Selected Answers for Core Connections Algebra

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Delphia Tate
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1 Selected Answers for Core Connections Algebra

2 Lesson (2x 3)(x + 2y 4) = 2x 2 + 4xy 11x 6y a: 12x 2 +17x 5 b: 4x 2 28x a: t(n) = (n 1) b: t(n) = 30!5 n a: b: c: d: e: f: 2x 3x 5x 7x 6x x a: 4(x + 2) b: 5(2x + 5y + 1) c: 2x(x 4) d: 3x(3xy y) a: (0, 8); It is the constant in the equation. b: ( 2, 0) and (4, 0); Students may notice that the product of the x-intercepts equals the constant term. c: (1, 9); Its x-coordinate is midway between the x-intercepts a: 1 b:! 7.24 c:! Core Connections Algebra

3 Lesson a: (x 6)(x + 2) b: (2x +1) 2 c: (x 5)(2x +1) d: (x + 4)(3x 2) a: x-intercepts ( 1, 0) and (3, 0), y-intercept: (0, 3) b: x-intercept (2, 0), no y-intercept c: x-intercepts ( 3, 0), ( 1, 0), and (1, 0), y-intercept (0, 2) d: x-intercept (8, 0), y-intercept (0, 20) 8-19 a: t(n) = 1 2 ( 1 2 )n!1 b: t(n) =!7.5! 2(n!1) (0.92) 5! $ a: (6, 9) b: (0 2) a: x = b: all real numbers c: c = y = 1 4 x Selected Answers 3

4 Lesson If x represents time traveled (in hours) and y represents distance between the two trains, then 82x + 66x = y. When y = 111, x = 0.75 hours, which is 45 minutes. So, the time when the trains are 111 miles apart is 4:10 p.m a: 9 units b: 15 units c: 10 units d: 121 square units a: (k 2)(k 10) b: (2x + 7)(3x 2) c: (x 4) 2 d: (3m +1)(3m 1) e: The largest exponent in each expression is a: = 25 b: 16 = 4 c: 1 = d: = a: x = 5 b: x = 6 c: x = 5 or 6 d: x = 1 4 e: x = 8 f: x = 1 4 or a: On average student backpacks get 0.55 pounds lighter with each quarter of high school completed. b: About 44% of the variation in student backpack weight can be explained by a linear relationship with the length of time spent in high school. c: The largest residual value is about 6.2 pounds and it belongs to the student who has completed 3 quarters of high school. d: (10) = 8.34 lbs e: A different model would be better because it looks like there is a curved pattern in the residual plot. 4 Core Connections Algebra

5 Lesson a: (2x + 5)(x 1) b: (x 3)(x + 2) c: (3x +1)(x + 4) d: It is not factorable because no integers have a product of 14 and a sum of a: explicit b: t(n) =!3+ 4(n!1) or a n =!3+ 4(n!1) c: t(50) = a 50 = 193 d: t(n) = 3! 1 3 (n!1) or a n = 3! 1 3 (n!1) a: In 7 weeks b: Joman will score more with 1170 points, while Jhalil will have a: Michelle is correct. One way to view this is graphically: The x-intercept always has a y-coordinate of 0 because it lies on the x-axis. b: ( 4, 0) , 46, 47; x + (x +1) + (x + 2) = a: 2 b: 3 c: 1 Lesson a: (x + 8)(x 8) b: (y 3) 2 c: (2x +1) 2 d: 5(x + 3)(x 3) a: 1 b: 20 x c: 5 t 3 d: x2 y a: ( 3, 7) b: (5, 1) a: 4, 8,12,16; t(n) = 4 + 4(n!1) b: 4, 8,16, 32; t(n) = 4(2) n!1 c: Answers will vary a: x = 1.5y + 5 b: x = 24 c: x = 2.5 d: x = 0 or a: Answers will vary. b: The largest residual value is about 17ºF and it belongs to the day after the 69.8ºF day. c: (55) = 60.0ºF d: The upper bound is given by y = x, and the lower bound is given by y =! x. Mitchell predicts tomorrow s temperature will fall between 42.9ºF and 76.9ºF. Despite the strong relationship between the variables, Mitchell s model is not very useful. Selected Answers 5

6 Lesson Vertex: (4, 9), x-intercepts: (1, 0) and (7, 0), y-intercept: (0, 7) a: 3; 7; 6; 2 b: it does not change the value of the number c: It tells us that a = 0. d: All equal 0. e: the result is always a: x-intercepts (2, 0), ( 4, 0), and (3, 0), y-intercept: (0, 18); b: x-intercepts (3, 0) and (8, 0), y-intercept: (0, 3) c: x-intercept (1, 0) and y-intercept (0, 4) a: See scatterplot at right. 45 minutes + 77 strokes = 122 b: There is a weak to moderate positive linear association between Diego s run time and the strokes taken for each match. There looks to be an outlier at 92 minutes. c: See graph shown below right. d: Every minute of improvement in time reduces the number of strokes by 0.7 on average. e: Answers will vary. Strookes Time (minutes) a: no solution b: (7, 2) a: The symbol represents greater than or equal to and the symbol > represents greater than. b: 5 > 3 c: x 9 d: 2 is less than 7. 6 Core Connections Algebra

7 Lesson This parabola should have x-intercepts ( 3, 0) and (2, 0) and y-intercept (0, 6) a: One is a product and the other is a sum. b: first: x = 2 or x = 1; second: x = a: x = 2 or x = 8 b: x = 3 or x = 1 c: x = 10 or x = 2.5 d: x = a: The line x = 0 is the y-axis, so this system is actually finding where the line 5x 2y = 4 crosses the y-axis. b: (0, 2) a: 4; Since the vertex lies on the line of symmetry, it must lie halfway between the x-intercepts. b: (4, 2) a: 2(x 2)(x +1) b: 4(x 3) a: (3x) 3/2 b: 81 1/x c: 17 x/3 Lesson a: x = 1 or 4 3 b: x = 0 or 6 c: x = 5 or The result must be the original expression because multiplying and factoring are opposite processes; 65x x a: x = 3 or 2 3 b: x = 2 or 5 c: x = 3 or 2 d: x = 1 2 or See graphs at right a: true b: false c: true d: true e: false f: false a: 1 b:! 1.6 c: 3 Selected Answers 7

8 Lesson a: y = x 2 + 2x 8 b: y = x 2 6x + 9 c: y = x 2 7x d: x 2 4x m = 1 2, (0, 4) a:! 1.4 and! 0.3 b: The quadratic is not factorable a: x = 4 or 10 b: x = 8 or a: 4 b: 10 c: 8 d: a: (1, 1) b: ( 2, 1 2 ) Lesson a: y = (x + 3) 2 + 6, ( 3, 6) b: y = (x 2) 2 + 5, (2, 5) c: y = (x + 4) 2 16, ( 4, 16) d: y = (x + 2.5) , ( 2.5, 8.25) a: ( 4, 1 2 ) b: ( 2, 3) c: ( 0, 5 2 ) d: (0, 4) ! 1.088; 8.8% monthly increase x-intercepts: ( 1, 0) and ( 2, 0), y-intercept: (0, 4), solution graph shown at right a: m = 3 4, b = 29 4 b: Yes, it makes the equation a true statement a: p = 3.97v , where p is power (watts) and v is VO 2 max (ml/kg/min). b: 280 watts. The measurements are rounded to the nearest whole number. c: = 13 watts d: r = The linear association is positive and weak. e: There is a weak positive linear association between power and VO 2 max, with no apparent outliers. An increase of one ml/kg/min in VO 2 max is predicted to increase power by 3.97 watts. 26.7% of the variability in the power can be explained by a linear relationship with VO 2 max. 8 Core Connections Algebra

Chapter 8. Lesson a. (2x+3)(x+2) b. (2x+1)(3x+2) c. no solution d. (2x+y)(y+3) ; Conclusion. Not every expression can be factored.

Chapter 8. Lesson a. (2x+3)(x+2) b. (2x+1)(3x+2) c. no solution d. (2x+y)(y+3) ; Conclusion. Not every expression can be factored. Chapter 8 Lesson 8.1.1 8-1. a. (x+4)(y+x+) = xy+x +6x+4y+8 b. 18x +9x 8-. a. (x+3)(x+) b. (x+1)(3x+) c. no solution d. (x+y)(y+3) ; Conclusion. Not every expression can be factored. 8-3. a. (3x+1)(x+5)=6x