common to numeratorand denominator.

Correct Answers:

• 5x+7• 3x+5

5. (1 pt) set9/s11p2.pgSimplify the expression x−1

−x−1 = ( )/( ).Hint: There isn’t much to simplify here, except that the sign ofthe leading term in the denominator should be positive.

Correct Answers:

• -x+1• x+1


Simplify the expression x2+2xx2−x = ( )/( ).

Hint: If you are having difficulties with this problem it’ s prob-ably because you are looking for something that is much com-plicated than the actual answer. Think about the constant termin numerator and denominator.

Correct Answers:

• x+2• x-1

7. (1 pt) First Library/set9/s11p4.pgCancel common polynomial and integer factors. and fill in theblanks.x2+11x+30x2+13x+40 = (x+ ) /(x+ )For this identity to hold, x must not equal .Hint: If you have difficulties seeing how to factor the numera-tor and denominator set them to zero, solve the resulting equa-tion, and deduce the appropriate linear factors from the solution.Then cancel the common factor in numerator and denominator.

Correct Answers:

• 6• 8

1

• -5

8. (1 pt) set9/s11p5.pgCancel common polynomial and integer factors. and fill in theblanks.

x2−6x+8x2−10x+24 = (x− ) /(x− )For this identity to hold, x must not equal .Hint: If you have difficulties seeing how to factor the numera-tor and denominator set them to zero, solve the resulting equa-tion, and deduce the appropriate linear factors from the solution.Then cancel the common factor in numerator and denominator.



Simplify the expression x2−1x+1 = ( )/( ).

Hint: Think about the binomial formulas. The answer is apolynomial. Enter 1 as the denominator.

Correct Answers:• x-1• 1


Simplify the expression x3+2x2−x−2x2+5x+6 = ( )/( ).

Hint: Find a linear factor that’s common to numerator and de-nominator. The denominator is easy to factor, set it to zero andsolve if you don’t see the factors. Then see if one of the twofactors is a factor of the numerator.

Correct Answers:• xˆ2-1• x+3


Simplify the expression x4−1x4+2x2+1 = ( )/( ).

Hint: Apply the binomial formulas. Think of x2 as a variable.Give it a name and rewrite the problem if necessary.

Correct Answers:• xˆ2-1• xˆ2+1


1x+5 + 1

x+2 = ( )/( ).1

x+5 −1

x+2 = ( )/( ).1

x+5 ×1

x+2 = ( )/( ).1

x+5 ÷1

x+2 = ( )/( ).Hint: Rational expressions work just like fractions.

Correct Answers:• 2*x+5+2• (x+5)*(x+2)• 2-5• (x+5)*(x+2)• 1• (x+5)*(x+2)• x+2

• x+5


3x+1 + 2

x+2 = ( )/( ).3

x+1 −2

x+2 = ( )/( ).3

x+1 ×2

x+2 = ( )/( ).3

x+1 ÷2

x+2 = ( )/( ).Hint: Rational expressions work just like fractions.

Correct Answers:

• (3+2)*x + 1*2+2*3• (x+1)*(x+2)• (3-2)*x -1*2+2*3• (x+1)*(x+2)• 3*2• (x+1)*(x+2)• 3*(x+2)• 2*(x+1)


1x2−16 + 1

x+4 = ( )/( ).1

x2−16 −1

x+4 = ( )/( ).1

x2−16 ×1

x+4 = ( )/( ).1

x2−16 ÷1

x+4 = ( )/( ).Hint: The main difference between this and the preceding prob-lems is that the second denominator is a factor of the first de-nominator.

Correct Answers:

• x-4+1• xˆ2-4ˆ2• -x+4+1• xˆ2-4ˆ2• 1• (xˆ2-4ˆ2)*(x+4)• 1• (x-4)


1x2+16x+64 + 1

x+8 = ( )/( ).1

x2+16x+64 −1

x+8 = ( )/( ).1

x2+16x+64 ×1

x+8 = ( )/( ).1

x2+16x+64 ÷1

x+8 = ( )/( ).Hint: Think about the binomial formulas

Correct Answers:

• x+8+1• (x+8)**2• -(x+8-1)• (x+8)**2• 1• (x+8)**3• 1• x+8

2


1x2+7x+12 + 1

x+3 = ( )/( ).1

x2+7x+12 −1

x+3 = ( )/( ).1

x2+7x+12 ×1

x+3 = ( )/( ).1

x2+7x+12 ÷1

x+3 = ( )/( ).Hint: Factor the quadratic denominator.

Correct Answers:

• x+4+1• (x+3)*(x+4)• -x-4+1• (x+3)*(x+4)• 1• (x+3)**2*(x+4)• 1• x+4

17. (1 pt) uumathLibrary/math1010fall2006-1/set9/s11p17.pgLet

f (x) =1x.

Thenf (x+1) = ( )/( ). andf ( f (x)) = ( )/( ).Hint: Take the definition of f and replace x with what ever youare evaluating f at.

Correct Answers:

• 1• x+1• x• 1


f (x) =1

x+1.

Thenf (x+1) = ( )/( ).and f ( f (x)) = ( )/( )

Hint: Take the definition of f and replace x with what ever youare evaluating f at.

Correct Answers:• 1• x+2• x+1• x+2


f (x) =x

x+1.

Thenf (x+1) = ( )/( ), andf ( f (x)) = ( )/( )Hint: This is much like the preceding two problems.

Correct Answers:• x+1• x+2• x• 2x+1


f (x) =x−1x+1

.

Thenf ( f (x)) = ( )/( )Hint: This is much like the preceding problem.

Correct Answers:• -1• x

21. (1 pt) uumathLibrary/math1010fall2006-1/set9/s11p21.pgIn order for the identity

1x+1

+a

x−1=

−2x2−1

to hold for all x, a must equal .Hint: Simplify the left side of this equation and compare whatyou get with the right side.

Correct Answers:• -1


3






1. (1 pt) Second Library/set10/s10p1.pgUse long division to divide a polynomial with remainder.

x2 +2x+4 = (x−1)× ( )+( )Correct Answers:

• x+3• 7

2. (1 pt) Second Library/set10/s10p2.pgUse long division to divide these two polynomials with remain-der:

x2 +4x+7 = (x+1)× ( )+( )

x2 +9x+21 = (x+4)× ( )+( )

Hint: This is like the preceding problem.

(Show hint after 1 attempts. )

Correct Answers:

• x+3• 4• x+5• 1

3. (1 pt) Second Library/set10/s10p3.pgUse long division to divide these two polynomials with remain-der:

x2 +2x−33 = (x−5)× ( )+( )x2−1x−71 = (x+8)× ( )+( )

Correct Answers:

• x+7• 2• x+-9• 1

4. (1 pt) Second Library/set10/s10p5.pgThis is like the preceding problems except that you divide by aquadratic term and obtain a linear remainder. Use long divisionto divide these two polynomials with remainder:

2x4 +11x3 +19x2 +x−29 = (x2 +4x+6)× ( )+()

Correct Answers:• 2*x**2+3*x-5• 3*x+1

5. (1 pt) Second Library/set10/s10p6.pgUse long division to divide these two polynomials with remain-der:6x4 + 2x3− 3x2 + 20x− 22 = (3x2− 2x + 5)× ( )+ (

)

Hint: This is exactly like the preceding problem.


Correct Answers:• 2x**2+2*x-3• 4*x-7

6. (1 pt) Second Library/set10/s10p12.pgThe polynomial

p(x) = 24x3−46x2 +29x−6

has three real roots. One of them is x = 23 Find the others and

list them in increasing sequence:and .

Hint: Divide p by(x− 2

3

).

(Show hint after 1 attempts. )1

Correct Answers:

• 0.5• 0.75

7. (1 pt) Second Library/set10/s10p17.pgThe polynomial

p(x) = x5− x4−13x3 +13x2 +36x−36

has five real roots. One of them is x = 1. List the other four inincreasing sequence:

, , , and .

Hint: Divide by (x−1) and solve the resulting quartic equationwhich is almost like a quadratic equation.


Correct Answers:

• -3• -2• 2• 3

8. (1 pt) Second Library/set10/s11p26.pgWhen two resistors S and T are connected in parallel their com-bined resistance R is given by the expression

R =1

1S + 1

T

.

This expression can be rewritten as a rational expression in Sand T . The numerator of that expression is and itsdenominator is

Hint: Rational expressions work exactly like fractions.


Correct Answers:

• S*T• S+T

9. (1 pt) Second Library/set10/s13p8.pgThe solution of the linear system

x +2y −5z = 12x −2y +z = 24x −2y +3z = 3

The solution of this system isx = , y = , and z = .

Hint: Modify your solution of the preceding problem.


Correct Answers:• 5/7• -11/28• -3/14

10. (1 pt) Second Library/set11/s14p7.pgPolynomials are functions or expressions that can be evaluatedin a finite number of additions, multiplications, and subtrac-tions. However, they require no division for their evaluation.(Fractions are considered constants in this context). Polynomi-als have a whole language associated with them that you need tounderstand. You also need to be able to manipulate polynomialexpressions to obtain their standard form.

Consider the polynomial

p(x) = (x2 +1)(x−2)−3x−1.

Its degree is and its leading coefficient is .In standard form it can be written asp(x) = x3 + x2 + x + .Note that some of these answers may be negative.

Correct Answers:• 3• 1• 1• -2• -2• -3

11. (1 pt) Second Library/set11/s11p23.pgIn order for the identity

ax+1

+b

x−1=

1x2−1

to hold for all x,a must equal andb must equal .

Hint: Simplify the left side of this equation and compare whatyou get with the right side.


Correct Answers:• -0.5• 0.5

12. (1 pt) Second Library/set14/s14p20.pgIt takes you 8 hours to dig a hole. It would take you and yourbrother 5 hours to dig that same hole together. If your brotherwas to dig the hole by himself it would take him hours.


2

13. (1 pt) Second Library/set14/s14p21.pgThe rational Equation

1x+1

− 2x−1

= 3.

has two solutions. The smaller is and the larger is .Correct Answers:

• -0.333333333333333• 0

14. (1 pt) Second Library/set14/s14p22.pgIf you write the following expression(

x−3x2

x3x−2

)2

as a single power of x then the exponent isCorrect Answers:

• -4

15. (1 pt) Second Library/set14/s14p23.pgIf you write the following expression(

x−1/3x1/6

x1/4x−1/2

)−1/3

as a single power of x then the exponent isCorrect Answers:

• -0.0277777777777778

16. (1 pt) Library/Rochester/setAlgebra23PolynomialZeros-/srw3 2 45.pgFind a degree 3 polynomial having zeros -8, 4 and 8 and thecoefficient of x3 equal 1.The polynomial is

Correct Answers:• (x+8)*(x-4)*(x-8)

17. (1 pt) Library/Rochester/setAlgebra23PolynomialZeros-/sw5 2 47.pgFind a degree 4 polynomial having zeros -7, -1, 2 and 8 and thecoefficient of x4 equal 1.The polynomial is

Correct Answers:• (x+7)*(x+1)*(x-2)*(x-8)


(4x5y−4/5)5(2y4)3/4

equals nxr/yt wheren, the coefficient, is:r, the exponent of x, is:t, the exponent of y, is:

Correct Answers:

• 1722.15585843961• 25• 1


(rs)−1(4s)6(4r)6

equals cresd wherethe coefficient c is , the exponent e of r is , the expo-nent d of s is .

Correct Answers:

• 16777216• 5• 5


(x2y3z6)7

(x6y3z)6

equals yrzs/xt wherer, the exponent of y, is:s, the exponent of z, is:t, the exponent of x, is:[NOTE: Your answers cannot be algebraic expressions.]

Correct Answers:

• 3• 36• 22

21. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 31.pgThe expression (

x−1y4z−3

y−2z2x−8

)−1

equals zr/(xsyt) wherer, the exponent of z, is:s, the exponent of x, is:t, the exponent of y, is:[NOTE: Your answers cannot be algebraic expressions.]

Correct Answers:

• 5• 7• 6

22. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 11.pgThe expression √

125−√

20

equals ×√

5.Correct Answers:

• 3

3


x3(

19

x2)

(54x−9)

equals c/xe wherethe coefficient c is , the exponent e is .

Correct Answers:

• 6• 4

24. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 1c.pgEvaluate the expression (−2)0.Your answer is

Correct Answers:

• 1

25. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 3a.pgThe expression 245−2 equals n/d wherethe numerator n isthe denorminator d is .

Correct Answers:

• 16• 25

26. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/srw1 2 5.pg

Evaluate the expression(

2−3

)2

.

[NOTE: Your answer cannot be an algebraic expression. ]

Correct Answers:

• 0.444444444444444

27. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 7c.pgThe expression

√81√36

equals / .Correct Answers:

• 9• 6

28. (1 pt) Library/Rochester/setAlgebra02ExponentsRadicals-/sw1 3 9a.pgThe expression (

8136

)−1/2

equals / .Correct Answers:

• 2• 3

29. (1 pt) Library/Rochester/setAlgebra05RationalExpressions-/Test2 1.pgWrite the following as a simple fraction in lowest terms.

(−6)−4 +(−6)−2

−6−3

Correct Answers:

• -6.16666666666667

30. (1 pt) Library/Rochester/setAlgebra05RationalExpressions-/srw1 4 50.pgMatch the expressions below with the letters labeling theirequivalent expressions.You must get all of the answers correct to receive credit.

1.√

t +h−√

th

2.√

t +h+√

th

A.1√

t +h+√

t

B.1√

t +h−√

tCorrect Answers:

• A• B

31. (1 pt) Library/ma117DB/set1/srw1 2 7a.pgEvaluate the expression

√512√

8

Your answer is

Correct Answers:

• 8

4

32. (1 pt) Library/ma117DB/set1/srw1 2 1 5.pgMatch the radical expressions below with the letters labelingtheir equivalent exponential expressions.

1. 4√173

2. 3√a4

3. 3√172

4. 4√a3

5. 1√17

A. 173/4

B. 17−1/2

C. a3/4

D. 172/3

E. a4/3

Correct Answers:

• A• E• D• C• B


5






1. (1 pt) First Library/set8/p13.pgThe equation

√x+1+

√x−1 = 2

has the solutionx = .Hint: To get rid of a square root isolate it on one side and squareon both sides.

Correct Answers:

• 1.25


Let u = 1 + 4i and v = 1 + 4i. Enter the real and imaginaryparts of the following expressions in the appropriate boxes.u+ v = + iu− v = + iu× v = + iu÷ v = + iHint: If you do not know how to handle these problems youneed to study complex numbers. Treat u and v like algebraicexpressions, but remember that

i2 =−1.

Correct Answers:

• 2• 8• 0• 0• -15• 8• 1• 0

3. (1 pt) First Library/set8/s8p2.pgThis problem is like the preceding one. Let u = 2 + 5i andv = 2+1i. Thenu+ v = + iu− v = + iu× v = + iu÷ v = + iHint: If you do not know how to handle these problems youneed to study complex numbers. Treat u and v like algebraicexpressions, but remember that

i2 =−1.

Correct Answers:

• 4• 6• 0• 4• -1• 12• 1.8• 1.6

4. (1 pt) First Library/set8/s8p3.pgThis problem is like the preceding one, except that the real orimaginary part may be negative. Let u = 2−5i and v =−4+1i.Thenu+ v = + iu− v = + iu× v = + iu÷ v = + i

Correct Answers:

• -2• -4• 6• -6• -3• 22• -0.764705882352941

1

• 1.05882352941176

5. (1 pt) First Library/set8/s8p4.pgLet u =−4+1i and v = 4−5i. Thenu+ v = + iu− v = + iu× v = + iu÷ v = + i

Correct Answers:

• 0• -4• -8• 6• -11• 24• -0.51219512195122• -0.390243902439024

6. (1 pt) First Library/set8/s8p5.pgComplete the following equations:i3 = + ii4 = + ii5 = + ii6 = + ii2001 = + iHint: All you need to know to solve this problem is that i2 =−1.

Correct Answers:

• 0• -1• 1• 0• 0• 1• -1• 0• 0• 1

7. (1 pt) First Library/set8/s8p6.pgComplete the following equations:(7+4i)2 = + i(7+4i)3 = + iHint: Remember the definition of powers with natural numbersas their exponents, and apply repeated complex multiplication.

Correct Answers:

• 33• 56• 7• 524

8. (1 pt) First Library/set8/s8p7.pgLet

u = 5−3i, v = 4+4i, w =−5+4i.Consider the equation

ux+ v = w.

Solve it for x using exactly the same ideas we used for solvinglinear equations with real coefficients. Ask what bothers you,

and get rid of it by doing the same thing on both sides of theequation.x = + iHint: Solve the given equation in terms of u, v, and w, and onlythen apply complex arithmetic to obtain the real and imaginaryparts of x.

Correct Answers:• -1.32352941176471• -0.794117647058823

9. (1 pt) First Library/set8/s8p8.pgThis is much like the preceding problem. Let

u =−8+7i, v = 4+4i, w = 9−8i.

Solve the following equation for x:

ux+ v = w.

x = + iHint: Proceed as in the preceding problem.

Correct Answers:• -1.09734513274336• 0.539823008849557

10. (1 pt) First Library/set8/s8p9.pgComplete the following equation. Your answers will be alge-braic expressions.

(a+bi)2 = + iHint: Think of i as an ordinary variable and then replace i2 with−1.

Correct Answers:• a**2-b**2• 2*a*b

11. (1 pt) First Library/set8/s8p11.pgComplete the following equations. Your answers will be alge-braic expressions.

(a+bi)(a−bi) = + i(a+bi)2− (a−bi)2 = + iHint: You can use some of the results in the preceding problemand the discussion of complex numbers.

Correct Answers:• a**2+b**2• 0• 0• 4*a*b

12. (1 pt) First Library/set8/s8p12.pgComplete the following equation. Your answers will be alge-braic expressions.

1a+bi = + iHint: This is just a special case of one of the formulas enteredearlier.

Correct Answers:• a/(a**2+b**2)

2

• -b/(a**2+b**2)

13. (1 pt) First Library/set8/s8p13.pgLet u = a+bi and v = c+di. Complete the following equations.Your answers will be algebraic expressions.u+ v = + iu− v = + iu× v = + iu/v = + iHint: Check the web page on complex numbers.

Correct Answers:• a+c• b+d• a-c• b-d• a*c - b*d• a*d + b*c• (a*c+b*d)/(c**2+d**2)• (b*c-a*d)/(c**2+d**2)

14. (1 pt) First Library/set8/s8p14.pgIn the first few problems, fill in the blanks to make aperfect square. For example, in

x2 +6x+ = (x+ )2

fill in 9 and 3 since

x2 +6x+9 = (x+3)2.

x2 +14x+ = (x+ )2.x2−8x+ = (x− )2.x2−20x+ = (x− )2.

Correct Answers:• 49• 7• 16• 4• 100• 10

15. (1 pt) First Library/set8/s8p15.pgThis is like the preceding problem, except that your answersmay be fractions.

x2 +3x+ = (x+ )2.x2−5x+ = (x− )2.x2 + 1

3 x+ = (x+ )2.Correct Answers:

• 2.25• 1.5• 6.25• 2.5

• 0.0277777777777778• 0.166666666666667

16. (1 pt) First Library/set8/s8p16.pgThis is like the preceding problem, except that your answersmay be negative

x2 + 73 x+ = (x+ )2.

x2− 57 x+ = (x+ )2.

x2 + 23 x+ = (x+ )2.

Correct Answers:• 1.36111111111111• 1.16666666666667• 0.127551020408163• -0.357142857142857• 0.111111111111111• 0.333333333333333

17. (1 pt) First Library/set8/s8p17.pgThis is like the preceding problem, except that you have to factorout the leading coefficient. For example, in

3x2 +3x+ = 3(x+ )2

fill in 34 and 1

2

3x2 +3x+34

= 3(x2 + x+14) = 3(x+

12)2.

2x2−6x+ = 2(x− )2.3x2 +4x+ = 3(x+ )2.

Correct Answers:• 4.5• 1.5• 1.33333333333333• 0.666666666666667

18. (1 pt) First Library/set8/s8p18.pgThis is like the preceding problem.9x2 +7x+ = 9(x+ )2.7x2−5x+ = 7(x− )2.

Correct Answers:• 1.36111111111111• 0.388888888888889• 0.892857142857143• 0.357142857142857

19. (1 pt) First Library/set8/s8p20.pgThis is like the preceding problems except that your answer isan algebraic expression.x2 +bx+ = (x+ )2.

Correct Answers:• b*b/4• b/2


3






1. (1 pt) First Library/set8/p13.pgThe equation √

x+1+√

x−1 = 2

has the solutionx = .Hint: To get rid of a square root isolate it on one side and squareon both sides.

Correct Answers:

• 1.25

2. (1 pt) First Library/set8/p14.pgThe equation √

x+√

2x = 1

has the solutionx = .Hint: using the methods discussed in class this gives rise to aquadratic equation with two solutions. Only one of those solu-tions works in the original equation.

Correct Answers:

• 0.17157287525381

3. (1 pt) set8/s8p20.pgYou have seen this problem before. I am assigning it again tojog your memory about completing the square.x2 +bx+ = (x+ )2.

Correct Answers:

• b*b/4• b/2

4. (1 pt) First Library/set8/s8p17.pgThis is like the preceding problem, except that you have to factorout the leading coefficient. For example, in

3x2 +3x+ = 3(x+ )2

fill in 34 and 1

2

3x2 +3x+34

= 3(x2 + x+14) = 3(x+

12)2.

4x2−2x+ = 4(x− )2.5x2 +4x+ = 5(x+ )2.

Correct Answers:

• 0.25• 0.25• 0.8• 0.4

5. (1 pt) First Library/set8/s8p18.pgThis is like the preceding problem.5x2 +6x+ = 5(x+ )2.9x2−5x+ = 9(x− )2.

Correct Answers:

• 1.8• 0.6• 0.694444444444444• 0.277777777777778

6. (1 pt) First Library/set8/s8p21.pgIn the next few problems of this set you are asked to solvequadratic equations. These are of the form

ax2 +bx+ c = 0.

There are usually two solutions that are either of the formr ± s or of the form r ± si where i2 = −1, and r and s arereal numbers. Enter r and s. Also enter ”i” if the solution is aconjugate complex pair of numbers, ”1” if both solutions arereal, or ”0” if there is only one real solution. In the last case,also enter s = 0.

For example, the equation

x2 + x+1 = 0

has the solution

x =−1/2±√

32

i.

Enter −1/2, sqrt(3)/2, and i here:x = ± here.

1

The equationx2 + x−1 = 0

has the solution

x =−1/2±√

52

.

Enter −1/2, sqrt(5)/2, and 1 here:x = ± here.The equation

x2 + x+14

= 0

only has the solutionx =−1/2.

Enter −1/2, 0, and 0 here:x = ± here.

Correct Answers:

• -0.5• 0.866025403784439• i• -0.5• 1.11803398874989• 1• -0.5• 0• 0

7. (1 pt) First Library/set8/s8p22.pgThe equation

x2−1x−12 = 0

has the solution x = ± .Correct Answers:

• 0.5• 3.5• 1


x2−10x+29 = 0


• 5• 2• i


x2−8x+16 = 0


• 4• 0• 0

10. (1 pt) First Library/set8/s8p27.pgQuadratic equations do not always occur in standard form.Sometimes they have to be converted to standard form usingour basic principle of doing the same thing on both sides to getwhere we want to go.

The equation

x+1x

= 2

has only one solution. It isx = .Hint:When you see the solution you will say ”of course”. As a firststep, multiply with x on both sides.

Correct Answers:

• 1


1− xx

= x

has two real solutions solution. They arex = ± .Hint:Begin by multiplying with x on both sides.

Correct Answers:

• -0.5• 1.11803398874989


x−12x+1

=x+1x−1

has two real solutions. Enter the smaller one here and thelarger one here .Hint:Begin by multiplying with 2x+1 and x−1 on both sides.

Correct Answers:

• -5• 0


x4−10x2 +9 = 0

has four solutions. Enter them in increasing order:x1 =x2 =x3 =x4 =Hint: Begin by thinking of x2 as the unknown.

Correct Answers:

• -3• -1• 1• 3

2


x−√

x−2 = 0has the solutionx = .Hint: Begin by thinking of

√x as the unknown.


15. (1 pt) First Library/set8/s8p34.pgThe height of a triangle is 8 inches less than its base. The areaof the triangle is 192 square inches. The height of the triangle is

inches and the base of the triangle is inches.Hint: The area of a triangle equals one half of base times height.



p(x) =−8x3−2x2 +3x.


Correct Answers:• 3• -8

• 0


p(x) = (x−8)(x−5).

The degree of p is , its leading coefficient is , and its con-stant term is ,Hint: Apply the distributive law to convert the polynomial tostandard form.

Correct Answers:

• 2• 1• 40


p(x) = (2x2−4x+7)(9x2 +12x−14).

Thenp(x) = x4 + x3 + x2 + x + ,Note: some of the coefficients may be negative.Hint: Apply the Distributive Law.

Correct Answers:

• 18• -12• -13• 140• -98


3

Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 13 is due : 12/05/2008 at 05:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.



You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/p13.pgIn this and the following 2 problems you are asked to solve equa-tions involving radicals. Enter your answers as numbers or frac-tions.

The solution of the equation√

2x+1 = 3 is x = .Correct Answers:

• 4

2. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/p14.pgThe solution of the equation

√2x+1 = 3

√x−1 is x = .

Correct Answers:

• 1.42857142857143

3. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p1.pgFor some of the problems in this set you may have to evaluateradical expressions. Your calculator may be able to do this, oryou can enter expressions like 10

13 into WeBWorK as 10(1/3)

or 10**(1/3). Note the parentheses around the exponent! If theexponent is 1/2 you may use sqrt instead. For example, you cansay sqrt(7) for 7(1/2) which is the same as sqrt(7).

Let’s practice entering radicals:Enter here the number 2

12 .

Enter here the number 323 .

Enter here the expression x23 .

Enter here the expression xpq .

Correct Answers:

• 1.4142135623731• 2.0800838230519• xˆ(2/3)• xˆ(p/q)

4. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p2.pgEvaluate the following powers and enter them as integers.

32 =23 =

Correct Answers:

• 9• 8

5. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p6.pgNote that in general ab does not equal a×b.Evaluate the following arithmetic expressions and enter them asan integer32−3×2 = . 62−6×2 = .

Correct Answers:

• 3• 24

6. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p7.pgNote that in general (a+b)2 doe not equal a2 +b2.

Evaluate the following arithmetic expressions and enter them asan integer(3+2)2− (32 +22) = .

(9+5)2− (92 +52) = .Correct Answers:

• 12• 90

7. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p8.pgInsert the appropriate symbol < or > .32 23

1

102 210

990 909

Correct Answers:

• >• <• >

8. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p10.pgEnter numerical values for the following powers. I recommendyou don’t use a calculator, to make sure you understand the con-cepts involved. Your answer needs to be a natural number, thesystem will not accept an arithmetic expression.9

32 = .

853 = .

2743 = .Correct Answers:

• 27• 32• 81

9. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p11.pgEnter numerical values for the following powers.

(52)32 = .

(23)53 = .

(33)43 = .

Hint: You take a power to a power by multiplying the exponents.Correct Answers:

• 125• 32• 81

10. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p12.pgRewrite the following expressions using just one rational expo-nent. Enter the numerator and denominator of the exponent.Cancel any common factors.u2u

32 = u

ab where a = and b = .

z3z13 = z


Hint: You multiply powers with the same base by adding theexponents.

Correct Answers:

• 7• 2• 10• 3

11. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p13.pgRewrite the following expressions using just one rational expo-nent. Enter the numerator and denominator of the exponent.Cancel any common factors.(u

32 )

27 = u


(z47 )

76 = z



• 3• 7• 2• 3

12. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p14.pgRewrite the following expressions using just one rational expo-nent. Enter the numerator and denominator of the exponent.Cancel any common factors.(u

32 )

45 = u


(z43 )

92 = z



• 6• 5• 6• 1

13. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p15.pgRewrite the following expressions using just one rational expo-nent. Enter the numerator and denominator of the exponent.Cancel any common factors.u

32 u

27 = u


u32 u

13 = u


u14 u

16 = u


Hint: You multiply two powers with the same base by addingthe exponents.

Correct Answers:• 25• 14• 11• 6• 5• 12


32

u27

= uab where a = and b = .

u32

u13


u14

u16


Hint: You divide powers with the same base by subtracting theexponents.


2

• 6• 1• 12


23 u

14

u12 u

16


u34 u

13

u23 u

56


Hint: Put together what you learned in the preceding few prob-lems.

Correct Answers:

• 1• 4• -5• 12


72 u

14

u13 u

1712


u154 u

13

u12 u

1912


Hint: Put together what you learned in the preceding few prob-lems.

Correct Answers:

• 2• 1• 2• 1

17. (1 pt) 1010Library/set7 Exponential and Logarithmic Functions-/s7p21.pgThe solution of the equation

(2x−1)13 −3 = 0

is x = .Hint: You need to take something to the power 3.

Correct Answers:

• 14

18. (1 pt) 1050Library/set8 Exponential and Logarithmic Functions-/1050s8p5.pg

The Figure above shows the graphs of four exponential func-tions, listed below. Match the functions with the colors, using bfor blue, r for red, g for green, and y for yellow.

: f (x) = 2x.: f (x) = 3x.

: f (x) =( 1

2

)x.

: f (x) =( 1

3

)x.

Hint: Look at f (1).Correct Answers:

• g• y• b• r


The lessons we learned about shifting graphs apply to expo-nential functions just as they apply to any other functions.

3

The Figure above shows the graphs of five exponential func-tions, listed below. Match the functions with the colors, using bfor blue, r for red, g for green, p for purple, and y for yellow.

: f (x) = 2x.: f (x) = 2x +1.: f (x) = 2x+1.: f (x) = 2x−1.: f (x) = 2x−1.

Hint: Look at f (0) and f (1), and at what happens when xbecomes more negative.

Correct Answers:

• r• g• p• y• b


The Figure above shows the graphs of four exponential func-tions, listed below. Match the functions with the colors, using bfor blue, r for red, g for green, and y for yellow.

: f (x) = 2x.: f (x) =−2x.: f (x) = 2−x.: f (x) =−2−x.

Hint: Look at that happens as x becomes more positive ormore negative.

Correct Answers:

• r• g• y• b

21. (1 pt) Library/ASU-topics/setInverseFunctions/sw4 8 17.pgAssume that the function f is a one-to-one function.(a) If f (3) = 2, find f−1(2).Your answer is

(b) If f−1(−5) =−9, find f (−9).Your answer is

Correct Answers:

• 3• -5

22. (1 pt) Library/ASU-topics/setInverseFunctions/srw2 9 7 16.pgEnter Yes or No in each answer space below to indicate whetherthe corresponding function is one-to-one.

4

1. f (x) = x3 +12. f (x) = x4 +53. f (x) =

√x

4. f (x) = 7x−3

Correct Answers:

• Yes• No• Yes• Yes

23. (1 pt) Library/ASU-topics/setInverseFunctions/rich1.pgThe graph of f is shown below.

Note: Click on a graph to view a larger graph.

Which of the following is a graph of f−1 ?

• A.

• B.

• C.

• D.

5

• E.

• F.Correct Answers:

• B

24. (1 pt) Library/ASU-topics/setInverseFunctions/srw2 9 41.pgFind the inverse function of

f (x) =√

3x+7

f−1(x) =

Correct Answers:

• (x**2-7)/3

25. (1 pt) Library/ASU-topics/setInverseFunctions/di2.pgFor the function f (x) = x3−4,

(a) sketch the graph of f(b) use the graph of f to sketch the graph of f−1

(c) enter the correct formula:

f−1(x) =Correct Answers:

• (x + 4)**(1/3)

26. (1 pt) Library/ASU-topics/setInverseFunctions/di1.pgEnter Yes or No in each answer space below to indicate whetherthe corresponding function is one-to-one.

1. f (x) = |x−1|2. f (x) = x4 +9, 0≤ x≤ 23. f (x) = x3− x4. f (x) =

√3x+1

Correct Answers:

• No• Yes• No• Yes

27. (1 pt) Library/ASU-topics/setInverseFunctions/srw2 9 63.pgThe function f (x) = (x+2)2 is not one-to-one. Choose a largestpossible domain containing the number 100 so that the functionrestricted to the domain is one-to-one.The largest possible domain is [ , );the inverse function is g(x) =Note: If your answer is ∞, enter infinity .

Correct Answers:

• -2• infinity• sqrt(x)-2

28. (1 pt) Library/ASU-topics/setInverseFunctions/bethinvfun1.pgAlgebraically find the inverse function of f (x) = 5x+2.f−1(x) =

Correct Answers:

• (x-2)/5

29. (1 pt) Library/ASU-topics/setInverseFunctions/garcia1.pg

Consider the graphs below.

Determine if the function in the graph is one-to-one.6

• A. The function is one-to-one.• B. The function is not one-to-one.

Determine if the function in the graph is one-to-one.






7



Correct Answers:

• A• B• B• B• A

30. (1 pt) Library/ASU-topics/setInverseFunctions/bethinvfun2.pgAlgebraically find the inverse function of f (x) = 1

x+4 .f−1(x) =

Correct Answers:

• 1/x-4

31. (1 pt) Library/ASU-topics/setInverseFunctions/faris1.pg

Note : You can click on the graph above to enlarge it.Use the above graph of f (x) to complete the following table

for values of its inverse function, f−1(x).

x -10 -2 6 -8 0f−1(x)

Correct Answers:

• 8• 4• -2• 7• 3

32. (1 pt) Library/SUNYSB/inverseFunction.pgFor each of the following, find the inverse f−1(x) of the func-tion. You can assume that f : R −→ R. If there is no inverse,enter -1.

Hint: you can write√

x as x carat (1/2) where carat is shift-6on most keyboards.

The inverse of f (x) = x+75 is

The inverse of f (x) = 5x+4 isThe inverse of f (x) = 3x isThe inverse of f (x) = x2 isThe inverse of f (x) = x

13 is

The inverse of f (x) = x5 isCorrect Answers:

• x*(5)-(7)• (x-(4))/(5)• x/(3)• -1• xˆ3• xˆ(0.2)

33. (1 pt) Library/SUNYSB/WebWorkInverse2.pgIf f is one-to-one and f (−13) = 13, thenf−1(13) =

8

and ( f (−13))−1 = .

If g is one-to-one and g(−11) = 10, theng−1(10) =

and (g(−11))−1 = .

If f is one-to-one and f (6) = 12, then f−1(12) = and( f (6))−1 = .

If g is one-to-one and g(15) = 15, then g−1(15) = and(g(15))−1 = .

If f (x) = 7x−11, thenf−1(y) =f−1(−3) =

Correct Answers:

• -13• 0.0769230769230769• -11• 0.1• 6• 0.0833333333333333• 15• 0.0666666666666667• (y+11)/7• 1.14285714285714


9

Hsiang-Ping Huang math1010fall2008-3WeBWorK assignment number 14 is due : 12/12/2008 at 05:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.



You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p1.pgYou can compute the following logarithms with your basicknowledge of powers.

For example, since23 = 8

we know thatlog2 8 = 3.

log5 25 = .log6 36 = .log3 27 = .log10 10,000 = .log10 0.001 = .logπ 1 = .

Hint: To get started observe that 52 = 25.Correct Answers:

• 2• 2• 3• 4• -3• 0

2. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p2.pgMore logarithms:

log2 4 = .log9 81 = .

log2 1024 = .log3 81 = .

Correct Answers:

• 2• 2• 10• 4


Let

L(x) = loga(x)

where we don’t know the base a. However, we do know that

L(2) = 0.28585 and L(3) = 0.45307.

Use this information to compute

L(4) = .L(a2) = .L(a3) = .L(65) = .

Correct Answers:

• 0.5717• 2• 3• 3.6946

1

4. (1 pt) set9 Exponential and Logarithmic Functions/1050s9p23.pgThe inverse of the function

f (x) = 10x

isf−1(x) =

The inverse of the function

f (x) = log10 x

isf−1(x) =

Correct Answers:

• log(x)• 10**x

5. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p27.pgThe remaining problems are true/false questions concerninglogarithmic and exponential identities. You don’t need to mem-orize these, they all flow from two facts:

Logarithms and Exponentials are inverses of each other.(Of course they need to have the same base.)

Exponential functions are just powers and logarithms arejust exponents.

For the following proposed identities enter T if they are true,and F if they are false. We assume that the expressions involvedmake sense. For example any base is positive and not equal to1, and logarithms are taken only of positive numbers.

loga(uv) = loga u+ loga v.loga(u+ v) = (loga u)(loga v).loga

( uv

)= loga u− loga v.

loga(u− v) = loga uloga v .

loga (uv) = (loga u)(loga v).loga (uv) = u(loga v).loga (uv) = v(loga u).

Correct Answers:

• T• F• T• F• F• F• T

6. (1 pt) Rochester/setAlgebra30LogExpEqns/sw6 3 25.pgFind x.(a) log10 x = 2x =

(b) log5 x = 4x =


7. (1 pt) Library/Rochester/setAlgebra30LogExpEqns/sw6 3 23.pgFind x.(a) log5 x = 2Your answer is

(b) log2 16 = xYour answer is


8. (1 pt) Rochester/setAlgebra29LogFunctions/sw6 3 17.pgEvaluate the expression, reduce to simplest form.(a) log3

( 181

)Your answer is

(b) log105√

10

Your answer is

(c) log10 0.001Your answer is

Correct Answers:• -4• 0.2• -3

9. (1 pt) Library/Rochester/setAlgebra29LogFunctions/srw4 3 23-26.pgEvaluate the following expressions.

(a) log3( 1

27

)=

(b) log6 1 =

(c) log5√

625 =

(d) 7log7 6 =Correct Answers:

• -3• 0• 2

2

• 6

10. (1 pt) Library/Rochester/setAlgebra29LogFunctions/sw6 3 7.pgExpress the equation in logarithmic form(a) 24 = 16.That is, write your answer in the form log2 A = B. ThenA =andB =

(b) 10−2 = 0.010000.That is, write your answer in the form log10 C = D. ThenC =andD =

Correct Answers:

• 16• 4• 0.01• -2

11. (1 pt) Library/Rochester/setAlgebra29LogFunctions-/beth1logfun.pgThe graph of the function f (x) = log3(x− 2) can be obtainedfrom the graph of g(x) = log3 x by one of the following actions:(a) shifting the graph of g(x) to the right 2 units;(b) shifting the graph of g(x) to the left 2 units;(c) shifting the graph of g(x) upward 2 units;(d) shifting the graph of g(x) downward 2 units;Your answer is (input a, b, c, or d)The domain of the function f (x) is .Note: Enter your answer using interval notation.The range of the function f (x) is .Note: Enter your answer using interval notation.The x-intercept of the function f (x) is .The vertical asymptote of the function f (x) has equation:

.

Correct Answers:

• a• (2,infinity)• (-infinity,infinity)• (3,0)• x=2

12. (1 pt) Library/Rochester/setAlgebra29LogFunctions-/problem10.pgIf logb 2 = x and logb 3 = y, evaluate the following in terms of xand y:

(a) logb 12 =

(b) logb 216 =

(c) logb4

27 =

(d) logb 27logb 2 =

Correct Answers:

• 2 * x + 1 * y• 3 * x + 3 * y• 2 * x - 3 * y• (3 * y)/(1 *x)

13. (1 pt) Library/Rochester/setAlgebra29LogFunctions/problem2.pgEvaluate the following expressions. Your answers must be exactand in simplest form.

(a) log3( 1

243

)=

(b) log5 1 =

(c) log6√

7776 =

(d) 7log7 12 =Correct Answers:

• -5• 0• 2.5• 12

14. (1 pt) Library/Rochester/setAlgebra29LogFunctions-/simplifying expressions.pgSimplify the following expressions. Your answers must be exactand in simplest form.

(a) log11 112x−2 =

(b) 2log2(−8−9q) =

(c) log64 0.0625k =

(d) 28log2 8−8log2 8 =Correct Answers:

• 2*x +{-2}• -8 +-9*q• (-2/3)*k• 1

15. (1 pt) Library/Rochester/setAlgebra29LogFunctions/ur le 1 4.pgSimplify:81log9 8 =8log64 81 =

Correct Answers:

• 64• 9

16. (1 pt) Library/Rochester/setAlgebra29LogFunctions/srw4 3 43.pgRewrite the expression

4logx−4log(x2 +1)+3log(x−1)3

as a single logarithm logA. Then the functionA =

Correct Answers:

• x**4*(x-1)**3/(x**2+1)**4

17. (1 pt) Library/Rochester/setAlgebra29LogFunctions/srw4 3 17-20.pgEvaluate the following expressions.

(a) log2 210 =

(b) log2 32 =

(c) log4 1024 =

(d) log4 48 =Correct Answers:

• 10• 5• 5• 8

18. (1 pt) Library/Rochester/setAlgebra29LogFunctions/sw6 3 3.pgExpress the equation in exponential form(a) log4 2 = 1

2 .That is, write your answer in the form 4A = B. ThenA =andB =

(b) log2116 =−4.

That is, write your answer in the form 2C = D. ThenC =andD =

Correct Answers:

• 0.5• 2• -4• 0.0625

19. (1 pt) Library/ma117DB/set7/srw4 2 35.pgThe graph of the function y = loga x goes through (37,1).Then a =

Correct Answers:

• 37

20. (1 pt) Library/maCalcDB/setAlgebra30LogExpEqns/srw4 2 30.pgFind x.(a) logx 64 = 2x =

(b) logx 49 = 2x =


21. (1 pt) Library/maCalcDB/setAlgebra30LogExpEqns-/solve easy eqn.pg

Solve for x in each of the following.(a) If logx 16 = 4

9 , then x = .(b) If 65x+7 = 7, then x = .Correct Answers:

• 512• -1.18279337349966

22. (1 pt) Library/maCalcDB/setAlgebra30LogExpEqns-/problem6a.pgSolve for x:

log2 x3 = 0

x =


23. (1 pt) Library/maCalcDB/setAlgebra30LogExpEqns/srw4 3 37-38.pg

(a) If log2 x = 2, then x = .(b) If log7 x = 4, then x = .Correct Answers:

• 4• 2401

24. (1 pt) Library/maCalcDB/setAlgebra30LogExpEqns/problem3.pgSolve for x:

log218

= x

x =Your answer must be exact an in simplest terms.

Correct Answers:• -3


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