Solve
Misc. (must do 200 before you do 300)
Sequences
Roman and his Snow Removal Business (also must be done in order).
Oil Changes and Engine Repair (must be done in order)
100
1. Solve each of the following: a. 4x - 9 = 11 b. 6x - 2 = 4x + 14
a. x = 5 b. x = 8
100
5. Find the x-intercept and the y-intercept of the following: 4x - 6y = 36
x-intercept: (9, 0) y-intercept: (0, -6)
100
9. For each of the following sequences a. Write the next three terms b. Describe whether it is arithmetic, geometric or neither c. If it is arithmetic find the common difference. If it is geometric find the common ratio. A. 4, 9, 14, 19, …
a. 24, 29, 34 b. Arithmetic c. d = 5
100
11.Roman shovels snow for winter work and charges $20 per sidewalk. a. Identify the independent and dependent quantities in this problem situation. b. Complete a table of values to describe this situation.
Independent = Number of sidewalks he shovels Dependent = How much he makes Independent Dependent units x 20x 3 60 6 120 9 180 12 240
100
See the diagram on page 17 of your packet entitled "Oil Changes and Engine Repair". Use the graphing calculator to write the equation of the line.
What is y = -73.07x + 650.27
200
2. Solve and graph each of the following inequalities on a number line. a. 2x + 3 < 17 b. 5(3x - 7) >= -20
a. x < 7 b. x >=1
200
6. Given the equation 9x + 3y = 18: a. Convert this equation to slope-intercept form
a. y = -3x + 6
200
9. For each of the following sequences a. Write the next three terms b. Describe whether it is arithmetic, geometric or neither c. If it is arithmetic find the common difference. If it is geometric find the common ratio. B. 200,100,50,25,…
a. 12.5, 6.25, 3.125 b. Geometric c. r = 1/2
200
c.Write an equation in function notation to represent this problem situation.
f(x) = 20x
200
Based upon the correlation coefficient, how accurately do you think this equation will help you make a prediction? Explain your answer.
The correlation coefficient is r = -.91399. Because r is not close to the number 1, this equation does not accurately represent the data.
300
2. Solve and graph each of the following inequalities on a number line. c. -3x + 8 < 19
c. x > -3.7
300
6. Given the equation 9x + 3y = 18: b. What is the y-intercept c. What is the x-intercept d. What is the slope
b. (0, 6) c. (2, 0) d. -3
300
9. For each of the following sequences a. Write the next three terms b. Describe whether it is arithmetic, geometric or neither c. If it is arithmetic find the common difference. If it is geometric find the common ratio. C. -14,-8, -2, 4, …
a. 10, 16, 22 b. Arithmetic c. d = 6
300
d. What function family does this belong to and how do you know?
Linear - the x term
300
Find the slope of the line. Describe in words what the slope represents.
The slope is -73.07 . This means that for each oil change that you receive, the cost of repairs for your car is $73.07 less. (Do the scatter plot, it helps you find out what the slope means).
400
3. Explain why each of the following has no solution: a. 2(3x - 5) = 6x + 7
a. -10 does not equal 7
400
7. The formula for the circumference of a circle is C = 2pir where C is the circumference and r is the radius. Convert the formula to solve for radius.
r = C/2pi
400
9. For each of the following sequences a. Write the next three terms b. Describe whether it is arithmetic, geometric or neither c. If it is arithmetic find the common difference. If it is geometric find the common ratio. D. 5/4, 5, 20, 80, … E. 4, 5, 7, 10 . . .
D. a. 320, 1280, 5120 b. Geometric c. r = 4 E. a. 14, 19, 25 b. Neither c. N/A
400
e. What is the slope of this line and what does it mean in terms of this problem? f. What is the y-intercept of this line and what does it mean in terms of this problem?
e. slope = 20. For each driveway he shovels, he will earn $20. f. y-intercept = 0. When he hasn't shoveled any driveways, he has not yet earned anything.
400
Find the x- and y-intercepts. Explain in terms of oil changes and engine repairs what each represents.
The x-intercept is (10, 0) and y-intercept is (0, 600). The x-intercept means that if you receive 10 oil changes you can expect to pay $0 in car repairs. The y-intercept means that if you receive 0 oil changes, you can expect to spend $600 in car repairs.
500
4. Sketch the graph of the following on a number line: -4 <= x < 3
Draw on board
500
8. To earn some extra money when it snows, Jack shovels sidewalks and driveways in his neighborhood. He earns $20 for each driveway and $15 for each sidewalk. In the last snow storm Jack made $120. a. Write an equation to model this scenario. b. If Jack shoveled three driveways, how many sidewalks did he shovel?
a. 120 = 20d + 15s b. s = 4
500
10. Given the sequence 17,10,3,-4,… a. Write the explicit formula for the sequence b. Find the 31st term of the sequence.
a. a_n = 17 - 7(n-1) b. -193
500
g. Roman is saving to buy a new cell phone. The phone will cost him $230. How many sidewalks will he need to shovel?
230 = 20x x = 11.5 He must shovel 12 driveways.
500
Use the equation to predict the cost of engine repairs if the car had four oil changes.
-73.07(4) + 650.27 = about $357.99
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