21. Output = Input  − 1 cap output , equals , cap input , minus 1

23. 40 25. add 6 or 6n; 30, 36, 42 27. add 3, then add 4, then add 5, and so on; 21, 28, 36 29. multiply by 3; 243, 729, 2187 31. The black square and dot each move clockwise one block

Image Long Description

33. 9216  in. 3 9216 . in. cubed 35. n + 10, where n is the number of months 37. 21 ; 4 n + 1 21 semicolon 4 n plus 1 39. − 13 ; 7 − 4 n ;  or  − 4 n + 7 negative 13 semicolon 7 minus 4 n semicolon , or , minus 4 n plus 7 46. 1.9 47. − 3 . 8 negative 3 . 8 48. 27 49. 0 50. − 0.4 negative 0.4 51. 7 52. 50% 53. 25% 54. 33.33% 55. 140% 56. 172% 57. 123%

Lesson 1-2 pp. 11-17

Got It? 1. rational numbers

2.

3. a. 26 < 6.25 square root of 26 less than , 6.25 or 6.25 > 26 6.25 , greater than square root of 26 b. a < c ; eh less than c semicolon a will be to the left of c on the number line.

4. a. Distr. Prop.

b. a + [ 3 + ( − a ) ]     = a + [ ( − a ) + 3 ] Comm.   = [ a + ( − a ) ] + 3 Assoc.   = 0 + 3 Inverse   = 3 Identity table with 5 rows and 3 columns , row1 column 1 , eh , column 2 plus left bracket 3 plus open negative eh close right bracket , column 3 , row2 column 1 , , column 2 equals eh plus left bracket open negative eh close plus 3 right bracket , column 3 cap comm. , row3 column 1 , , column 2 equals left bracket eh plus open negative eh close right bracket plus 3 , column 3 cap assoc. , row4 column 1 , , column 2 equals 0 plus 3 , column 3 cap inverse , row5 column 1 , , column 2 equals 3 , column 3 cap identity , end table

Lesson Check 1. Answers may vary. Sample: the number of times a cricket chirps 2. Answers may vary. Sample: the change in number of people on a bus after a stop 3. Answers may vary. Sample: the outdoor temperature in tenths of a degree. 4. Inv. Prop. of Add. 5. Assoc. Prop. of Mult. 6. multiplicative inverse 7. Both properties result in the original term; 0 is the additive identity, whereas 1 is the multiplicative identity. 8. The equation illustrates the Comm. Prop. of Add. 9. Answers may vary. Sample: 2 square root of 2 is not a rational number because it cannot be written as a quotient of integers.

Exercises 11. y, natural numbers; p, rational numbers

13.

15.

17.

19.

21.

23. > greater than 25. < less than 27. > greater than 29. > greater than 31. > greater than 33. < less than 35. Distr. Prop. 37. Assoc. Prop. of Mult. 39. Ident. Prop. of Add. 41–48. Answers may vary. Samples are given. 41. − 5 negative 5 43. − 1 1 4 negative , 1 , and 1 fourth 45. 1 2 3 1 , and 2 thirds 47. 4 49. 50  in . × 50  in . × 50  in . square root of 50 , in . . times . square root of 50 , in . times square root of 50 , in . 51. natural numbers 53. irrational numbers 55. irrational numbers 57. 8, 1, 1 3 , − 2 , − 3 1 third , comma minus square root of 2 comma minus 3 59. 5.73, 1 4 , − 0.06 , − 3 3 , − 17 1 fourth , comma minus , 0.06 , comma , negative 3 square root of 3 , comma negative 17 61. Answers may vary. Sample: 7 63. Answers may vary. Sample: 2 square root of 2 and 2 square root of 2 75. add 4; 20, 24, 28 76. add 1; 12, 13, 14 77. add 1; 0, 1, 2 78. 2 1 4 2 , and 1 fourth 79. 11 2 3 11 , and 2 thirds 80. 1 1 2 1 , and 1 half 81. 5 82. 38 83. 15

Lesson 1-3 pp. 18-24

Got It? 1. H 2. 150 − 2 d , 150 minus 2 d comma with d = d equals the number of days 3. a. 18 b. Yes; the numerator will become 2 x 2 − y 2 , 2 x squared , minus , y squared , comma not 2 x 2 − 2 y 2 . 2 x squared , minus 2 , y squared , . 4. Let x = x equals the number of two-point shots, y = y equals the number of three-point shots, z = z equals the number of one-point free throws. 2 x + 3 y + 1 z ; 2 x plus 3 y plus 1 z semicolon 42 points 5. a. − 3 j 2 − 7 k + 5 j negative 3 , j squared , minus 7 k plus 5 j b. 12 a − 53 b 12 eh minus 53 b

Lesson Check 1. 2 + b 3 fraction 2 plus b , over 3 end fraction 2. 4 k + m 4 k plus m 3. 12 4. 13 5. − 5 negative 5 6. − 5 negative 5 7. The student did not distribute the − 1 . 3 p 2 q + 2 p − ( 5 q + p − 2 p 2 q ) = 3 p 2 q + 2 p − 5 q − p + 2 p 2 q = 5 p 2 q + p − 5 q negative 1 . , 3 p squared , q plus 2 p minus open 5 q plus p minus , 2 p squared , q close equals , 3 p squared , q plus 2 p minus 5 q minus p plus , 2 p squared , q equals , 5 p squared , q plus p minus 5 q 8. A constant is a term with no variables, whereas a coefficient is the numerical factor in a term. 9. Answers may vary. Sample: Both algebraic expressions and numerical expressions represent a quantity using numbers, operations and grouping symbols. An algebraic expression includes variables when representing a quantity. Examples: numerical expression: 3 + 6 ( 5 − 2 ) ; 3 plus 6 open 5 minus 2 close semicolon algebraic expression: 2 z + 3 z ( 6 + 5 z ) . 2 z plus 3 z open 6 plus 5 z close .

Exercises 11. 8 ( x + 3 ) 8 open x plus 3 close 13. 130 − 10 w , 130 minus 10 w comma with w = w equals number of weeks 15. 250 − 60 w , 250 minus 60 w comma with w = w equals number of weeks 17. − 16 negative 16 19. − 12 negative 12 21. 4 ft 23. 1600 ft 25. $1331 27. $1610.51 29. Let x = x equals the number of 3-run home runs and y = y equals the number of 2-run hits; 3x + 2y; 14 31. 2 s + 5 2 s plus 5 33. 6 a + 3 b 6 eh plus 3 b 35. − 0.5 x negative 0.5 x 37. 4 g − 2 4 g minus 2 39. 3 41. 37 43. 10 45. $ 84 m fraction dollars 84 , over m end fraction 47. 5 x 2 2 fraction 5 , x squared , over 2 end fraction 49. y 51. − 2 x 2 + 2 y 2 negative 2 , x squared , plus , 2 y squared 53. 8 . 5 x − 15 8 . 5 x minus 15 55. No; John did not use the opposite of a sum correctly; − ( x + y ) + 3 ( x − 4 y ) ; − x − y + 3 x − 12 y ; 2 x − 13 y negative open x plus y close plus 3 open x minus 4 y close semicolon negative x minus y plus 3 x minus 12 y semicolon 2 x minus 13 y 57. Distr. Prop. 59. Opposite of a Difference 67. − 1 . 5 , − 2 , − 1 . 4 , − 0 . 5 negative 1 . 5 comma negative square root of 2 comma negative 1 . 4 comma negative 0 . 5 68. − 5 6 , − 3 4 , − 3 8 , 1 2 negative , 5 sixths , comma minus , 3 fourths , comma minus , 3 eighths , comma , 1 half 69. − 20 , 0.2 , 1 2 , 2 negative 20 comma 0.2 comma , 1 half , comma square root of 2 70. − 3 , − 0.5 , − 1 4 , 3 4 negative 3 comma negative 0.5 comma negative , 1 fourth , comma , 3 fourths 71. 7 x − 4 7 x minus 4 72. − p − 2 q 3 negative p minus , fraction 2 q , over 3 end fraction 73. 2 b − 28 2 b minus 28 74. 2 k − 2 m 2 k minus 2 m

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