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Chapter 1A1DDAADADD5. The phrase twice the sum of a number squared and 6 couldbe written as 2n2 6.6. The reflexive property of equality states that if a b thenb a.7. The absolute value of a number is its distance from 0 onthe number line.8. If the absolute value of any expression is equal to a negativenumber, then the solution is the empty set.9. When adding or subtracting a negative number to both sidesof an inequality, the inequality symbol must be reversed.10. Writing a solution in the form {x x 5} is called set buildernotation.11. If a compound inequality contains the word “or”, the solutionwill be the intersection of the solution sets of thetwo inequalities.12. If 3x 1 10, then 3x 1 10 and 3a 1 10.After you complete Chapter 1A4. The commutative property is true for addition andmultiplication only.AChapter 13Glencoe Algebra 2 For those statements that you mark with a D, use a piece of paper to write an example ofwhy you disagree. Did any of your opinions about the statements change from the first column?timedropsminutesdrops.per milliliter.millilitersper minute.Chapter 15AnswersGlencoe Algebra 2Sample answer: Please excuse my dear Aunt Sally. (parentheses;exponents; multiplication and division; addition and subtraction)4. Think of a phrase or sentence to help you remember the order of operations.Remember What You learnedoperations, different people might get different answers.3. Why is it important for everyone to use the same order of operations for evaluatingexpressions? Sample answer: If everyone did not use the same order ofMultiply the difference of 13 and 5 by the sum of 9 and 21. Add the result to 10. Thendivide what you get by 2. [(13 5)(9 21) 10] 22. Read the following instructions. Then use grouping symbols to show how the instructionscan be put in the form of a mathematical expression.c. {14 [8 (3 12)2]} (63 100) (3 12)b. 9 [5(8 6) 2(10 7)] (8 6) and (10 7)a. [(3 22) 8] 4 (3 22)1. There is a customary order for grouping symbols. Brackets are used outside ofparentheses. Braces are used outside of brackets. Identify the innermost expression(s) ineach of the following expressions.Read the Lesson 8 60and is measured inof solution and is measured inand is measured inand is measured indrop factorvolumeflow rate Write the expression that a nurse would use to calculate the flow rate of an IV if a doctororders 1350 milliliters of IV saline to be given over 8 hours, with a drop factor of 20 dropsper milliliter. Do not find the value of this expression. 1350 20t representsd represents theF represents theADThe order of operations must be followed so that everyexpression will have only one value.Chapter ResourcesV represents the3. All real numbers are in the set of rational numbers.2.1. Algebraic expressions contain at least one variable.StatementCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.STEP 2A or DAnswers Reread each statement and complete the last column by entering an A or a D.STEP 2STEP 1A, D, or NSV dto control the flow rate for IVs. Nametthe quantity that each of the variables in this formula represents and the units in whicheach is measured. Nurses use the formula F Read the introduction to Lesson 1-1 in your textbook.PERIOD8:03 AM Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure). Decide whether you Agree (A) or Disagree (D) with the statement.Expressions and FormulasLesson Reading GuideGet Ready for the Lesson1-1NAME DATE5/19/06 Read each statement.Before you begin Chapter 1Equations and InequalitiesAnticipation GuidePERIODA2-01-873971STEP 11NAME DATELesson 1-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A1(Lesson 1-1)Glencoe Algebra 2
Chapter 1Expressions and FormulasStudy Guide and InterventionA28. (7 32)2 62 4016 23 41 221 18 24abd49.2Chapter 125. a b c 7.45 dc b 2122. 319. ac bd 31.316. 6627.Glencoe Algebra 28.7a db c 54.426. b c 4 d 15a 6b 5cdc2 1b d24. d(a c) 6.1bd21.18.423. cd 20. (b c)2 4a 81.817. 5(6c 8b 10d) 215Evaluate each expression if a 8.2, b 3, c 4, and d .1213. 8(42 8 32) 24046 9 3 1515.8 26 4 214.4 6 1 2412. 6(7) 4 4 5 3834.2511. 14 (8 20 2) 79. 20 22 6 116. 52 10. 12 6 3 2(4) 6 65. (5 23)2 52 1444. 9(32 6) 1353. 2 (4 2)3 6 4Examplenp500To calculate the number of reams of paper needed to print nnp.5004 3r , where V is the volume of the3Chapter 17Glencoe Algebra 24. A person’s basal metabolic rate (or BMR) is the number of calories needed to support hisor her bodily functions for one day. The BMR of an 80-year-old man is given by theformula BMR 12w (0.02)(6)12w, where w is the man’s weight in pounds. What is theBMR of an 80-year-old man who weighs 170 pounds? 1795 calories3. Sarah takes 40 breaths to blow up the beach ball. What is the average volume of air perbreath? about 1250 cm3sphere and r is its radius. What is the volume of the beach ball in cubic centimeters?(Use 3.14 for .) 50,015 cm32. The volume of a sphere is given by the formula V 1. Her beach ball has a radius of 9 inches. First she converts the radius to centimetersusing the formula C 2.54I, where C is a length in centimeters and I is the same lengthin inches. How many centimeters are there in 9 inches? 22.86 cmFor a science experiment, Sarah counts the number of breaths needed for her to blow up abeach ball. She will then find the volume of the beach ball in cubic centimeters and divideby the number of breaths to find the average volume of air per breath.For Exercises 1–3, use the following information.ExercisesYou cannot buy 8.6 reams of paper. You will need to buy 9 reams to print 172 copies. 8.6r (172)(25)50043,000 500Substitute n 172 and p 25 into the formula r is the number of reams needed. How many reams of paper must you buy to print172 copies of a 25-page booklet?copies of a booklet that is p pages long, you can use the formula r , where rAnswers7.2. 11 (3 2)2 141. 14 (6 2) 17Find the value of each expression.Replace each variable with the given value.3x2 x(y 5) 3 (3)2 3(0.5 5) 3 (9) 3( 4.5) 27 13.5 13.5Evaluate 3x2 x(y 5) if x 3 andy 0.5.(continued)Formulas A formula is a mathematical sentence that uses variables to express therelationship between certain quantities. If you know the value of every variable except onein a formula, you can use substitution and the order of operations to find the value of theunknown variable.Expressions and FormulasStudy Guide and InterventionPERIOD8:03 AMExercises[18 (6 4)] 2 [18 10] 2 8 2 4Evaluate [18 (6 4)] 2.Example 2Simplify the expressions inside grouping symbols.Evaluate all powers.Do all multiplications and divisions from left to right.Do all additions and subtractions from left to right.1-1NAME DATE5/19/06Example 1Order ofOperations1.2.3.4.PERIODA2-01-873971Order of Operations1-1NAME DATELesson 1-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A2(Lesson 1-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Glencoe Algebra 2
Chapter 1Expressions and FormulasSkills Practice6(7 5)6.415. [ 9 10(3)]3128. [3(5) 128 22]5 85A325220. 7s 2v 19. 9r2 (s2 1)t 1052wr225(F 32) gives the temperature in degrees Celsius9Chapter 18Glencoe Algebra 2for a given temperature in degrees Fahrenheit. What is the temperature in degreesCelsius when the temperature is 68 degrees Fahrenheit? 20 C22. TEMPERATURE The formula C 21. TEMPERATURE The formula K C 273 gives the temperature in kelvins (K) for agiven temperature in degrees Celsius. What is the temperature in kelvins when thetemperature is 55 degrees Celsius? 328 K018.17. w[t (t r)] rv3s216.15. 2(3r w) 7414. s2r wt 313. (4s)2 144 8(13 37)611.3234 5ab d2c121e141d(b c)ac12cac4 2de229C 32 gives the temperature in degrees522. 2ab2 (d 3 c) 6720.18. ac3 b2de 7016.14. (c d)b 8Chapter 19AnswersGlencoe Algebra 225. AGRICULTURE Faith owns an organic apple orchard. From her experience the last fewseasons, she has developed the formula P 20x 0.01x2 240 to predict her profit P indollars this season if her trees produce x bushels of apples. What is Faith’s predictedprofit this season if her orchard produces 300 bushels of apples? 486024. PHYSICS The formula h 120t 16t2 gives the height h in feet of an object t secondsafter it is shot upward from Earth’s surface with an initial velocity of 120 feet persecond. What will the height of the object be after 6 seconds? 144 ftFahrenheit for a given temperature in degrees Celsius. What is the temperature indegrees Fahrenheit when the temperature is 40 degrees Celsius? 40 F23. TEMPERATURE The formula F 21. 9bc 19. b[a (c d) 2 ] 20617. (b de)e2 115.13. ab2 d 451312. 5 9 ( 1)2 4( 9) 53( 8)2Evaluate each expression if a , b 8, c 2, d 3, and e .1[6 42]29.1[ 5 5( 3)]48. [4(5 3) 2(4 8)] 16 17. 18 {5 [34 (17 11)]} 4110.6. ( 2)3 (3)(8) (5)(10) 185. 20 (5 3) 52(3) 85 54. 12 [20 2(62 3 22)] 883. 1 2 3(4) 2 3Answers3v t5s t12. s 2r 16v 110. 2st 4rs 8411. w(s r) 29. 6r 2s 0Evaluate each expression if r 1, s 3, t 12, v 0, and w .7. (168 7)32 43 15234. 5 3(2 12 2) 73. (3 8)2(4) 3 972. 4(12 42) 161. 3(4 7) 11 20PERIOD8:03 AM 72. 9 6 2 1 13Expressions and FormulasPracticeFind the value of each expression.1-1NAME DATE5/19/061. 18 2 3 27PERIODA2-01-873971Find the value of each expression.1-1NAME DATELesson 1-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A3(Lesson 1-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Glencoe Algebra 2
Chapter 1RA4Chapter 1subtraction10 3(4 6) 41017 minGlencoe Algebra 26. Use your formula to compute the numberof minutes it would take to broil a 2 inchthick steak.Sample Answer: T 5(w 1) 12or T 5w 75. Write a formula for T in terms of w.D, where T is time in hours, D is the distance (200 miles),S5.75.04.44.03.63.33.02.82.6Time (hours)1 25S S, where S is your speed. Determine your fuel rate for302Chapter 111Glencoe Algebra 2You can make it to your aunt’s house on time, but won’t have enoughgas to get home.the speeds needed to get to your aunt’s. Will you make it?formula M 4. Cost depends on the cost of gasoline, the number of total miles of the trip, andyour car’s fuel efficiency (mi/gal). The miles per gallon can be found using theAbout 8.5 gallons3. How many gallons of gas can you buy?Now determine if you can afford enough gasoline to make the trip and return.You will miss the party for all speeds 50 mph and less, assuming an11 A.M. departure.2. For which speed(s), will you miss the surprise birthday party?757065605550454035Speed (mph)and S is the speed. Determine travel time to your aunt’s house at various speeds.miles per hour (mph), T 1. A simple formula relates the travel time, depending on your average speed inAnswers3. GUESS AND CHECK Amandareceived a worksheet from her teacher.Unfortunately, one of the operations in anequation was covered by a blot. Whatoperation is hidden by the blot?236 in2rA steak has thickness w inches. Let T bethe time it takes to broil the steak. It takes12 minutes to broil a one inch thick steak.For every additional inch of thickness,the steak should be broiled for 5 moreminutes.the following information.COOKING For Exercises 5 and 6, use56 miFirst determine at which speed you must travel to arrive by 3:00.8:03 AM2. GEOMETRY The formula for the areaof a ring-shaped object is given by A (R2 r2), where R is the radius of theouter circle and r is the radius of theinner circle. If R 10 inches and r 5inches, what is the area rounded to thenearest square inch?10 6 10 12 or 10(6 12)d. The formula for the3Traveling on a BudgetEnrichmentPERIODYou are traveling to your aunt’s house 200 miles away for a surprise birthday party.The party starts at 3 P.M. but you cannot leave from your house before 11 A.M. Youmust fill your gas tank before the trip. Gasoline is 3.50 per gallon and you have 30.Will you make it to the party and make it back home?1-1NAME DATE5/19/06number of miles that Rick can drive on ggallons of gasoline is given by m 21g.How many miles can Rick drive on 8worth of gasoline?is given by g 4. GAS MILEAGE Rick has d dollars. Theformula for the number of gallons ofgasoline that Rick can buy with d dollarsExpressions and FormulasWord Problem PracticePERIODA2-01-8739711. ARRANGEMENTS The chairs in anauditorium are arranged into tworectangles. Both rectangles are 10 rowsdeep. One rectangle has 6 chairs perrow and the other has 12 chairs per row.Write an expression for the total numberof chairs in the auditorium.1-1NAME DATELesson 1-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A4(Lesson 1-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Glencoe Algebra 2
Chapter 1Properties of Real NumbersLesson Reading GuideA5Chapter 112Glencoe Algebra 2A commuter is someone who travels back and forth to work or anotherplace, and the commutative property says you can switch the order whentwo numbers that are being added or multiplied. An association is agroup of people who are connected or united, and the associativeproperty says that you can switch the grouping when three numbers areadded or multiplied.4. How can the meanings of the words commuter and association help you to remember thedifference between the commutative and associative properties? Sample answer:Remember What You LearnedThe quantities a, b, and c are used in the same order, but they are groupeddifferently on the two sides of the equation. The second equation uses thequantities in different orders on the two sides of the equation. So thesecond equation uses the Commutative Property of Multiplication.3. Consider the equations (a b) c a (b c) and (a b) c c (a b). One of theequations uses the Associative Property of Multiplication and one uses the CommutativeProperty of Multiplication. How can you tell which property is being used in eachequation? The first equation uses the Associative Property of Multiplication.natural numberswhole numbersintegersNWZ{all nonterminating, nonrepeating decimals}{ , 3, 2, 1, 0, 1, 2, 3, }{0, 1, 2, 3, 4, 5, 6, 7, 8, }{1, 2, 3, 4, 5, 6, 7, 8, 9, }Exercises67Q, R1539 36 N, W, Z, Q, R7.Q, RQ, RChapter 113I, RGlencoe Algebra 220. 0.02 Q, R17. 2 5 14. 42 I, R11. 4.1 7 Q, R8. 26.1 Q, RAnswers19. 894,000 N, W, Z, Q, R81313. 1 Z, Q, R10.Q, R18. 33.3 Q, RN, W, Z, Q, R123. 0 W, Z, Q, R16. 5 25 I, R6. 342. 81 Z, Q, R15. 11.2 Q, R12.9.5. 73 N, W, Z, Q, R1.4. 192.0005 Q, Rnaturals (N), wholes (W), integers (Z), rationals (Q), reals (R)rationals (Q), reals (R) 25 25 5mName the sets of numbers to which each number belongs.b.11a. 3{all rationals and irrationals}{all numbers that can be represented in the form , where m and n are integers andnn is not equal to 0}Name the sets of numbers to which each number belongs.irrational numbersIExamplerational numbersQAnswersSample answer: (12 18) 45 30 45 75;12 (18 45) 12 63 752. Write the Associative Property of Addition in symbols. Then illustrate this property byfinding the sum 12 18 45 in two different ways. (a b) c a (b c);decimal because there is a block of digits, 57, that repeats forever, sothis number is rational. The number 0.010010001 is a non-repeatingdecimal because, although the digits follow a pattern, there is no blockof digits that repeats. So this number is an irrational number.1. Refer to the Key Concepts box on page 11. The numbers 2.5 7 and 0.010010001 bothinvolve decimals that “go on forever.” Explain why one of these numbers is rational andthe other is irrational. Sample answer: 2.5 7 2.5757 is a repeatingRead the Lessoncoupon amounts or add the amounts for the scanned coupons andmultiply the sum by 2.real numbersR8:03 AM Describe two ways of calculating the amount of money you saved by using coupons if yourregister slip is the one shown on page 11. Sample answer: Add all the individualfrom the total amount of purchases so that you save money by usingcoupons. Why are all of the amounts listed on the register slip at the top of the page followed bynegative signs? Sample answer: The amount of each coupon is subtractedPERIODAll real numbers can be classified as either rational or irrational. Theset of rational numbers includes several subsets: natural numbers, whole numbers,and integers.Properties of Real NumbersStudy Guide and InterventionReal Numbers1-2NAME DATE5/19/06Read the introduction to Lesson 1-2 in your textbook.PERIODA2-01-873971Get Ready for the Lesson1-2NAME DATELesson 1-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A5(Lesson 1-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Glencoe Algebra 2
Chapter 1Properties of Real NumbersStudy Guide and Interventiona ( a) 0 ( a) aa(b c) ab ac and (b c)a ba caInverseDistributiveA63(4 16p)4 4.2k 5.4j5(12 18c)645 190a 70bChapter 123. 3(m z) 5(2m z) 13m 8z21. (3g 3h) 5g 10h 2g 13h19. 3x 5 2x 3 5x 214Glencoe Algebra 24 4 ,5 5Simplify each expression.17. 11515. 15 15, Chapter 12j 7Comm. ( )344 153 4 3 , 1526.11(15d 3) (8 10d)32Glencoe Algebra 210d 324. 2x 3y (5x 3y 2z) 3x 2z22. a2 a 4a 3a2 1 2a2 3a 120. x y z y x z 018. 316. 1.25 1.25, 0.8Name the additive inverse and multiplicative inverse for each number.Assoc. ( )14. (10b 12b) 7b (12b 10b) 7bMult. Iden.13. 0.6[25(0.5)] [0.6(25)]0.512. 15x(1) 15xMult. Inv.Assoc. ( )10. 2r (3r 4r) (2r 3r) 4rAdd. Iden.8. 3a 0 3a 5y1 111. 5yDistributive9. 2(r w) 2r 2wComm. ( )7. 3 x x 3Name the property illustrated by each equation.25. 6(2 v) 4(2v 1) 8 2v20 2n216. (18 6n 12 3n)340 105c14. 2(15 45c) 14 p r453131p r r p4552Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.18. 50(3a b) 20(b 2a)8.75m12.12.7x 16Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. 14( j 2) 3j(4 7)0.7x 915. (7 2.1x)3 2(3.5x 6)140g 120h13. 4(10g 80h) 20(10h 5g)62.4e 39f10.2r 39.2s6. 8(2.4r 3.1s) 6(1.5r 2.4s)2k j58. 5.5j 8.9k 4.7k 10.9j 9. 1.2(7x 5) (10 4.3x)4a 3bab5. 12 3410. 9(7e 4f) 0.6(e 5f ) 11. 2.5m(12 8.5)77 4p7. 4(20 4p) 80g 26h4. 10(6g 3h) 4(5g h)51s 13t2. 40s 18t 5t 11s13. (4j 2k 6j 3k)5Commutative Property ( )Distributive PropertySimplify.a.Answers20a1. 8(3a b) 4(2b a)Simplify each expression.Exercises9x 3y 12y 0.9x 9x ( 0.9x) 3y 12y (9 ( 0.9))x (3 12)y 8.1x 15y11 1 aa6. 30 I, R5. 9 Z, Q, RN, W, Z, Q, R4.1232. 525 Z, Q, R3. 0.875 Q, R1. 34 N, W, Z, Q, RPERIOD8:03 AMSimplify 9x 3y 12y 0.9x.If a is not zero, then aa 0 a 0 aIdentityProperties of Real NumbersSkills PracticeName the sets of numbers to which each number belongs.1-2NAME DATE5/19/06Example(a b) c a (b c)a 1 a 1 a(a b) c a (b c)AssociativeMultiplicationa b b aAdditiona b b aCommutativePropertyFor any real numbers a, b, and cReal Number Properties(continued)PERIODA2-01-873971Properties of Real Numbers1-2NAME DATELesson 1-2A1-A23Page A6(Lesson 1-2)Glencoe Algebra 2
Chapter 1Properties of Real NumbersPractice2536 Q, R6. 16 Z, Q, RI, R2. 7 7. 35 Z, Q, RI, R3. 24y 1yMult. Inv.14Distributive17. 5(x y) 5x 5yComm. ( )14. 3x 2y 3 2 x yDistributiveAdd. Iden.18. 4n 0 4nAdd. Inv.15. (6 6)y 0y12. 7n 2n (7 2)nAssoc. ( )10. 7x (9x 8) (7x 9x) 8A716 1130.29. 2(4 2x y) 4(5 x y) 4a 1 Chapter 116 11false; counterexample: 5 4 54Glencoe Algebra 2 a1 b 1b . Explain your reasoning.Chapter 1RationalsIrrationalsReal Numbers3. VENN DIAGRAMS Make a Venndiagram that shows the relationshipbetween natural numbers, integers,rational numbers, irrational numbers,and real numbers.Integersstatement is true or false: If a b, it follows that a 710Commutative Property ofMultiplication32. NUMBER THEORY Use the properties of real numbers to tell whether the followingCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.NaturalNumbers13y5 31x 12y (2x 12y)6 54 11(10a 15) (8 4a)52Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.31. TRAVEL Olivia drives her car at 60 miles per hour for t hours. Ian drives his car at50 miles per hour for (t 2) hours. Write a simplified expression for the sum of thedistances traveled by the two cars. (110t 100) mi 12 8x 6y28.27. 3(r 10s) 4(7s 2r) 5r 58s26. 4c 2c (4c 2c) 4c25. 8x 7y (3 6y) 8x y 35 6 5 , 6 3524. 11a 13b 7a 3b 4a 16b522. 5620. 1.6 1.6, 0.62523. 5x 3y 2x 3y 3xSimplify each expression.11 1121. ,16 161072. MODELS What property of realnumbers is illustrated by the figurebelow?Distributive Property17bcAnswersGlencoe Algebra 2c 25; it is a natural number.7. a 7, b 24c 245 or 7 5 ; it is not anatural number.6. a 7, b 14c 13; it is a natural number.5. a 5, b 12For each set of values for a and b,determine the value of c. State whetherc is a natural number.aThe lengths of the sides of the right triangleshown are related by the formulac2 a2 b2.RIGHT TRIANGLES For Exercises 5–7,use the following information.I. always II. sometimes, · 2 2 2Answers19. 0.4 0.4, 2.5Name the additive inverse and multiplicative inverse for each number.16.Assoc. ( )13. 3(2x)y (3 2)(xy)Mult. Iden.11. 5(3x y) 5(3x 1y)Comm. ( )9. 5x (4y 3x) 5x (3x 4y)8. 31.8 Q, RW, Z, Q, R4. 08:03 AMName the property illustrated by each equation.5.N, W, Z, Q, RPERIOD4. NUMBER THEORY Consider thefollowing two statements.I. The product of any two rationalnumbers is always another rationalnumber.II. The product of two irrational numbersis always irrational.Determine if these statements arealways, sometimes, or never true.Explain.Properties of Real NumbersWord Problem Practice1. MENTAL MATH When teachingelementary students to multiply andlearn place value, books often showthat 54 8 (50 4) 8 (50 8) (4 8). What property is used?1-2NAME DATE5/19/061. 6425PERIODA2-01-873971Name the sets of numbers to which each number belongs.1-2NAME DATELesson 1-2A1-A23Page A7(Lesson 1-2)Glencoe Algebra 2
EnrichmentChapter 1Does each number, a, have an inverse, a , such thata a a a i? The integer inverse of 3 is 3 since 3 3 0, and 0 is the identity for addition. But the set does notcontain 3. Therefore, there is no inverse for 3.Inverse:A8 1 is the inverse of 1 since ( 1)( 1) 1, and 1 is the identity.1 is the inverse of 1 since (1)(1) 1, and 1 is the identity.Each member has an inverse.Inverse:Chapter 118Glencoe Algebra 28. {rational numbers}, addition yes4. {multiples of 5}, multiplication no7. {irrational numbers}, addition nono6. { 1 , 2 , 3 , }, multiplication no 12 , 22 , 32 , , addition2. {integers}, multiplication no5. {x, x2, x3, x4, } addition no3.1. {integers}, addition yesTell whether the set forms a group with respect to the given operation.ExercisesThe set { 1, 1} is a group with respect to multiplication because all four properties hold.1( 1) 1; 1(1) 1The identity for multiplication is 1.Identity:Associative Property: ( 1)[( 1)( 1)] ( 1)(1) 1; and so onThe set is associative for multiplication.Is the set { 1, 1} a group with respect to multiplication?Closure Property:( 1)( 1) 1; ( 1)(1) 1; (1)( 1) 1; (1)(1) 1The set has closure for multiplication.Example 2Chapter 119Glencoe Algebra 2Sample answer: When you look at your reflection, you are looking atyourself. The reflexive property says that every number is equal to itself.In geometry, symmetry with respect to a line means that the parts of afigure on the two sides of a line are identical. The symmetric property ofequality allows you to interchange the two sides of an equation. Theequal sign is like the line of symmetry.3. How can the words reflection and symmetry help you remember and distinguish betweenthe reflexive and symmetric properties of equality? Think about how these words areused in everyday life or in geometry.Remember What You Learned2. When Louisa rented a moving truck, she agreed to pay 28 per day plus 0.42 per mile.If she kept the truck for 3 days and the rental charges (without tax) were 153.72, howmany miles did Louisa drive the truck? 3(28) 0.42m 153.72Read the following problem and then write an equation that you could use tosolve it. Do not actually solve the equation. In your equation, let m be the numberof miles driven.Sample answer: An equation is a statement that says that twoalgebraic expressions are equal.c. How are algebraic expressions and equations related?Sample answer: Equations contain equal signs; expressions do not.b. How are algebraic expressions and equations different?Sample answer: Both contain variables, constants, and operationsigns.1. a. How are algebraic expressions and equations alike?Read the LessonAnswersThe set is not a group with respect to addition because only three of the four properties hold.Is there some number, i, in the set such that i a a a ifor all a? 0 1 1 1 0; 0 2 2 2 0; and so on.The identity for addition is 0.(220 A) IP or P (220 A) I 66 Write an equation that shows how to calculate your target heart rate.and desired intensity level (I ) To find your target heart rate, what two pieces of information must you supply? age (A)Read the introduction to Lesson 1-3 in your textbook.PERIOD8:03 AMIdentity:Associative Property: For all numbers in the set, does a (b c) (a b) c?0 (1 2) (0 1) 2; 1 (2 3) (1 2) 3; and so on.The set is associative for addition.Does the set {0, 1, 2, 3, } form a group with respect to addition?Closure Property:For all numbers in the set, is a b in the set? 0 1 1, and 1 isin the set; 0 2 2, and 2 is in the set; and so on. The set hasclosure for addition.Solving EquationsLesson Reading GuideGet Ready for the Lesson1-3NAME DATE5/19/06Example 1A set of numbers forms a group with respect to an operation if for that operationthe set has (1) the Closure Property, (2) the Associative Property, (3) a memberwhich is an identity, and (4) an inverse for each member of the set.PERIODA2-01-873971Properties of a Group1-2NAME DATELesson 1-3Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A1-A23Page A8(Lessons 1-2 and 1-3)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Glencoe Algebra 2
Chapter 1Solving EquationsStudy Guide and InterventionPERIODdivision25A9nChapter 15n11. n 8n 320Glencoe Algebra 2The quotient of five times a number and the sum of thenumber and 3 is equal to the difference of the number and 8.square of the number is equal to four times the number.10. 2(n3 3n2) 4n Twice the sum of the cube of a number and three times the9. 3n 35 79 The difference of three times a number and 35 is equal to 79.Write a verbal sentence to represent each equation. Sample answers are given.8. 23 more than the product of 7 and a number 7n 237. four times the square of a number increased by five times the same number 4n 2 5n6. the product of 3 and the sum of 11 and a number 3(11 n)5. the sum of 100 and four times a number 100 4n4. the difference of nine times a number and the quotient of 6 and the same number3. 7 less than fifteen times a number 15n 7 140140 10040 5Solve 100 8x 140.c21 3m 32 43y 604801285n 98 n22814. 100 20 5r 1611.8. 3x 17 5x 13 151x 322. 17 9 a 85. 7 Solve 4x 5y 100 for y.a c3k2m 5m 20, for mnChapter 124.5n 120nm 22. 3(2j k) 108, for j j 18 qf 24 2d21Answers43Glencoe Algebra 210325. 4x 3y 10, for y y x 23. 3.5s 42 14t, for s s 4t 12df21. 6, for f244rp st 720. 2xy x 7, for x x 2y 1s 10, for t2t3pq19. 12, for pr17.h 118. h 12g 1, for g g 1216. a 3b c, for b b 2015. 2x 75 102 x 912. 4.5 2p 8.7 2.19. 5(4 k) 10k 46. 8 2(z 7) 33. 5t 1 6t 5 41(100 4x)54y 20 x5y Solve each equation or formula for the specified variable.13. 4n 20 53 2n 5 10. 120 7. 0.2b 10 504.1. 3s 45 15Example 24x 5y 1004x 5y 4x 100 4x5y 100 4xSolve each equation. Check your solution.Exercises100 8x100 8x 100 8xxExample 1cFor any real numbers a, b, and c, if a b,abthen a c b c and, if c is not zero, .Multiplication and DivisionProperties of EqualityAnswers2. four times the sum of a number and 3 4(n 3)1. the sum of six times a number and 25 6n69n Six times the difference of a number and twois equal to 14.Example 2Write a verbal sentence torepresent 6(n 2) 14.
Chapter 1 A3 Glencoe Algebra 2 Answers Answers (Lesson 1-1) Skills Practice Expressions and Formulas Find the value of each expression. 1. 18 2 3 27 2. 9 6 2 1 13 3. (3 8) 2 (4) 3 97 4. 5 3(2
