Chapter Operations and Expressions Homework.. Substitute for x in x. Substitute for x in x. Substitute for x in x 9 : : : 9 8. Substitute for x in 0 x : 0 0. Substitute for x in x x. Substitute for x in x x : 0 :. Substitute 0 for T in T : 0 88 The student s average test score was 88.. Substitute 8.77 for M in M.8 : 8.77.8. There were approximately. million female students in college in 009. 8. a. 0. a. Number of Pairs Total Cost (dollars) n n The expression n represents the total cost of the n pairs of socks. b. Substitute 9 for n in n : 9 7 So, the total cost of 9 pairs of socks is $7. Speed Limit (miles per hour) Driving Speed (miles per hour) 0 0 0 0 s s The expression s represents the driving speed if the speed limit is s miles per hour.. a. b. Substitute for s in s : 70 So, if the speed limit is miles per hour, the person will be driving 70 miles per hour. Width (feet) Area (square feet) 0 0 0 0 w 0w The expression 0w represents the area of the garden (in square feet) if the width is w feet. b. Substitute 0 for w in 0w : 00 00 So, the area of the garden will be 00 square feet if the width is 0 feet.. 8 x Substitute 8 for x in 8 x : 88 0. x Substitute 8 for x in x : 8 8. x Substitute 8 for x in x 0. x 7. x Substitute 8 for x in x 7 : 8 : 87 Substitute 8 for x in x : 8 0. The quotient of and the number. Two less than the number 8. The sum of and the number 0. The product of the number and. The sum of the number and. The quotient of the number and Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 7. Substitute for x and for y in the expression y x 9 : 8. Substitute for x and for y in the expression 8 xy : 0. Substitute for x and for y in the expression x y :. a. t t 8 So, the elevator rises,,, or 8 yards after,,, or seconds, respectively.. x y Substitute 9 for x and for y in the expression x y 9 :. x y Substitute 9 for x and for y in the expression x y 9 :. Substitute 78 for b and 99 for d in the expression b d : 7899 7 So, the new balance is $7 after a check is written for $99. 8. Substitute 9000 for T and 0 for n in the expression T n: 9000 0 0 So, if 0 students go on a ski trip that costs $9000, the cost per student is $0. 0. Substitute 0 for E and 7 for t (009 is 7 years after 99) in the expression E t : 07 8 So, if the average verbal score was 0 points in 009, the average math score was 8.. a. n n 9 So, the cost of,,, or loaves is $, $, $9, or $, respectively. b. Each loaf costs $. The price per loaf is a constant while the number of loaves is a variable. In the expression n, the constant is and the variable is n. b. The elevator is rising at a rate of yards per second. The speed is a constant while the number of seconds rising is a variable. In the expression, t, the constant is and the variable is t. c. Answers may vary. Example: For each additional second the elevator rises, the total distance risen increases by yards.. Answers may vary. 8. Answers may vary. 70. Answers may vary. Homework.. The numerator of is.. 8 9. 8. 7 9 0. 0 7 7... 0 7 7 7 7 7 7 8 7 7 7 c. Answers may vary. Example: For each additional loaf purchased, the total cost increases by $. 8. 0. 9 7 7 7 7 7 7 7 7 9 9 8 9 Copyright 0 Pearson Education, Inc.
8 ISM: Elementary and Intermediate Algebra... 8. 0.... 8. 0.. 8 8 7 9 79 7 7 9 7 7 7 7 7 7 8 8 7 7 8 78 7 7 9 9 9 9 7 9 9 9 9 8 8 0 7 7 7 7 9 9 8 8 8 8 9. The LCD is 9: 8 9 9 9 9 9. The LCD is : 9 8 8 8. The LCD is 7: 7 7 7 7 7 7 7 7 0. The LCD is :. The LCD is 7: 9 7 9 7 9 7 7 7 7 7 7 7. 8. 0.... 7 is undefined since division by 0 is not 0 defined. 0 0 798 7 90 790 90 7 790 0 0 97 97 97 97 8. Substitute for x and for z in the expression z x : 70. Substitute for w, for x, for y, and for z in the expression y w : z x 9 7. Substitute for x, for y, and for z in the expression y y : x z The LCD is : 0 7. 7 8 0.90 7 99. The LCD is : 7 7 7 7 7. 9. Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 9 78. 80. Answers may vary. Example: ¼ ¼ 9.8 70 00 / 8. The quotient of and the number. 88. Total Time (hours) Cost per Hour (dollars per hour) t t So, if a session lasts for t hours, the total cost per hour will be t dollars. ¼ 90. a. i. 8. The perimeter of a rectangle is given by the expression L W. Substitute for W and for L in the expression. The LCD is : 9 8 7 The perimeter of the picture is 7 feet. 8. Let m be the fraction of income for mortgage and f be the fraction of income for food. The fraction remaining is given by the expression m f. Substitute for m and for f in the expression. m f So, of the income remains. ii. iii. 7 7 8 7 7 8 b. Answers may vary. Example: The product of a fraction and its reciprocal equals. 9. Answers may vary. Example: For addition of fractions, one cannot simply add the numerators and denominators. First get a common denominator, then add numerators, keeping the common denominator. 9 9. Answers may vary. Example: The student should have multiplied the numerator by instead of the denominator. Rewrite as and then multiply across. 7 7 7 9. a. i. The distance between 0 and is units. units ii. The distance between 0 and is units. units Copyright 0 Pearson Education, Inc.
0 ISM: Elementary and Intermediate Algebra iii. The distance between 0 and is units. units b. The distance between 0 and a number on a number line is equal to the absolute value of the number. 98. a. i. ii. 7 iii. 8 b. When adding two numbers with different signs, if the positive number is farther from 0 on a number line, the result will be positive. c. i. ii. 7 iii. 8 d. When adding two numbers with different signs, if the positive number is closer to 0 on a number line, the result will be e. i. 0 ii. 77 0 iii. 99 0 f. When adding two numbers with different signs, if the two numbers are the same distance from 0 on a number line, the result will be 0. g. i. ii. 7 iii. 0 h. Answers may vary. Example: When adding two numbers with different signs, take the absolute value of the two numbers and subtract the smaller absolute value from the larger. The sign of the result is the same as the sign of the number with the larger absolute value. 00. Answers may vary. Example: The denominator of a fraction is the name of the things it represents. The numerator of a fraction is the number of those things it represents. When we add two fractions with the same denominator, we keep the same denominator, or name, and add the two numerators, or number of things. Homework.. 9 9.. because is a distance of units from 0 on a number line. 8. because is a distance of unit from 0 on a number line. 0.. 9 9 9. The numbers have different signs so subtract Since is greater than, the sum is positive.. The numbers have the same sign so add the absolute values. The numbers are negative, so the sum is Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 8. The numbers have different signs so subtract 9 9 Since 9 is greater than, the sum is 9 0. The numbers have different signs so subtract Since is greater than, the sum is positive.. The numbers have the same sign so add the absolute values. 9 9 The numbers are negative, so the sum is 9. The numbers have different signs so subtract 8 8 Since 8 is greater than, the sum is positive. 8. 88 0 because the numbers are opposites and the sum of opposites is 0. 8. 77 0 because the numbers are opposites and the sum of opposites is 0. 0. The numbers have different signs so subtract 7 7 Since 7 is greater than, the sum is positive. 7. The numbers have different signs so subtract 89 7 89 7 Since 89 is greater than 7, the sum is 89 7. The numbers have the same sign so add the absolute values. 7 9 7 9 9 The numbers are negative, so the sum is 7 9 9. 7, 7, 0 because the numbers are opposites and the sum of opposites is 0. 8. The numbers have the same sign so add the absolute values..7 9.9.7 9.9. The numbers are negative, so the sum is.7 9.9. 0. The numbers have different signs so subtract 7 0. 70..7 Since 7 is greater than 0., the sum is positive. 0. 7.7. The numbers have different signs so subtract 7.0 9. 7.0 9. 7.79 Since 7.0 is greater than 9., the sum is positive. 7.0 9. 7.79. The numbers have different signs so subtract Since is greater than, the sum is positive.. The numbers have different signs so subtract Since is greater than, the sum is Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra 8. The numbers have the same sign so add the absolute values. 9 The numbers are negative, so the sum is 0. The numbers have different signs so subtract 9 8 Since is greater than, the sum is... 798..8 0.0 8, 87. 8, 0.87,9. 7 0.08 98 8. Substitute for a and for b in the expression b a and then find the sum:. x Substitute for x in the expression and then find the sum:. x 8 Substitute for x in the expression and then 8 find the sum:. The balance is.0 70 dollars. The numbers have different signs so subtract 70.0 70.0 7.0 Since 70 is greater than.0, the sum is positive:.0 70 7.0 So, the balance is $7.0. 8. We can find the final balance by finding the balance after each transaction. Transaction Balance = Paycheck.00 9.00.00 FedEx Kinko's.00 0.7 0. ATM 0..0 8.7 Barnes and Noble 8.7 7.9.7 So, the final balance is $.7. 70. The new balance is 79 0. The numbers have different signs so subtract 79 0 79 0 09 Since 79 is greater than 0, the sum is 79 0 09 So, the new balance is 09 dollars. 7. The balance after sending the check is 87 00 7. The balance after buying the racquet is 7 9. The balance after buying the outfit is 87 709. So, the final balance is 709 dollars. 0. Substitute for b and for c in the expression b c and then find the sum: Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 7. The current temperature is 8. The numbers have different signs so subtract 8 8 Since is greater than 8, the sum is 8 So, the current temperature is F. 7. a. 78. a. Retail Price (dollars) Sale Price (dollars) 0 0 00 00 0 0 00 00 r r From the last row of the table, we see that the expression r represents the sale price (in dollars). b. Evaluate r for r 70. 70 So, if the retail price is $70, the sale price is $. Decrease in Temp Current Temp (F) (F) x x From the last row of the table, we see that the expression x represents the current temperature (in F ). b. Evaluate x for x 7. 7 9 The current temperature is 9 F. 80. If a is positive and b is negative (but with a larger absolute value), the sum a b will be b units a units 8. If a b is positive, then both numbers are positive, or the numbers have opposite signs but the number with the larger absolute value is positive. 8. a. Substitute for a and for b: a b b. Substitute for a and for b: b a c. The results are the same. d. Substitute for a and 9 for b: a b9 b a 9 The results are the same. e. Answers may vary. f. Yes; when adding two quantities, the order of the addition does not matter. Homework.. 7 7. 99. 8. 7 7 0. 7 7. 7 7. 77 77. 00 7 00 7 7 8. 99 99 87 0..8.7.8.7...7 7..7 7. 9....... b a + b a. 9. 7.8 9. 7.8. Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra 8. 0.. 7 7 9 9 9 9 9 7. 8 So, the current temperature is F.. The change in temperature is F. 8. a. 9 9 The change in temperature is F.. 0. 9 8. ( ) 0.....9. ( 8). 9 ( 9) 8. 0.. 78.9.87 0.78 8,. ( 08.9) 8, 80. b. To estimate the change in temperature over the past hour, we divide the change over three hours by. The estimated change in temperature over the past hour is F. c. Answers may vary. Example: The change in temperature is affected by the time of day in addition to the weather conditions. Thus, temperature change need not be uniform. 0. 9, 0 9, 0 0, 7 The change in elevation is 0,7 feet.. a. Change in Year Population Population 00 8 00 8 8 007 7 7 008 7 7 009 9 9 8 00 97 97 9 0 98 98 97 b. The population increased the most from 00 to 007. The change in population is. c. The population decreased the most from 007 to 008. The change in population is 7. d. No; the change in population is the difference between births and deaths. An increase of 8 wolves means there were 8 more births than deaths. 9 8.7 97 Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions. a. Add the changes in the number of billions of bushels of corn harvested from 00 to 0: 0.8 0.. 0.8.0...8 So, there were.8 billion bushels of corn harvested in 0.. a. 8. a. b. Increasing corn harvests are indicated by positive changes. Thus, harvests were increasing during the periods 00 007, 008 009, and 00 0. c. Decreasing corn harvests are indicated by negative changes. Thus, harvests were decreasing during the periods 00 00, 007 008, and 009 00. Current Value (dollars) Change in Value (dollars) 0 0 0 0 x x From the last row of the table, we see that the expression x represents the change in value (in dollars) of the stock. b. Evaluate x for x : 9 So, if the current value is $, the stock has increased in value by $9 from last year. Change in Population Current Population 0 0 80 0 0 80 0 0 80 0 0 80 c c 80 From the last row of the table, we see that the expression c 80 represents the current population. b. Evaluate c 80 for c : 80 79 So, if the change in population is, the current population would be 79 due to the decrease in population of deer in the past year. 70. Evaluate a c for a and c 7 : 7 7. Evaluate c a for a and c 7 : 7 7 7. Evaluate b a for a and b : 7 7. x Evaluate the expression for x : 9 78. x Evaluate the expression for x : 0 80. x Evaluate the expression for x : 8. The student changed the order of subtraction without changing the sign of the result. 8. a. i. 88 ii. 99 iii. b. Answers may vary. Example: Since the quantity decreased, the final number is smaller than the beginning number. When finding the change in quantity, we subtract the beginning number from the final number. Since the final number is smaller, the result will be 8. a. i. 0 ii. iii. 79 b. Answers may vary. Example: The results are all positive. c. 7 7 Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra d. Answers may vary. Example: To multiply two negative numbers, multiply their absolute values. 88. Answers may vary. Example: In the first situation, the values were on the same side of 0 on a number line, so we subtract to find the distance between the two values on the number line. In the second situation, the values are on opposite sides of 0 on a number line. In this case, we add the distance each number is from 0 to get the overall distance between the numbers. 90. Answers may vary. Example: It is impossible to find the sign. If x is greater than y, then x y is If x is less than y, then x y is positive. Homework.. 9% 9.0% 0.9. %.0% 0.0. 0.0 % 8..8% 0.08 0. 0.089 8.9%. 0.7.8 ; so, 7% of $ is $.8. 0.08 000 0 ; so, 8% of 000 students is 0 students.. 0.0 00 ; so,.% of 00 cars is cars.. 8. Since the numbers have different signs, the product is negative: 0 0. Since the numbers have the same sign, the 8 9 7 product is positive:. Since the numbers have different signs, the product is negative: 0. Since the numbers have different signs, the quotient is negative: 7 9. Since the numbers have different signs, the 8 quotient is negative: 8. Since the numbers have the same sign, the quotient is positive: 0. Since the numbers have the same sign, the 9 9 product is positive:. Since the numbers have different signs, the 008 8 quotient is negative:. Since the numbers have the same sign, the 0. 0. 0.09 product is positive:. Since the numbers have different signs, the.7. 9.88 product is negative: 8. Since the numbers have different signs, the quotient is negative: 0. 0. 0. 0. Since the numbers have different signs, the 9 quotient is negative: 9. Since the numbers have the same sign, the 7 quotient is positive: 7 89 8. Since the numbers have different signs, the product is negative: 7 7. Since the numbers have the same sign, the 7 product is positive: 8. Since the numbers have different signs, the quotient is negative: 8 0 8 7 8 7 0 0. Since the numbers have the same sign, the quotient is positive: 9 0 0 8 0 8 9 7. 9. 9 7 7. 7 7 9 8. 9 Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 7 0. 8 8 9 9 9 9 9 9 9 78. 80. 89. 8.9 0.9... 8. 70. 7. 7. 7. 9 7 8 0 8 0 8 0 0 0 0 0 8 9 8 9 9 9 7 7 7 7 0 0 7 8. 8..98.7 7.8 9 0.87 7 7 7.9 8 8. Evaluate ac for a and c 8 : 8 8 88. Evaluate b a for a and b : 90. Evaluate bc for b and c 8 : 8 9. Evaluate a for a and c 8 : c 9. 8 w ; Evaluate the expression for w 8 : 8 Copyright 0 Pearson Education, Inc.
8 ISM: Elementary and Intermediate Algebra 9. w ; Evaluate the expression for w 8 : 8 98. 00. 0. 0. a. 9. million. million So, twice as many Americans attend Major League Baseball games regularly than attend National Football League games regularly..7 million viewers.. million viewers So, there were about. times as many viewers of Good Morning America than of The Early Show. b. 0. a. b. c mushrooms 0. c mushrooms c cooked noodles c cooked noodles For each cup of cooked noodles, a half cup of sliced mushrooms is required. c cooked noodles c cooked noodles c mushrooms c mushrooms For each cup of sliced mushrooms, cups of cooked noodles are required. 9, 78,0.0 8,79,89 The population of New York is about.0 times as great as the population of New Jersey. 7, 9.7, 99 The land area of Alaska is about.7 times as large as the land area of California. 70,. c. Alaska: 7, 9 7,,9 8.87 California:,99 9,88,0 7.00 Michigan:, 80 8,79,89 8.7 New Jersey: 77 9,78,0 0. New York: 7, d. New Jersey has the greatest population density, while Alaska has the least. 08. a. e. The person is not correct. Answers may vary. Example: Although Michigan has a larger population than New Jersey, it also has a larger land area which serves to lower its population density. 80 dollars 8. 90 dollars 9 b. For each $ he pays towards his Sears account, he should pay about $. towards his Visa account. 0. 0.90.0 90. 0.0 The new balance would be 0.0 dollars.. 89.0 8.0 0 8.0 8.0 The new balance is $8.0.. a. b. c. The first statement is clearer because it indicates an operation as well. From parts (a) and (b), we see that just having one negative number and one positive number is not enough to guarantee that the result is d. Answers may vary.. a. Negative; the quotient of two numbers with opposite signs is b. Negative; the quotient of two numbers with opposite signs is c. No; the variables a and b can take on positive or negative values, so the sign of the result is not clear without knowing the signs of a and b. 8. Answers may vary. Example: 0 0. If ab is positive, we can say that the two numbers have the same sign. We cannot say if the two numbers are positive or negative, but we do know they have the same sign. Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 9. If b a is negative, we can say that the two numbers have different signs. We cannot say which is positive and which is negative, but we do know they have different signs.. a. b. Multiplying by itself an even number of times yields as the result, while doing so an odd number of times results in. c. Since the number of s is even, the result will be. d. Since the number of s is odd, the result will be.. a. Answers may vary. Example:,, b. Answers may vary. Example: 0., 0., 0. c. For to equal, x must be. x Homework... 9 7 8. 7 77 9 8. 0. 7 7 7 9 7. 8 8. 880 0. 7 8. 0.. 9 7 9 8 8.. 9 8. 8 0. 7. 9 0. 0 0 0. 7 7 0 8. 8 8 0. 0 9.. 8 8 0 8 89. 8. 8 8 8 Copyright 0 Pearson Education, Inc.
0 ISM: Elementary and Intermediate Algebra 0.. 7 0 0. 8. 8. 7 0. 7 7 0 7 0 0 7 7 9. 9.. 97 8 7. Evaluate ac b for a, b, and c : 7. Evaluate c a abc for a, b, and c : 8 7. Evaluate c b for b and c : 9 7 78. Evaluate cb a for a, b, and c : 8 a b 80. Evaluate for a, b, and c : c b 8 9 9 8. Substitute a, b, c, and d 7 in the expression a b c d : 7 7 8. 70. 8...978.. 0..98 8..9 98,.78. 99.8.8. 89. 0.9 8. Substitute a, b, c, and d in the expression a b c d : 8 8. Substitute a, b, c 8, and d in the expression a b c d : 8 8 88. Evaluate x for x : 9 Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 90. Evaluate x for x : 9 9. Evaluate x x for x : 9 9. 8 x Evaluate the expression for x : 8 9. xx 98. a. Evaluate the expression for x : 0 Years since 008 Number of Militia Groups 0 70 9 79 7 9 7 9 7 9 t 7t 9 From the last row of the table, we see that the expression 7t 9 represents the number of militia groups t years after 008. b. Substitute 8 for t in 7t 9 : 789 000 9 9 So, in 0 (8 years after 008) the number of militia groups is predicted to be 9. 00. a. Years Since 990 Percent 0.08.8.8.8.8 t.t8 From the last row of the table, we see that the expression.t 8 represents the percentage of companies offering traditional benefit plans t years since 990. b. Substitute 7 for t in.t 8 :.7 8 9.7 8. So,.% of companies in 07 will offer traditional benefit plans. 0. The increase in revenue from electronic gaming software from 00 to 0 was 0.0(.) billion dollars. To find the revenue from electronic gaming software (in billions of dollars) in 0, we add 0.0(.) to.:. 0.0(.)..00 7. The revenue from electronic gaming software was about $7. billion in 0. 0. The increase in the number of people participating in the Supplemental Nutrition Assistance Program from 00 to 0 was 0.0(0) million. To find the number of people participating in the Supplemental Nutrition Assistance Program (in millions) in 0, we add 0. 0.0(0) to 0: 0 0.0(0) 0.. About. million people participated in the Supplemental Nutrition Assistance Program in 0. 0. The decrease in the number of U.S. troop deaths in the Afghanistan War from 00 to 0 was 0.7(99). To find the number of U.S. troop deaths in the Afghanistan War in 0, we subtract 0.7(99) from 99: 99 0.7(99) 99 8.8 The number of U.S. troop deaths in the Afghanistan War was in 0. Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra 08. The decrease in the revenue from televisions from 009 to 00 was 0.07(7.) billion dollars. To find the revenue from televisions (in billion of dollars) in 00, we subtract 0.07(7.) from 7.: 7.0.07(7.) 7..9. The revenue from televisions was about $. billion in 00. 0. Substitute for r in the expression r : 7 So, the volume is.0 cubic inches.. In the first line, the student only squared instead of. Should be: 9. The student did not perform multiplication and division in the correct order (from left to right). 8.. a. 8 b. c. Yes, the order makes a difference: L-R: 8 (part (a)) R-L: (part (b)) d. Order of operations dictates that we multiply and divide from left to right in the order that they appear. Therefore, 8 8. a. 9 b. 7 9 c. The results are the same. d. 7 7 The results are the same. e. Answers may vary. Example: In each case, the results should be the same. f. Yes; this is the associative property of addition. g. Answers may vary. Example: For a series of additions, the way in which the additions are grouped does not matter. 0. a. i. ii. iii. iv. 87 8 v. vi. 9 b. n when n is an even counting number. Answers may vary. Example: The product of an even number of negative numbers is positive. c. n when n is an odd counting number. Answers may vary. Example: The product of an odd number of negative numbers is. Answers may vary. Chapter Review Exercises. 8. 7. 99. 8 8 0. Since the numbers have different signs, the product will be negative: 8. Since the numbers have different signs, the 8 quotient will be negative: 7. 0 8 8. 8 Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 9. 7 7. 9 0 90 0.. 8 8 0 0.... 8 0... 8 8 8 00 0 7 9 9 9 9 9 9 7 7 8 8 0 0. 7 0 7. 78 8. 89 89 89 9. 7 7 0. 7 9 9. 7 7 7 7. 8 8 8 8. 9. 0. 8 88 7. 9. 8...7..7 0.9 Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra. 8 88. 88 0 8 8 9...7. 9. 8.8. 7 7 7 9 8 8 8 0 9. 7. 8 8. 7 7 77 9 7 9 9 9. 0. 9 9 8 8 8 8 8 7 7. 7. 97. 0.. 8... Substitute for W and for L in the expression L W : 0 0 0 0 So, the perimeter of the rectangle is yards.. 789 800 0.99.0 789 800 0.9 989 0.9 09.9 The student now owes the credit card company $09.9.. 7,800,00 700 The plane had a change in altitude of 700 feet.. a. 8 The change in temperature is F. Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions b. Divide the change for the past three hours by to estimate the change over hour. The estimated change for the past hour is F. c. Answers may vary. Example: Temperature need not change uniformly. 7. a..9 8.. The change in annual individual contributions to the Democratic nominee from 99 to 000 was $. million. 8. b. 0 9 9 The change in annual individual contributions to the Republican nominee from 00 to 008 was 9 million dollars. c. 9 The greatest change in annual individual contributions to the Democratic nominee occurred between 00 and 008. The change was $9 million. d. 9 9. 7.7 The greatest change in annual individual contributions to the Republican nominee occurred between 000 and 00. The change was $7.7 million.. messages per day.0 9.7 messages per day The number of messages sent or received per day in 0 is.0 times larger than the number of messages sent or received per day in 009. 9. 7% 7.0% 0.7 0..9% 0.09. 0.87 7. So, 87% of $ is $7... 0.089 7 So, 8% of 9 students is 7 students.. 9 0. 9 9 098. 9. The new balance is 9. dollars.. Substitute for a and for c in the expression ac c a : 8 8 0. Substitute for a, for b, and for c in the expression b ac: 7. Substitute for a, for b, and for c in a b c : the expression 7. Substitute for a, for b, and for c in b c the expression : a 8. Substitute for c in the expression c c : 0 0 9. Substitute for a, for b, for c, and 0 for d in the expression a b c d : 7 7 0 0 0. x Evaluate the expression for x : Copyright 0 Pearson Education, Inc.
ISM: Elementary and Intermediate Algebra. 7 x Evaluate the expression for x : 7 7. x. Evaluate the expression for x : x Evaluate the expression for x : 89. Substitute 0 for T and for n. 0 0 Each player must pay $0 for the team to join the softball league.. a. Time Volume of Water (hours) (cubic feet) 0 0000 000 000 0 00 000 t 0 t 00 From the last row of the table, we see that the expression 0t 00 represents the volume of water (in cubic feet) remaining in the basement after water has been pumped out for t hours. b. Substitute 7 for t in 0t 00 : 0700 0 00 0 After 7 hours of pumping, there will be 0 cubic feet of water remaining in the basement.. The decrease in the number of Americans who flew to Europe from 007 to 0 was 0.88(.) million. To find the number of Americans who flew to Europe in 0, we subtract 0.88(.) (in millions) from. million:. 0.88...00 0.799 The number of Americans who flew to Europe in 0 was about 0.8 million. Chapter Test. 8 8. Since the two numbers have the same sign, the 7 9 product will be positive:. 9. 7 8. 7. 0 8 7. 0 9 0 7 8. Since the two numbers have different signs, the product will be negative: 0. 0. 0.08 9. 0.. 7 8 7 7 0 7 0 8 0 8 0 8 0 0 0 0 8.. 7 7 789 9 Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 7. 7 0 0 0. 7 8 8 7 7. 99 The current temperature is F. 7. a...8 0.7 The change in the tax audit rate from 00 to 00 was 0.7 audit per 000 tax returns. 8. b..8 9.0. The change in the tax audit rate from 999 to 00 was. audits per 000 tax returns. c. From 00 to 00, the change was. audits per 000 returns..9.9 9. The average ticket price in 0 was about.9 times the average price in 99. 9. Substitute for a, for b, and for c in a the expression ac : b 0 0 0 0. Substitute for a, for b, for c, and for d in the expression a b c d :. Substitute for a, for b, and for c in the expression ab c : 8. Substitute for a, for b, and for c in the expression b ac: 0 0. x x Evaluate the expression for x : 0 0.. a. 0 x Evaluate the expression for x : 0 Years since First - Class Mail Volume 00 (billions of pieces) 0.9078..9 78..978..978..978. t.9t 78. From the last row of the table, we see that the expression.9t 78. represents the U.S. Postal Service first-class mail volume (in billions of pieces) in the year that is t years since 00. b. Substitute 8 for t in.9t 78. :.98 78. 9. 78. 9 So, the first-class mail volume will be 9 billion pieces in 08.. The decrease in the number of California methamphetamine labs busted from 00 to 0 was 0.9(0). To find the number of California methamphetamine labs busted in 0, we subtract 0.9(0) from 0: 0 0.90 0 8.07 7.9 The number of California methamphetamine labs busted in 0 was about 8. Copyright 0 Pearson Education, Inc.
8 ISM: Elementary and Intermediate Algebra Cumulative Review of Chapters and. a. Answers may vary. Example: 9. The line and the y-axis intersect at the point 0, 0,. so the y-intercept is 0. The line and the x-axis intersect at the point, 0., 0, so the x-intercept is. a. b. W and L are variables because their values are not fixed... c. P is a constant because the perimeter is fixed at inches.. The x-coordinate is.. Independent variable: t Dependent variable: V. a. b. The revenue was the most in 0.. a. b. The input t leads to the output B, so the balance is $ thousand after months. c. The output B originates from the input t 7, so the balance will be $ thousand after 7 months. d. The line and the B-axis intersect at the point 0, 0, so the B-intercept is 0, 0. The original balance was $0 thousand when she was laid off. e. The line and the t-axis intersect at the point 0,0, so the t-intercept is 0,0. The checking account will be depleted after 0 months. c. The revenue was the least in 007. d. The annual revenue decreased the most between 008 and 009. The change in annual revenue was 9.8 0. 0. billion dollars. e. The annual revenue increased the most from 007 to 008 and from 00 to 0. The change in annual revenue was 0. 9..0 billion dollars. 7. The input x leads to the output y, so y when x. 8. The output y originates from the input x, so y when x. b. Draw a line that comes close to the points to create the linear model. See the graph in part (a). c. The line and the c-axis intersect at the point 0,, so the c-intercept is 0,. The average monthly basic rate for cable TV in 990 was $. Copyright 0 Pearson Education, Inc.
Chapter : Operations and Expressions 9. d. The output c originates roughly from the input t 0, so the average monthly basic rate for cable TV will be $ in 00. e. For 08, the input is t 8. The input t 8 leads roughly to the output c 0, so the average monthly basic rate for cable TV will be $0 in 08. 8 9 7. 0 0 0 0.. 7 7 7 7 7 8 9 0 9 0 8 8 7. 79 0 0 0 0 8. 7 9 8 8 9 9. 8 The change in temperature is 8 F. 0. 9 80 8 8 The student will now owe the credit card company $8.. Substitute for a, for b, for c, and 7 for d in the expression a b c d : 7 7 0 0. Substitute for a, for b, and for c in the expression b ac: 90 90 9. x x Evaluate the expression for x : 7. x 7 Evaluate the expression for x : 787. Evaluate 00 v. a. for v : 00 00 00 0 7. 7 A stock value today of $ represents about a 7.% growth of the investment. Years since Sales 00 (thousands of motorcycles) 0 0 t t From the last row of the table, we see that the expression t represents the sales (in thousands of motorcycles) in the year that is t years since 00. b. Evaluate t for t : 8 In 07 ( years after 00), the motorcycle company will sell thousand motorcycles. Copyright 0 Pearson Education, Inc.