Selected Answers for Core Connections, Course 2

Transcription

1 Selected Answers for Core Connections, Course 2

2 Lesson x x = 2 b: 2x 2 + 4x x = 2x 2 + 3x Parts a, c, and d match the perimeter a: or d: or b: 5 24 c: 3 6 or 1 2 e: f: or a: About 12. There are 6 possible outcomes and 72 divided by 6 is 12. b: About 36. Half of the possible outcomes are even. c: 30 times a: One possible answer: $13 is one third of $39. b: One possible answer: 17 feet is 8 less than 25 feet. c: One possible answer: 38 lbs. is twice as much as 19 lbs a: 5 < 2 b: 8 > 1 c: 5 < 0 d: 15 < 14 Lesson a: Mat A = 4x + 2 2x 1, Mat B = 4x 2x + 6 4, 1 < 2; Mat B is larger b: Mat A = 5x x 1, Mat B = 5x 2x _ 4 + 6, 2 = 2, Equal a: It should have one pair of opposite sides labeled x and the other pair labeled 4x. b: One is four times the length of the other. c: One is 6 feet, the other 24 feet a: 92 b: 42 c: 5 d: 2 e: 53 d: 1 2 or a: 2(x 3) = 2x 6 b: 5(x + 7) = 5x + 35 c: 10x + 20 = 10(x + 2) Quadrilateral (or parallelogram); See graph at right. y x % is $ Core Connections, Course 2

3 Lesson a: b: c: a: n + 7 b: 2x a: 7 is the constant term when the expression is not simplified (5 is the constant term when the expression is written in simplified form). b: 2 and 4x and x c: Possible answer: 3m + 17 d: 4 and 11 are coefficients; 37 is a constant term; 4x 2, 11y, and 37 are the three terms; 4x 2 +11y 37 is an expression (but so are 4x 2, 11y, and 37); x and y are variables. e: 8 and m + n are factors of 8(m + n), which is a product. 5 m m is a quotient; The entire expression is a sum a: $123 b: 75%; $615 c: $ or 17 times a: P = 4x + 6, A = 4x + 4 b: P = 4x + 12, A = 2x + 5 Lesson a: x < 1 b: x 10 x x a: No b: Yes c: Yes d: Yes a: 30 b: 21 b: P = 4x + 4 a: 32 cm b: 26 cm a: One possible answer: A triangle has a long side that is twice as long as the short side; the medium side is two more than the short side; the total perimeter is 74 units; how long is the short side?; other scenarios could involve ages, distances, etc. b: Possible answer: short side length, long side length, and medium side length c: Possible answer: total perimeter a: 1.5 gallons b: 20 minutes Selected Answers 3

4 Lesson (x + 1) = 12 or 3x+3 = 12 b: x = She is correct. b: x + 1 = 4 c: = a: 25(3x 2) b: 16x(2x + 3) c: 10(4m + 3) d: 9m(7m 6) a: x = 4 b: x = 4 c: x = A and D are equivalent because they both equal positive 4; B, C, and E are equivalent because they all equal a: 58.8x 29.7 b: 3 5 x Lesson a: Correct b: Incorrect a: x 4 b: 2x a: 2 < 4 b: 20 = 20 c: 13 < 24 d: 8 < a: 9 b: a: P = 40.3 yds, A = 77 sq yds b: P = 60 ft, A= 150 sq ft x is number of yards gained by Alston, x + 3x + 3x + 10 = 430; 180 yds. 4 Core Connections, Course 2

5 Lesson a: x = 7 b: x = a: 224 students b: 50% c: 10% a: 91% b: 88.5% a: 4(5y 21) b: 24b (b + 4) a: 13 b: c: 5.04 d: acres a: x = 6 b: x = a: d: or b: 0.12 c: 7 80 e: or f: 1.8 or P = 17 un, P = 8.5 un b: A= 12 sq un, A= 3 sq un a: 6 b: 9 c: a: See graph at right. Trapezoid b: 24 sq un p , 0 p 10 less than or equal to 10 sections but greater than or equal to 0 sections, since there cannot be a negative number of trim pieces. Selected Answers 5

6 Lesson Let p represent the number of pepperoni pizzas, p = (p 8) + 3p = veggie, 24 pepperoni, 72 combo pizzas a: Both work but adding 5 to both sides will isolate the x term. b: x = a: 2.5 b: s = 14 t = 40 c: Answers will vary, but the scale factor should be between 0 and a: A = sq ft, P = 35.9 ft b: A = sq mi, P = 49.2 mi c: A = sq cm, P = 17 cm d: A = sq cm, P = cm a: 30(3k 2) b: 6d(5d 3) a: Cannot be determined b: Yes, Mat B greater c: Yes, Mat A greater Lesson a: x = 4 b: x = 19 c: x = a: n 3 b: 3x + 9 c: 5x height = x = 18cm, base = 3x = 54 cm a: 1 7 b: 1 13 c: a: No, has addition. b: Yes, c: No, has subtraction a: m = 3 feet b: m + 7 = 2m + 4; 3 feet c: 10 feet a: x = 5 b: x = 8 c: x = Lower= 320 feet = x 355, Middle= 675 feet = x, Upper= 1430 feet = x a: 71 b: 102 c: 72 d: a: 3(4) + 7, 2(7) + 5 b: 6(3) + 7, 4(7) 3 c: 5(5) 2, 2(9) blocks/hour $ $12.99s $100, s 3.89 ; She can buy 3 shirts. 6 Core Connections, Course 2

7 Lesson a: x = 0 b: No solution c: All numbers a: Incorrect b: Correct a: No, fractional coefficients are more complex. b: Yes, all constants are together on one side of the mat. c: Most simple because x is isolated. d: Part C is most efficient a: $80; See diagram at right. b: $8 c: $12 $16 $16 4 = $64 0% 20% 20% 4 = 80% $80 100% a: 4(4x 1) b: 5x( 2 + x) c: 6(5y 4x) a: 2x + 7 = 13, x = 3 b: 3j +15 = 27, j = 4 c: 2n + 4(6) = 44, n = 10 Lesson a: Add 37 b: x = a: x = 1 b: x = 1.5 c: x = 8.36 d: x = Reasoning will vary. a: 57 lb b: 8.5 lb c: 76 lb a: 0.4 b: 2 c: d: 4 15 e: 4.8 f: Fraction answers will vary. a: 1 3, 33.3%, 0.3 b: 14 40, 35%, 0.35 c: %, 0.9 d: 12 75, 16%, a: x + 6 b: y 5 c: 2x + 3 d: 5y e: 11; 3; 13; 40 Selected Answers 7