Chapter 2 Section 2.1 Practice Exercises x 2 x + 3 1
|
|
- Cameron Casey
- 6 years ago
- Views:
Transcription
1 Intermediate Algebra 7th Edition Martin Gay SOLUTIONS MANUAL Full download at: Intermediate Algebra 7th Edition Martin Gay TEST BANK Full download at: Chapter 2 Section 2.1 Practice Exercises x 2 x x + 7 = x = x 2 x x = x = x = x x 12 x 2 = 12 x = x = = 3 2.5t = 3 2.5t = 2.5t 0.5 = 2.5t 12 x ( x 2) = 3( x + 3) x x + 2 = 3x x + 2 = 3x x + 2 3x = 3x x 8x + 2 = 12 8x = x = = t 3. 8x x = 5x x 2 x 4 = x x 4 x = x + 11 x 3x 4 = 11 3x = x = 15 3 x 15 = 3 3 8x = x = x 0.03 = 0.2 x (0.15x 0.03) = 100(0.2 x ) 100(0.15x) 100(0.03) = 100(0.2 x) + 100(0.12) 15x 3 = 20 x x 20 x = x = 5 5x = ( x 5) = 6 x 3 5 x 15 = 5 5 3x 15 = 6 x 3 3x 15 6 x = 6 x 3 6 x 3x 15 = 3 3x = x 3 = 4( x + 5) 4 x 3 = 4 x + 20 x = 3 3x = 12 3 x = 12 4 x 3 4 x = 4 x x 3 = x = 4
2 5. y y 1 = y y 1 = y 2 20 y 5 = 5 10 y 4 y = 5 6 y = 5 6 y 5 = 6 6 y = 5 6 This equation is false no matter what value the variable x might have. Thus, there is no solution. The solution set is { } or. 9. 5x 2 = 3 + 5( x 1) 5x 2 = 3 + 5x 5 5x 2 = 2 + 5x 5x = 2 + 5x + 2 5x = 5x 5x 5x = 5x 5x 0 = 0 Since 0 = 0 is a true statement for every value of x, all real numbers are solutions. The solution set is the set of all real numbers or {x x is a real number}. 26 Copyright 2017 Pearson Education, Inc.
3 ISM: Intermediate Algebra Vocabulary, Readiness & Video Check Equations with the same solution set are called equivalent equations. 2. A value for the variable in an equation that makes the equation a true statement is called a solution of the equation. 3. By the addition property of equality, y = 3 and y 7 = 3 7 are equivalent equations. 4. By the multiplication property of equality, 5. 2y = 3 and 2 y = x 5 3 expression 6. 2(x 3) = 7 equation x + 1 = 2 x x x equation expression are equivalent equations. 9. The addition property of equality allows us to add the same number to (or subtract the same number from) both sides of an equation and have an equivalent equation. The multiplication property of equality allows us to multiply (or divide) both sides of an equation by the same nonzero number and have an equivalent equation. 10. distributive property 11. to make the calculations less tedious 12. When solving a linear equation and all variable terms subtract out and: a. you have a true statement, then the equation has all real numbers for which the equation is defined as solutions. b. you have a false statement, then the equation has no solution. Chapter 2: Equations, Inequalities, and Problem Solving Exercise Set x = 18 2 x 2 = 18 2 x = 9 Check: 2 x = 18 2( 9) = 18 True The solution is = y = y = y Check: 25 = y = 25 True The solution is y 8.6 = 6.3 y = y = 2.3 Check: y 8.6 = = 6.3 True The solution is y 3 = y 5y 3y = y = 14 2 y = y = 7 Check: 5y 3 = y 5(7) (7) = 32 True The solution is x = x 10.3 = x = x = x = 2.1 Check: x = (2.1) = 2.3 True The solution is 2.1.
4 Copyright 2017 Pearson Education, Inc. 27
5 Chapter 2: Equations, Inequalities, and Problem Solving x + 14 = 6 x x 6 x = x = 6 2 x = (3n 2) n = 11(n 1) 12n + 8 n = 11n n + 8 = 11n n + 11n = 11 8 ISM: Intermediate Algebra 2 2 2n = 3 x = 3 Check: 4 x + 14 = 6 x + 8 4(3) (3) + 8 Check: 3 n = (3n 2) n = 11(n 1) 26 = 26 True The solution is x 15x + 8 = 4 x x + 8 = 4 x x 4 x = = 6 x = True Check: x = 5 The solution is 3. 13x 15x + 8 = 4 x (5) 15(5) + 8 4(5) x x 5 The solution is 5. 2 = 2 True x + x = x x = x + 6 5x = 0 x = 0 Check: 6 + 3x + x = x = x x = x + 4 x = x = 25 x = (0) = 6 True The solution is (4 x + 3) = 7 x + 5 8x + 6 = 7 x + 5 x + 6 = 5 x = 1 Check: 2(4 x + 3) = 7 x + 5 2(4( 1) + 3) 7( 1) + 5 2( 1) = 2 True The solution is x = 4( x 5) 6 x = 4 x 20 2 x = 20 x = 10 Check: 6 x = 4( x 5) 6( 10) 4( 10 5) Check: x + x = = True 0 = 60 True The solution 6 is ( 1 5 ) 6
6 26. T h e s o l u t i o n i s r r = r r = 10(7) (4r) r = 70 8r r = 70 7r = 70 r = 10
7 28 Copyright 2017 Pearson Education, Inc.
8 ISM: Intermediate Algebra Chapter 2: Equations, Inequalities, and Problem Solving Check: 4r r = Check: 2 z = z + z (10) = 7 True The solution is h h = h + h 1 = h + 3(h 1) = h + 3h 3 = 3 4h 1 = 3 4h = 4 h = 1 Check: 2 + h + h 1 = ( 1 ) The solution is = 5 True (2 x + 3) = 0.1(2 x + 3) 10[2.4(2 x + 3)] = 10[ 0.1(2 x + 3)] 48x + 72 = 2 x 3 50 x = 75 x = 1.5 Check: 2.4(2 x + 3) = 0.1(2 x + 3) 2.4(2( 1.5) + 3) 0.1(2( 1.5) + 3) 2.4( 3 + 3) 0.1( 3 + 3) 2.4(0) 0.1(0) 0 = 0 True The solution is 1.5. The solution is = 3 3 True 36. 6(4n + 4) = 8(3 + 3n) 24n + 24 = n 24n n = n 24n x = 0.1x (0.3x + 2.4) = 10(0.1x + 4) 3x + 24 = 1x x = 16 x = 8 Check: 0.3x = 0.1x (8) (8) = 4.8 True The solution is z + 7 z 1 2 = z z = 8 z + z z = 8z + 4(z 1) 2z = 8z + 4z 4 2z 9 = 12z 4 10 z = 5 1 z = 2 24 = 24 0 = 0 Therefore, all real numbers are solutions ( x + 2) + 4 = 4 x 8 4 x = 4 x 8 4 x + 12 = 4 x 8 12 = 8 This is false for any x. Therefore, no solution exists, ( x 4) + x = 6( x 2) 8 5x 20 + x = 6 x x 20 = 6 x = 20 This is true for all x. Therefore, all real numbers are solutions ( x 2) = 8( x 3) + x 9 x 18 = 8x 24 + x 9 x 18 = 9 x = 24 This is false for any x. Therefore, no solution exists,. Copyright 2017 Pearson Education, Inc. 29
9 Chapter 2: Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra 44. a + 7 = a + 7 = a + 7 = 20 2a = 13 a = x 7 = 2 x 7 4 x 2 x = x = 0 x = x + 2( x + 4) = 5( x + 1) + 3 3x + 2 x + 8 = 5x x + 8 = 5x = 0 Therefore, all real numbers are solutions. 50. (w + 0.2) = 0.3(4 w) w 0.2 = w w + 0.3w = w = 1.4 w = (8 + 2c) = (3c 5) c = c = c c = c c = c = c = c 54. 9c 3(6 5c) = c 2(3c + 9) 9c c = c 6c 18 24c 18 = 5c 18 24c + 5c = c = 0 c = 0 30 Copyright 2017 Pearson Education, Inc.
10 ISM: Intermediate Algebra Chapter 2: Equations, Inequalities, and Problem Solving x 2( x + 4) = 8( x 2) x 2 x 8 = 8x x 8 = 8x 10 8x 8x = = 2 This is false for any x. Therefore, the solution set is. n n = n n = (n + 1) 8(2 n) = 4(5) 3n n = 20 11n 13 = 20 11n = 33 n = y 18 4 y = 12 y 13 6 y 18 = 12 y 13 6 y 12 y = y = 5 5 y = (2 x 3) (10 x + 7) 2 = (12 x 5) (4 x + 9) 1 8x x 7 2 = 12 x x x + 3 = 16 x 5 2 x = 8 x = (2 y 1) 2 = (3y 5) (2 y 1) 2 = 10 1 (3y 5) (2 y 1) 20 = 5(3y 5) y 22 = 15y y = 27 y 27 = [8 4(n 2)] + 5n = [5(1 n) 6n] 3[8 4n + 8] + 5n = [5 5n 6n] 3(16 4n) + 5n = (5 11n) 48 12n + 5n = n 48 7n = 10 22n 15n = n = Sum means to add: The sum of 8 and a number: 8 + x Copyright 2017 Pearson Education, Inc. 31
11 Chapter 2: Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra 70. The difference means to subtract. The difference of 8 and a number: 8 x 72. Two more than three times a number: 3x ( 4) = 12 not 12; 3( x 4) = 10 3x + 12 = 10 3x = 2 3 x 2 = 3 3 x = x + 7 = x + 21 not x + 7; 3 x 5x + 7 = x + 7 = 3 5x 3 3 x + 21 = 5x 21 = 4 x 21 4 x = = x x 3 = 5x 3 Since the two sides of the equation are identical, the equation is true for any value of x. All real numbers are solutions x 2 = 5x 7 Subtracting 2 from a number and subtracting 7 from the same number will not result in equal numbers for any value of x. There is no solution. 82. answers may vary 84. answers may vary y 10 = 1.1y y = 1.1y + 22 From this we see that K = x + 4 = x x + 4 = 6 x 6 3 x + 24 = 2 x From this we see that K = answers may vary 32 Copyright 2017 Pearson Education, Inc.
12 ISM: Intermediate Algebra Chapter 2: Equations, Inequalities, and Problem Solving x x 3 = 6 x( x + 4) + x 2 7 x x 3 = 6 x x + x 2 7 x x 3 = 7 x x 2 x 3 = 24 x 3 = 22 x x = x( x + 1) + 16 = x( x + 5) x 2 + x + 16 = x 2 + 5x x + 16 = 5x 16 = 4 x x = y = y = Check: y = (5.217) = True x = x = x = x = 9.62 Check: 1.25x = (9.62) = 8.15 True Section 2.2 Practice Exercises 1. a. In words: first integer plus second odd integer plus third odd integer Translate: x + (x + 2) + (x + 4) Then x + (x + 2) + (x + 4) = x + x x + 4 = 3x + 6 b. In words: side + side + side + side Translate: x + 2x + (x + 2) + (2x 3) Then x + 2x + (x + 2) + (2x 3) = x + 2x + x x 3 = 6x 1 Copyright 2017 Pearson Education, Inc. 33
13 Chapter 2: Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra 2. If x = number of passengers at Los Angeles International Airport, in millions, then x = passengers at Chicago s O Hare airport, and 2x 31.9 = passengers at Atlanta s Hartsfield-Jackson airport. In words: passengers at + passengers + passengers at Los Angeles at O Hare Hartsfield-Jackson Translate: x + (x + 3.1) + (2x 31.9) Then x + (x + 3.1) + (2x 31.9) = x + x x 31.9 = 4x Let x = the first number, then 3x 8 = the second number, and 5x = the third number. The sum of the three numbers is 118. x + (3x 8) + 5x = 118 x + 3x + 5x 8 = x 8 = x = 126 x = 14 The numbers are 14, 3x 8 = 3(14) 8 = 34, and 5x = 5(14) = Let x = the original price. Then 0.4x = the discount. The original price, minus the discount, is equal to $270. x 0.4 x = x = 270 x = 270 = The original price was $ Let x = width, then 2x 16 = length. The perimeter is 160 inches. 2( x) + 2(2 x 16) = x + 4 x 32 = x 32 = x = 192 x = 32 2x 16 = 2(32) 16 = 48 The width is 32 inches and the length is 48 inches. 6. Let x = first odd integer, then x + 2 = second odd integer, and x + 4 = third odd integer. The sum of the integers is 81. x + ( x + 2) + ( x + 4) = 81 3x + 6 = 81 3x = 75 x = 25 x + 2 = 27 x + 4 = 29 The integers are 25, 27, and 29. Vocabulary, Readiness & Video Check % of a number > the number % of a number < the number. 34 Copyright 2017 Pearson Education, Inc.
14 ISM: Intermediate Algebra Chapter 2: Equations, Inequalities, and Problem Solving % of a number = the number % of a number > the number. First Integer All Described Integers 5. Four consecutive integers 6. Three consecutive odd integers 7. Three consecutive even integers 8. Four consecutive even integers 9. Three consecutive integers 10. Three consecutive even integers 11. Four consecutive integers 12. Three consecutive odd integers 31 31, 32, 33, , 33, , 20, , 94, 96, 98 y y, y + 1, y + 2 z (z is even) z, z + 2, z + 4 p p, p + 1, p + 2, p + 3 s (s is odd) s, s + 2, s distributive property 14. The original application asks you to find three numbers. The solution x = 45 only gives you the first number. You need to INTERPRET this result. Exercise Set The perimeter is the sum of the lengths of the four sides. x + ( x 5) + x + ( x 5) = x + x + x + x 5 5 = 4 x Let x = first odd integer, then x + 2 = second odd integer, and x + 4 = third odd integer. x + ( x + 2) + ( x + 4) = x + x + x = 3x Find the sum of y quarters worth 25 each, 7y dimes worth 10 each, and (2y 1) nickels worth 5 each. 25y + 10(7 y) + 5(2 y 1) = 105y 25y y + 10 y 5 The total amount is (105y 5) cents. 8. 4x + 5(3x 15) = 4x + 15x 75 = 19x The length of the side denoted by? is = 8. Similarly, the length of the unmarked side is (x + 14) (x + 8) = x + 14 x 8 = 6. The perimeter of the floor plan is 18 + (x + 8) (x + 14) = 2x + 64 Copyright 2017 Pearson Education, Inc. 35
15 Chapter 2: Equations, Inequalities, and Problem Solving 12. Let x = the number. 2( x + 3) = 5x 1 4 x 2 x + 6 = x 1 x = 7 The number is Let x = the first number, then x 6 = the second number, and 2x = the third number. x + ( x 6) + 2 x = x 6 = x = 312 x = 78 x 6 = 72 2x = 156 The numbers are 78, 72, and % of 70 = = = 7 7 million acres are not federally owned % of 881 = Approximately 284 tornadoes occurred in the United States during June Let x be the number of people employed in the restaurant industry. Then x is 10% of 147 million. x = 0.10(147 million) = 14.7 million There were 14.7 million people employed in the restaurant industry in the U.S. in From the circle graph, 39% of time is spent on role-specific tasks. 39% of 47 = An average worker would spend 18.3 hours on role-specific tasks. 24. The percents in the circle graph sum to 100% x x = 100 3x + 58 = 100 3x = 42 x = 14 2x = 2(14) = 28 28% of an average worker s time at work is spent on x + x + ( x + 10) = 180 5x + 10 = 180 5x = 170 x = 34 3x = 3(34) = 102 x + 10 = = 44 The angles measure 34, 44, and 102. ISM: Intermediate Algebra 28. (2 x) + (3.5x) + (3x + 7) = x + 7 = x = 68 x = 8 2x = 2(8) = x = 3.5(8) = 28 3x + 7 = 3(8) + 7 = 31 The sides measure 16 centimeters, 28 centimeters, and 31 centimeters x + (9.2 x 3) + 7.3x + (9.2 x 3) = x 6 = x = 330 x = x = 7.3(10) = x 3 = 9.2(10) 3 = 89 The sides measure 73 feet, 73 feet, 89 feet, and 89 feet. 32. Let x = the first odd integer, then x + 2 = the second odd integer and x + 4 = the third odd integer. x + x x + 4 = 327 3x + 6 = 327 3x = 321 x = 107 The numbers are 107, 109, Let x = first integer, then x + 1 = second integer, and x + 2 = third integer. x + ( x + 1) + 3( x + 2) = 2637 x + x x + 6 = x + 7 = x = 2630 x = 526 x + 1 = 527 x + 2 = 528 The score for Alabama was 526, for Louisiana was 527, and for Michigan was x + (3x 11) + (2 x + 11) = 66 x + 3x x + 11 = 66 6 x = 66 x = 11 3x 11 = 3(11) 11 = 22 2x + 11 = 2(11) + 11 = Copyright 2017 Pearson Education, Inc.
16 ISM: Intermediate Algebra Year Percent of Increase in Social Network Users Predicted Percent of Increase 2015 x 11% x 11 22% x % Total 66% 38. Let x be the decline in the number of travel agent jobs (in hundreds). Then x 17 is the decline in the number of reporter or correspondent jobs and 2x 21 is the decline in the number of flight attendant jobs. x + ( x 17) + (2 x 21) = 318 x + x x 21 = x 38 = 318 Chapter 2: Equations, Inequalities, and Problem Solving 44. Let x be the population in This population, decreased by 1.96%, is the 2014 population of 80.9 million. x x = x = 80.9 x 82.5 The population of Germany in 2004 was 82.5 million. 46. Let x be the size of the workforce prior to layoffs. 0.15x = 11, 000 x 73, 333 Prior to layoffs, Dana s workforce was 73,333 people. 48. Let x = measure of complement; then 2x + 30 = measure of angle. x + 2 x + 30 = 90 4 x = 356 3x = 60 x = 89 x = 20 x 17 = = 72 2x + 30 = 2(20) + 30 = 70 2x 21 = 2(89) 21 = 157 The angles measure 20 and 70. The predicted declines are: travel agent jobs: 89 hundred; 50. Let x = base angle; then 3x 10 = third angle. reporter or correspondent jobs: 72 hundred 2 x + 3x 10 = 180 flight attendant jobs: 157 hundred 5x 10 = Let x be the number of seats in Gillette Stadium. Then x + 11,200 is the number of seats in AT&T Stadium and x 3800 is the number of seats at CenturyLink Field. x + ( x + 11, 200) + ( x 3800) = 213, 800 x + x + 11, x 3800 = 213, 800 3x = 213, 800 3x = 206, 400 x = 68, 800 x + 11,200 = 68, ,200 = 80,000 x 3800 = 68, = 65,000 Gillette Stadium seats 68,800, AT&T Stadium seats 80,000, and CenturyLink Field seats 65, Let x be the price of the textbook before tax. x x = x = x The human anatomy book cost $ before tax. 5x = 190 x = 38 3x 10 = = 104 The angles measure 38, 38, and Let x = length of side of pentagon, then x + 7 = length of side of square. 5x = 4( x + 7) 5x = 4 x + 28 x = 28 x + 7 = = 35 The pentagon has a side length of 28 inches and the square has a side length of 35 inches. 54. Let x = first integer, then x + 1 = second integer, and x + 2 = third integer, and x + 3 = fourth integer. ( x + 1) + ( x + 3) = x + 4 = x = 106 x = 53 x + 1 = 54 x + 2 = 55 x + 3 = 56 The integers are 53, 54, 55, and 56. Copyright 2017 Pearson Education, Inc. 37
17 Chapter 2: Equations, Inequalities, and Problem Solving 56. Let x be the payroll for the Montreal Canadiens. Then x 5,049,585 was the payroll for the San Jose Sharks. x + ( x 5, 049, 585) = 129, 215, x 5, 049, 585 = 129, 215, x = 134, 265, 304 x = 67,132, 652 x 5, 049, 585 = 67,132, 652 5, 049, 585 = 62, 083, 067 The payroll for the Montreal Canadiens was $67,132,652 and the payroll for the San Jose Sharks was $62,083, Let x be the number of passengers at Los Angeles International Airport, in millions. Then x is the number of passengers at Chicago s O Hare airport, and 2x 31.9 is the number of passengers at Atlanta s Hartsfield- Jackson airport. x + ( x + 3.1) + (2 x 31.9) = x 28.8 = x = x = 63.7 x = = x 31.9 = 2(63.7) 31.9 = 95.5 The numbers of passengers are: Los Angeles: 63.7 million; Chicago: 66.8 million; Atlanta: 95.5 million 60. ( x + 2) + 2 x + x + (2 x 3) = x 1 = x = 111 x = 18.5 x + 2 = = x = 2(18.5) = 37 2x 3 = 2(18.5) 3 = 34 The bases measure 18.5 meters and 37 meters, and the sides measure 20.5 meters and 34 meters. 62. Let x be the energy cost of an LED bulb. Then x + 26 is the energy cost of a CFL bulb, and 6x + 18 is the energy cost of an incandescent bulb. x + ( x + 26) + (6 x + 18) = 476 8x + 44 = 476 8x = 432 x = 54 x + 26 = = 80 6x + 18 = 6(54) + 18 = 342 The energy costs are: LED bulb: $54 CFL bulb: $80 Incandescent bulb: $342 ISM: Intermediate Algebra 64. Let x be the number of medals won by the Netherlands. Then Canada won x + 1 medals and Norway won x + 2 medals. x + ( x + 1) + ( x + 2) = 75 3x + 3 = 75 3x = 72 x = 24 x + 1 = = 25 x + 2 = = 26 In the 2014 winter Olympics, the Netherlands won 24 medals, Canada won 25 medals, and Norway won 26 medals. 66. Let x = height, then 2x + 12 = length. 2( x) + 2(2 x + 12) = x + 4 x + 24 = x + 24 = x = 288 x = 48 2x + 12 = 2(48) + 12 = 108 The height is 48 inches and the length is 108 inches ab + 6bc = 0( 1) + 6( 1)(9) = 0 6(9) = 54 2n 2 + 3m 2 = 2( 2) 2 + 3(7) 2 = 2(4) + 3(49) = = lwh = 1 (37.8)(5.6)(7.9) = answers may vary 76. Let x be the measure of an angle. Then its complement measures (90 x) and its supplement measures (180 x). 180 x = 2(90 x) x = 180 2x x = x x = 230 x = 50 The angle measures y = 80.6x y = 80.6(17) The average number of cigarettes smoked by an American adult is predicted to be 684 in Copyright 2017 Pearson Education, Inc.
18 ISM: Intermediate Algebra 80. The average number of cigarettes smoked daily in 2017 is predicted to be This does not represent the average number of cigarettes smoked by an American smoker, because it is the average for all Americans, both smokers and non-smokers. 82. Let x be the first odd integer. Then x + 2 is the next consecutive odd integer. 7 x = 5( x + 2) x = 5x x = 5x x = x = 32 No such odd integers exist. R = C 60 x = 50 x x = 5000 x = x = 50(500) = 25, = 30, computer boards must be sold to break even. It costs $30,000 to produce the 500 boards. 86. The company makes a profit if it makes and sells more products than the break-even number. Section 2.3 Practice Exercises 1. I = PRT I = PRT PR PR I = T or T = PR I PR 2. 7 x 2 y = 5 7 x 2 y 7 x = 5 7 x 2 y = 5 7 x 2 y = 5 7 x 2 2 y = 7 x Chapter 2: Equations, Inequalities, and Problem Solving 3. A = P + Prt A P = P + Prt P A P = Prt A P Prt = Pt Pt A P A P = r or r = Pt Pt 4. Let P = 8000, r = 6% = 0.06, t = 4, n = 2. nt r A = P 1 + n A = A = 8000(1.03) 8 A 8000( ) A 10, Russ will have $10, in his account. 5. Let d = 190 and r = 7.5. d = rt 190 = 7.5t 190 = 7.5t = t 3 They spent 25 1 hours cycling, or 25 hours 3 20 minutes. Vocabulary, Readiness & Video Check x + y = 5 y = 5 2 x 2. 7 x y = 3 y = 3 7 x y = x or y = 7 x 3 3. a 5b = 8 a = 5b r + s = 10 s = 10 7r 5. 5 j + k h = 6 5 j + k = h + 6 k = h 5 j + 6 Copyright 2017 Pearson Education, Inc. 39
19 Chapter 2: Equations, Inequalities, and Problem Solving 6. w 4 y + z = 0 w + z = 4 y z = 4 y w 7. That the specified variable will equal some expression and that this expression should not contain the specified variable. 8. The only way to check the solution is in the formula used, because if the wrong formula is used, a wrong answer may seem to check correctly. Exercise Set W = gh W = gh h h W = g 10. y = mx + b y b = mx y b mx = m m x = y b m A = Prt + P A = P(rt + 1) A P(rt + 1) = rt + 1 rt + 1 A P = rt + 1 A = 5H (b + B) A = 5Hb + 5HB A 5HB = 5Hb A 5HB = 5Hb ISM: Intermediate Algebra h 5H 5H g = W h 4. V = lwh V lwh = wh wh 16. A 5HB = b 5H b = A 5HB 5H S = 2πr 2 + 2πrh V = l S 2 r 2 2 rh wh π = π l = V S 2πr 2 2πrh = wh 6. 2 x + 3y = 17 2 x + 3y 2 x = 17 2 x 3y = 17 2 x 3y = 17 2 x 2πr S 2πr 2 2πr h = = h 2πr S 2πr 2 2πr 3 3 y = 17 2 x 3 8. A = 3M 2 N A + 2N = 3M 2N = 3M A 2 N = 3M A 2 2 N = 3M A A = P(1 + rt) A = P + Prt A P = Prt A P Prt = Pr Pr A P = t Pr t = A P Pr
20 Intermediate Algebra 7th Edition Martin Gay SOLUTIONS MANUAL Full download at: Intermediate Algebra 7th Edition Martin Gay TEST BANK Full download at: intermediate algebra 7th edition pdf intermediate algebra 7th edition answers intermediate algebra 7th edition access code intermediate algebra 7th edition pdf free intermediate algebra 7th edition pearson beginning algebra 7th edition pdf beginning algebra 7th edition martin-gay pdf intermediate algebra martin-gay 6th edition
Chapter w. 5. a. 3(2x 7) = 3(2x) + 3( 7) = 6x a. 4(9x + 1) + 6 = 36x = 36x Subtract 7x 1 from 2x + 3 translates to
Chapter Section. Practice Exercises. a. The numerical coefficient of t is, since t is t. b. The numerical coefficient of x is. c. The numerical coefficient of since w means w. d. The numerical coefficient
More informationPearson Learning Solutions
Answers to Selected Exercises CHAPTER REVIEW OF REAL NUMBERS Section.. a. b. c.. a. True b. False c. True d. True. a. b. Ú c.. -0. a. b. c., -, - d.,, -, -, -.,., - e. f.,, -, -,, -.,., -. a. b. c. =.
More information1.4 Properties of Real Numbers and Algebraic Expressions
0 CHAPTER Real Numbers and Algebraic Expressions.4 Properties of Real Numbers and Algebraic Expressions S Use Operation and Order Symbols to Write Mathematical Sentences. 2 Identify Identity Numbers and
More informationCHAPTER 2 Solving Equations and Inequalities
CHAPTER Solving Equations and Inequalities Section. Linear Equations and Problem Solving........... 8 Section. Solving Equations Graphically............... 89 Section. Comple Numbers......................
More informationChapter 1. Worked-Out Solutions. Chapter 1 Maintaining Mathematical Proficiency (p. 1)
Chapter Maintaining Mathematical Proficiency (p. ). + ( ) = 7. 0 + ( ) =. 6 + = 8. 9 ( ) = 9 + =. 6 = + ( 6) = 7 6. ( 7) = + 7 = 7. 7 + = 8. 8 + ( ) = 9. = + ( ) = 0. (8) =. 7 ( 9) = 6. ( 7) = 8. ( 6)
More information2.1 Simplifying Algebraic Expressions
.1 Simplifying Algebraic Expressions A term is a number or the product of a number and variables raised to powers. The numerical coefficient of a term is the numerical factor. The numerical coefficient
More informationMassachusetts Tests for Educator Licensure (MTEL )
Massachusetts Tests for Educator Licensure (MTEL ) BOOKLET 2 Mathematics Subtest Copyright 2010 Pearson Education, Inc. or its affiliate(s). All rights reserved. Evaluation Systems, Pearson, P.O. Box 226,
More informationMath 101, Basic Algebra. Solving Linear Equations and Inequalities
Math 101, Basic Algebra Author: Debra Griffin Name Chapter 2 Solving Linear Equations and Inequalities 2.1 Simplifying Algebraic Expressions 2 Terms, coefficients, like terms, combining like terms, simplifying
More informationChapter 1 ( )? Chapter 1 Opener. Section 1.1. Worked-Out Solutions. 2π π = π. Try It Yourself (p. 1) So, x = 95.3.
Chapter Chapter Opener Try It Yourself (p. ). + ( ) 7.. + 8. ( ) +. 7. ( 7) + 7 7. 8 () 0 + 8. 7. ( 7) 8 0.. 8. Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees). a. The sum of the
More information4. Smaller cylinder: r = 3 in., h = 5 in. 6. Let 3x the measure of the first angle. Let x the measure of the second angle.
Chapter : Linear Equations and Inequalities in One Variable.6 Check Points. A, b A bh h h h The height of the sail is ft.. Use the formulas for the area and circumference of a circle. The radius is 0 ft.
More informationEquations and Solutions
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and
More informationCopyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. + + 0 The solution set is [0, ).. () The solution set is [, ). 0. >.. > >. The solution set is (., ).. The solution set
More informationTurn to Section 4 of your answer sheet to answer the questions in this section.
Math Test Calculator MINUTES, QUESTIONS Turn to Section of your answer sheet to answer the questions in this section. For questions -, solve each problem, choose the best answer from the choices provided,
More information4 and m 3m. 2 b 2ab is equivalent to... (3 x + 2 xy + 7) - (6x - 4 xy + 3) is equivalent to...
NAME: SCORE: Find the answer choice that best answers the question. Write your answer choice in the blank provided beside each question. You must show all work necessary to solve the problem to receive
More informationWithout actually dividing the number, is the number divisible by 2, 3, and/ or 5? Why?
Math 40 Final Exam Review Part I No Calc 1. (2 pts) Round the number 38,756 to the nearest thousand. 2. (6 pts ) Consider the whole number 312. Without actually dividing the number, is the number divisible
More informationSolutions to Practice Problems in the Text
Solutions to Practice Problems in the Text Chapter One: Fundamentals of Mathematical Modeling Practice Set 1-1. d = rt 1 = 0t [Divide both sides by 0.] t =. hours. d = rt 170 = r(.) [Divide both sides
More informationSection 2.1 Objective 1: Determine If a Number Is a Solution of an Equation Video Length 5:19. Definition A in is an equation that can be
Section 2.1 Video Guide Linear Equations: The Addition and Multiplication Properties of Equality Objectives: 1. Determine If a Number Is a Solution of an Equation 2. Use the Addition Property of Equality
More information6. 5x Division Property. CHAPTER 2 Linear Models, Equations, and Inequalities. Toolbox Exercises. 1. 3x = 6 Division Property
CHAPTER Linear Models, Equations, and Inequalities CHAPTER Linear Models, Equations, and Inequalities Toolbox Exercises. x = 6 Division Property x 6 = x =. x 7= Addition Property x 7= x 7+ 7= + 7 x = 8.
More informationWRITING EQUATIONS through 6.1.3
WRITING EQUATIONS 6.1.1 through 6.1.3 An equation is a mathematical sentence that conveys information to the reader. It uses variables and operation symbols (like +, -, /, =) to represent relationships
More informationCONTINUE. Feeding Information for Boarded Pets. Fed only dry food 5. Fed both wet and dry food 11. Cats. Dogs
1 Feeding Information for Boarded Pets Cats Dogs Total Fed only dry food 5 7 Fed both wet and dry food 11 3 34 Total The table above shows the kinds of foods that are fed to the cats and dogs currently
More informationChapter 2 Homework Support Pages 2-A1 Writing Equations Pages The quotient of t and forty is the same as twelve minus half of s.
Chapter Homework Support Pages Algebra 1H -A1 Writing Equations Pages 7-7 Translate each sentence into an equation. (See Example 1 and Study Tip on page 70.) 1. The sum of twice r and three times s is
More informationMy Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
More information(A) 20% (B) 25% (C) 30% (D) % (E) 50%
ACT 2017 Name Date 1. The population of Green Valley, the largest suburb of Happyville, is 50% of the rest of the population of Happyville. The population of Green Valley is what percent of the entire
More informationSY14-15 Algebra Exit Exam - PRACTICE Version
Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your
More information2.1 Solving Equations Using Properties of Equality Math 085 Chapter 2. Chapter 2
2.1 Solving Equations Using Properties of Equality Math 085 Chapter 2 Chapter 2 2.1 Solving Equations Using Properties of Equality 2.2 More about Solving Equations 2.3 Application of Percent 2.4 Formulas
More informationApplications of Quadratic Equations
33 Chapter 6 Quadratic Equations and Inequalities Section 6. Applications of Quadratic Equations. Verbal model: Selling price per doz eggs.6 Number eggs sold Number eggs purchased 6.6 6.6.3 6.6 9.6.6.3.8
More informationQUESTIONS 1-46 REVIEW THE OBJECTIVES OF CHAPTER 2.
MAT 101 Course Review Questions Valid for Fall 2014, Spring 2015 and Summer 2015 MIDTERM EXAM FINAL EXAM Questions 1-86 are covered on the Midterm. There are 25 questions on the midterm, all multiple choice,
More informationEx: Determine if the following are true or false. Ex: Determine whether 4 is a solution of x + 6 = 10
2.1 Solving Equations Using Properties of Equality True and False Equations Ex: Determine if the following are true or false. 1) 3 + 4 = 7 2) 3 + 4 = 8 3) x + 6 = 10 Ex: Determine whether 4 is a solution
More informationThe ACCUPLACER (Elementary Algebra) is a 12 question placement exam. Its purpose is to make sure you are put in the appropriate math course.
About the ACCUPLACER Test The ACCUPLACER (Elementary Algebra) is a 12 question placement exam. Its purpose is to make sure you are put in the appropriate math course. A student whose score is 67 or higher
More informationSection 2.1 Solving Linear Equations Part I: Addition Property of Equality
Section 2.1 Solving Linear Equations Part I: Addition Property of Equality What is a Linear Equation? Definitions A linear equation in one variable can be written in the form A, B and C, with A 0. The
More informationWesterly High School. Math Department. Summer Packet
Westerly High School Math Department Summer Packet for students entering their JuniorSenior Year Summer Note: Enclosed, students will find a most recent SAT Non-Calculator Practice Test via The College
More informationChapter 1. Chapter 1 Opener. Section 1.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 1) x = g =
Chapter Chapter Opener Try It Yourself (p. ) m m + m + m m.. g + g g + g. + g g 0 y + y y a a + a... + ( n.). + ( n) + (.). + n. n +.. n.. k + ( k) k + + ( k) k + k k k + k + k +. + ( ).. + 0. ( ) + Section..
More informationMATH 0030 Lecture Notes Section 2.1 The Addition Property of Equality Section 2.2 The Multiplication Property of Equality
MATH 0030 Lecture Notes Section.1 The Addition Property of Equality Section. The Multiplication Property of Equality Introduction Most, but not all, salaries and prices have soared over the decades. To
More informationSAT & ACT Foundations
E SAT & ACT Foundations SA M PL MATHEMATICS (800) MY TUTOR Focusing on the Individual Student MYTUTOR.COM Copyright Statement The ACT & SAT Skills Book, along with all Summit Educational Group Course Materials,
More informationMath 0301 Course Review. 1) 8 less the quotient of 52 and 4. 2) The product of 7 and 25. 9) 5x 3.2y + 6.8z 1.1x + 0.2y 10) (11x 9) (43x 2)
Simplify: Math Course Review ) 8 less the quotient of and. ) The product of 7 and. (7)( )() ) 9 less than the product of and 8. ) ( 8) ( ) ) 7(8) ( [ 9]) ) 9 { 8[ ()] + } 7) 7 ( ) ( ) 8) 9 ( ) + 7 9) x.y
More informationEquations, Inequalities, and Problem Solving
CHAPTER Equations, Inequalities, and Problem Solving. Linear Equations in One Variable. An Introduction to Problem Solving. Formulas and Problem Solving.4 Linear Inequalities and Problem Solving Integrated
More informationFull file at
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) b + 17 = 11 1) 28 28 C) 6 6 2) 1 = b + 6 2) 7 5 C) 7 5 3) t 7 = 12 3) 5 19
More informationChapter 3. Equations and Inequalities. 10/2016 LSowatsky 1
Chapter 3 Equations and Inequalities 10/2016 LSowatsky 1 3-1B Write Equations Main Idea: Write algebraic equations from verbal sentences and problem situations. LSowatsky 2 Vocabulary: Equation mathematical
More informationChapter 1-2 Add and Subtract Integers
Chapter 1-2 Add and Subtract Integers Absolute Value of a number is its distance from zero on the number line. 5 = 5 and 5 = 5 Adding Numbers with the Same Sign: Add the absolute values and use the sign
More informationName: Class: Date: ID: A
Name: Class: Date: ID: A 6A Short Answer Solve the equation. 1.!5d! 24 =!4(d + 6)! d Write the inequality for the graph. 2. 3. 4. 5. Solve the inequality. 6. p + 7
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers
More informationThis is Solving Linear Systems, chapter 3 from the book Advanced Algebra (index.html) (v. 1.0).
This is Solving Linear Systems, chapter 3 from the book Advanced Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
More informationSection 10.1 Radical Expressions and Functions. f1-152 = = = 236 = 6. 2x 2-14x + 49 = 21x = ƒ x - 7 ƒ
78 CHAPTER 0 Radicals, Radical Functions, and Rational Exponents Chapter 0 Summary Section 0. Radical Expressions and Functions If b a, then b is a square root of a. The principal square root of a, designated
More information5-2 Dividing Polynomials. Simplify. ANSWER: 4y + 2x (3a 2 b 6ab + 5ab 2 )(ab) 1 ANSWER: 3a + 5b (x 2 6x 20) (x + 2) ANSWER:
1. 4y + 2x 2 8. (10x 2 + 15x + 20) (5x + 5) 2. (3a 2 b 6ab + 5ab 2 )(ab) 1 3a + 5b 6 9. (18a 2 + 6a + 9) (3a 2) 3. (x 2 6x 20) (x + 2) 10. 4. (2a 2 4a 8) (a + 1) 11. 5. (3z 4 6z 3 9z 2 + 3z 6) (z + 3)
More informationMultiplication and Division
UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac
More informationCHAPTER 1 Equations and Inequalities
CHAPTER Equations and Inequalities Section. Linear Equations... Section. Mathematical Modeling...6 Section. Quadratic Equations... Section.4 The Quadratic Formula...9 Mid-Chapter Quiz Solutions...4 Section.
More informationMATHCOUNTS State Competition Countdown Round Problems This section contains problems to be used in the Countdown Round.
MATHCOUNTS 2011 State Competition Countdown Round Problems 1 80 This section contains problems to be used in the Countdown Round. National Sponsors Raytheon Company * National Defense Education Program
More informationCHAPTER 8 Quadratic Equations, Functions, and Inequalities
CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER Use the diagram below. 9.3 cm. A = (9.3 cm) (6.2 cm) = cm 2. 6.
1. Use the diagram below. 9.3 cm A = (9.3 cm) (6.2 cm) = 57.66 cm 2 6.2 cm A rectangle s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle s area rounded to the correct number of significant
More information2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution x + 2 = 4x + 38 ANSWER: 4 ANSWER:
1. 13x + 2 = x + 38 9. MULTIPLE CHOICE Find the value of x so that t figures have the same perimeter. 2. 3. 6(n + ) = 18 7. 7 = 11 + 3(b + 5) 1 5. 5 + 2(n + 1) = 2n 6. 7 3r = r (2 + r) 7. 1v + 6 = 2(5
More informationLesson 7: Literal Equations, Inequalities, and Absolute Value
, and Absolute Value In this lesson, we first look at literal equations, which are equations that have more than one variable. Many of the formulas we use in everyday life are literal equations. We then
More information2-1 Writing Equations
Translate each sentence into an equation. 1. Three times r less than 15 equals 6. Rewrite the verbal sentence so it is easier to translate. Three times r less than 15 equals 6 is the same as 15 minus 3
More informationExample 1: Twenty-six less than three times a number is the same as the sum of negative two and five times the number. Find the number.
Section 2.4 continued : Application Problems Tips for solving application problems 1. Read the entire problem. What are you trying to find? What information is given? 2. Plan your approach to the problem.
More informationSolving for a Variable
2- Solving for a Variable Objectives Solve a formula for a given variable. Solve an equation in two or more variables for one of the variables. Vocabulary formula literal equation Who uses this? Athletes
More informationEquations, Inequalities, and Problem Solving
For use by Palm Beach State College only. Chapter Equations, Inequalities, and Problem Solving. Simplifying Algebraic Expressions. The Addition Property of Equality. The Multiplication Property of Equality.4
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.1) Examine the dotplots below from three sets of data Set A
1. (1.1) Examine the dotplots below from three sets of data. 0 2 4 6 8 10 Set A 0 2 4 6 8 10 Set 0 2 4 6 8 10 Set C The mean of each set is 5. The standard deviations of the sets are 1.3, 2.0, and 2.9.
More informationTopic 1. Solving Equations and Inequalities 1. Solve the following equation
Topic 1. Solving Equations and Inequalities 1. Solve the following equation Algebraically 2( x 3) = 12 Graphically 2( x 3) = 12 2. Solve the following equations algebraically a. 5w 15 2w = 2(w 5) b. 1
More informationReview: Expressions and Equations
Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number
More information1.2 Algebraic Expressions and Sets of Numbers
Section. Algebraic Expressions and Sets of Numbers 7. Algebraic Expressions and Sets of Numbers S Identify and Evaluate Algebraic Expressions. Identify Natural Numbers, Whole Numbers, Integers, and Rational
More informationALGEBRA 1 FINAL EXAM TOPICS
ALGEBRA 1 FINAL EXAM TOPICS Chapter 2 2-1 Writing Equations 2-2 Solving One Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations with the Variable on Each Side 2-5 Solving Equations Involving
More informationINTERMEDIATE ALGEBRA REVIEW FOR TEST 1
INTERMEDIATE ALGEBRA REVIEW FOR TEST 1 Write the set using the roster method. 1) a) { is a counting number less than 7} b) { is a whole number between 4 and 8} Let A = {0, 2, 4, 6, 8, }, B = {0,, 6, 9},
More informationName Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
More informationProblems About Combining Problems About Separating (page 59)
LESSON Name 11 Problems About Combining Problems About Separating (page 59) Story problems have patterns. Addition Pattern Subtraction Pattern Teacher Note: Review Hint #1, Word Problem Cues. + some +
More informationMath 40 Chapter 2 Lecture Notes. Professor Miguel Ornelas
Math 40 Chapter 2 Lecture Notes Professor Miguel Ornelas 1 M. Ornelas Math 40 Lecture Notes Section 2.1 Section 2.1 Addition and Multiplication Properties of Equality Addition Property of Equality If A
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationMATH 410 Notes Simplifying Algebraic Expressions
MATH 410 Notes 2016 1.9 - Simplifying Algebraic Expressions Commutative Property: a + b = b + a and a b = b a Associative Property: a + (b + c) = (a + b) + c and a (b c) = (a b) c Distributive Property:
More informationArithmetic Review 1. Solve Solve: = =
Arithmetic Review 1 Simplify: 1. -15 (-6) Solve 1. 5.6 (.1)=. - * -7 1..4 (.)=. 7 9 14. 9 1 = 4. 16 (-4) * 6 15. 7 = 9 5. ( 49 * 6 * 16 ) 10 6. 17 0 = Solve: 1 1 16. 5 + = 7. 1 + 50 Solve 1. + = 15 5 9.
More informationChapter 1 Functions and Graphs. ( x x ) ( y y ) (1 7) ( 1 2) x x y y 100. ( 6) ( 3) x ( y 6) a. 101.
Chapter Functions and Graphs... ( ) ( y y ) ( 7) ( ) y y y ( 6) ( ) 6 9 5 5 6y 6y 6y9 9 ( y ) y y Solution set:. 5. a. h, k 6, r ; ( ) [ y( 6)] ( ) ( y6) ( y6) b. ( ) ( y) [ ( )] ( y) So in the standard
More informationAlgebra I Midterm Exam Review
Chapter 1: Expressions, Equations, and Functions Lesson 1.1 Variables and Expressions Write a verbal expression for each algebraic expression. 23f 5m 2 + 2c 3 4n 1 7 Write an algebraic expression for each
More information[1] [2.3 b,c] [2] [2.3b] 3. Solve for x: 3x 4 2x. [3] [2.7 c] [4] [2.7 d] 5. Solve for h : [5] [2.4 b] 6. Solve for k: 3 x = 4k
1. Solve for x: 4( x 5) = (4 x) [1] [. b,c]. Solve for x: x 1.6 =.4 +. 8x [] [.b]. Solve for x: x 4 x 14 [] [.7 c] 4. Solve for x:.x. 4 [4] [.7 d] 5. Solve for h : 1 V = Ah [5] [.4 b] 6. Solve for k: x
More informationFoundations of High School Math
Foundations of High School Math This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to
More informationReady To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting
Ready To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting Find these vocabulary words in Lesson 2-1 and the Multilingual Glossary. Vocabulary equation solution of an equation Solve
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationSolve each absolute value equation x 7 = x 9 = (3x 12) = - 12
Solve each absolute value equation. 16. 3x 7 = 11 17. - 4 x 9 = - 16 18. 2(3x 12) = - 12 19. Explain why there can be one, two or no solutions to an absolute value equation. 5. Solve each equation for
More informationMATH 410 Notes Simplifying Algebraic Expressions
MATH 410 Notes 2015 1.9 - Simplifying Algebraic Expressions Commutative Property: a + b = b + a and a b = b a Associative Property: a + (b + c) = (a + b) + c and a (b c) = (a b) c Distributive Property:
More informationQuadratic Applications Name: Block: 3. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
Quadratic Applications Name: Block: This problem packet is due before 4pm on Friday, October 26. It is a formative assessment and worth 20 points. Complete the following problems. Circle or box your answer.
More informationMini-Lecture 2.1 Simplifying Algebraic Expressions
Copyright 01 Pearson Education, Inc. Mini-Lecture.1 Simplifying Algebraic Expressions 1. Identify terms, like terms, and unlike terms.. Combine like terms.. Use the distributive property to remove parentheses.
More informationPractice Math Exam. Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Math Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the angle of rotation in the figure? a. 30 c. 90 b. 60 d. 120 2. The image shown
More informationChapter 2. Worked-Out Solutions. Chapter 2 Mathematical Practices (p. 52) Chapter 2 Maintaining Mathematical Proficiency (p. 51)
Chapter Chapter Maintaining Mathematical Proficiency (p. ). 6 8 Chapter Mathematical Practices (p. ). x + < x. x > x +.. = 6. =. The solution is x .. x + x +. + = + =. = = 6. + =
More informationName: Hour Date. Chapter 1 Checklist. Section Assignment Date Signature. Chapter 1 Vocabulary. Video 1-1A and notes
Name: Hour Date Chapter 1 Checklist Section Assignment Date Signature Chapter 1 Vocabulary 1-1: Expressions and Formulas Video 1-1A and notes Practice - p. 7: #13, 15, 17, 19, 21, 23 Video 1-1B and notes
More informationCP Algebra 2. Summer Packet. Name:
CP Algebra Summer Packet 018 Name: Objectives for CP Algebra Summer Packet 018 I. Number Sense and Numerical Operations (Problems: 1 to 4) Use the Order of Operations to evaluate expressions. (p. 6) Evaluate
More informationALGEBRA I EOC REVIEW PACKET Name 16 8, 12
Objective 1.01 ALGEBRA I EOC REVIEW PACKET Name 1. Circle which number is irrational? 49,. Which statement is false? A. a a a = bc b c B. 6 = C. ( n) = n D. ( c d) = c d. Subtract ( + 4) ( 4 + 6). 4. Simplify
More information14. The quotient of t and forty is the same as twelve minus half of s. 16. The sum of one-third a number and 25 is as much as twice the number.
Lesson -1 p. 74-7, Translate each sentence into an equation. (See Example 1 and Study Tip on page 70.) 1. The sum of twice r and three times s is identical to thirteen. 14. The quotient of t and forty
More information15. (,4)
CHAPTER Algebra Toolbox CHAPTER Functions Graphs, and Models; Linear Functions Toolbox Exercises. {,,,,5,6,7,8} and { xx< 9, x N} Remember that x N means that x is a natural number.. (,7]. (,7 ] 5. (,)
More information3 x 2 x 2. Algebraic Equation
33337_020.qxp 2/27/06 :0 AM Page 66 66 Chapter 2 Solving Equations and Inequalities 2. Linear Equations and Problem Solving Equations and s of Equations An equation in x is a statement that two algebraic
More information2015 Practice Test #1
Practice Test # Preliminary SATNational Merit Scholarship Qualifying Test IMPORTANT REMINDERS A No. pencil is required for the test. Do not use a mechanical pencil or pen. Sharing any questions with anyone
More informationIntroduction. Table of contents
Introduction The advanced manufacturing sector is changing. New innovative and digital technologies are constantly being developed. Today s and tomorrow s employees need the right kind of mathematical
More informationUNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS
UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS This unit investigates quadratic functions. Students study the structure of quadratic expressions and write quadratic expressions in equivalent forms.
More informationACCUPLACER Sample Questions for Students
ACCUPLACER Sample Questions for Students 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College Board. All other products and services may
More informationWork. Work. Work. Directions: Choose the best answer. Answer ALL questions. Show ALL work in column 2. If. Common Core Algebra I Regents Review #2
Name Date Due: Common Core Algebra I Regents Review #2 Directions: Choose the best answer. Answer ALL questions. Show ALL work in column 2. If there is no mathematical work to be shown, write an explanation
More informationCHAPTER 1 Functions Graphs, and Models; Linear Functions. Algebra Toolbox Exercises. 1. {1,2,3,4,5,6,7,8} and
CHAPTER Algebra Toolbox CHAPTER Functions Graphs, and Models; Linear Functions Algebra Toolbox Exercises. {,,,4,,6,7,8} and { xx< 9, x } Remember that x means that x is a natural number.. Yes.. Yes. Every
More information2.5 Compound Inequalities
Section.5 Compound Inequalities 89.5 Compound Inequalities S 1 Find the Intersection of Two Sets. Solve Compound Inequalities Containing and. Find the Union of Two Sets. 4 Solve Compound Inequalities Containing
More informationSTUDENT NAME DATE PERIOD. Math Algebra I. Read each question and choose the best answer. Be sure to mark all of your answers.
FORMTIVE MINI SSESSMENT Third Grading Period 009-0 February -5 STUENT NME TE PERIO Math lgebra I Read each question and choose the best answer. Be sure to mark all of your answers. Simplify this expression:
More informationAlgebra Readiness. Curriculum (445 topics additional topics)
Algebra Readiness This course covers the topics shown below; new topics have been highlighted. Students navigate learning paths based on their level of readiness. Institutional users may customize the
More informationEx: Determine if the following are true or false. Ex: Determine whether 4 is a solution of x + 6 = 10
21 Solving Equations Using Properties of Equality True and False Equations Ex: Determine if the following are true or false 1) 3 + 4 7 True 2) 3 + 4 8 False 3) x + 6 10 Sometimes Sometimes x 4 : 4+610
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationCheck 4. Substitute n = 1 in each equation. a) P = 2n b) P = 3n = 2(1) = 3(1) = 2 = 3
Lesson 4.1 Writing Equations to Describe Patterns Practice (pages 154 162) Check 4. Substitute n = 1 in each equation. a) P = 2n b) P = 3n = 2(1) = 3(1) = 2 = 3 c) P = 4n d) P = 5n = 4(1) = 5(1) = 4 =
More informationgraphs, Equations, and inequalities 2
graphs, Equations, and inequalities You might think that New York or Los Angeles or Chicago has the busiest airport in the U.S., but actually it s Hartsfield-Jackson Airport in Atlanta, Georgia. In 010,
More information2-1 More on Solving Equations Wednesday, May 26, :22 PM
2-1 More on Solving Equations Wednesday, May 26, 2010 12:22 PM Objective: Students will solve basic equations Remember: Algebra is an Arabic word meaning: to "undo" and "balance" Solve: Solve b. Chapter
More informationCh 1. The Language of Algebra
Ch 1 The Language of Algebra 1-1 Writing Expressions and Equations Writing Expressions Buying CDs: 1 CD = $15 2 CD = $15 x 2 3 CD = $15 x 3 n number of CDs? $15 x n Algebraic Expression Writing Expressions
More information