Answers, Tools Week 5. The test itself if under the Resource link, Week 5 as a Word document.
1. The answer must be 6, since only this value would give you 2 y values for the same x value, in this case 6.
2. The y intercept is -3, since b is -3, so one point is (0,-3), Since the slope is 2, go over 1 and up 2 to get another point, so this would be (1, -1). You could have other points, as long as the slope is 2 from the point (0,-3)
3. Your sketch must loop back on itself, allowing the vertical line test to make the graph not a function
4. Range would be the age of the person, so something like 0-120 or so.
5. The slope is rise over run. The run goes from 1 to 4, or a value of 3. The rise goes from 4 to 3, or a value of -1. The slope is -1/3. Find b. Plug one of the points into this equation: y = -1/3x + b. Solve for b. I will pick the first point, (1,4). This gives you: 4=-1/3(1) + b, Add 1/3 to both sides. 4 1/3 = b. so, y = -1/3x + 4 1/3
6. This graph looks like a V. The bottom of the V is at the point (-1,0). It then goes through points (-2,1) and (0,1)
7. y = 3x + 9/5
8. (13)(13)(13)(7)(7)(7)
9. 3x^2 – 2x + 1 + 2(2x^2-4x-2) or 3x^2 – 2x + 1 + 4x^2 -8x -4 or 7x^2 – 10x – 3
10. 3x^2 – 2x + 1 – (2x^2-4x-2) or 3x^2 – 2x + 1 – 2x^2 + 4x + 2 or x^2 +2x + 3
11. (3x^2 – 2x + 1)(2x^2-4x-2) or 6x^4 – 16x^3 + 4x^2 – 2
12. 3.21 x 10^(-8)
13. 5,430,000
14. 3y^2/5x^4
15. 54x^6
16 1
Problem Solving Exam
You are the teacher of a 2nd grade class of 31 students. You are on a field trip, and one of your mother chaperones gives you a hundred dollar bill to buy ice cream treats at the local shop. The shop sells $1 sandwiches, $2 small cones, and $5 mondo cones. The mother says she wants every child to get a treat, and that all the money must be used. She also says, since she does not want to be considered cheap, that the total number of the mondo cones purchased must be one more than the sum of the number of sandwiches and small cones combined. How many of each treat should you buy?
Answer: mondo cones = 16, small cones = 5, sandwiches = 10
Equations: s + c + m = 31
s + 2c + 5m = 100
s + c + 1 = m
Easiest to use for substitution? The last one, since it is already solved for m. Plub it into the other 2 equations, then put a couple of lines through this equation, since you will no longer need it. It has served the purpose to change the problem into one with only 2 equations and 2 variables.. These 2 new equations are now:
s + c + (s + c + 1) = 31
s + 2c + 5(s + c + 1) = 100
Now pick one the these equations and solve for a variable. Then plug it into the other equations so you now will only have 1 variable left. I will solve for s in the first equations and plug the answer into the second.
s + c + (s + c + 1) = 31 or 2s + 2c + 1 = 31 or 2s + 2c = 30 or 2s = 30 – 2c or s = 15-c
plug s = 15-c in for the second equation, giving you this equation:
(15-c) + 2c + 5((15-c) + c + 1) = 100 or 15-c + 2c + 5(16) = 100
or 15 + c + 80 = 100 or c=5. So, you buy 5 cones. Now plug 5 in for c in one of the equations above with just 2 variable.. one of these:
s + c + (s + c + 1) = 31
s + 2c + 5(s + c + 1) = 100
I will pick the first one, and plug c=5 into it and solve for s
s + c + (s + c + 1) = 31 or s + 5 + (s + 5 + 1) = 31 or 2s + 11 = 31
or 2s = 20 or s=10. So you buy 10 sandwiches. Now plug c=5 and s = 10 into one of the original equations. I will pick the first: 10 + 5 + m = 31
or 15 + m = 31 or m = 16. Answer: s = 10, c = 5, m = 16