Practice Exam 2
Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work.
Problem 1 The number of people y in town who will buy a Lake Tahoe sweatshirt if it is offered at x dollars can be modeled by the equation
50x + y = 2000
A. Find the y-intercept and interpret this number in the context of sweatshirt purchases.
B. Find the x-intercept and interpret this number in the context of sweatshirt purchases.
C. Find the slope and interpret this number in the context of sweatshirt purchases.
Problem 2 The length of a rectangle is 18 inches less than three times its width. The perimeter of the rectangle is 52 inches. Find the dimensions of the rectangle.
Problem 3 To buy your $25,000 car, you had to get loans from two different sources for the $25,000. The first source charged 6% interest and the second source charged 8% interested per year. If the total amount of interest that you will pay for the first year is $1800, how much did you borrow from each source?
Problem 4
Sketch the graphs of the following lines and find the x and y intercepts is they exist.
A. 2x - 5y = 10
B. y = 4
C. y + 2/3 x = 4
D. x = -3
E. The line that passes through the point (2,4) and has slope -3/2.
Problem 5
A. Find the slope of the line that is parallel to the line that passes through the points (2,-3) and (5,6).
B. Find the slope of the line that is perpendicular to the line that passes through the points (0,2) and (2,3).
Problem 6
Find the equation of the line in slope intercept form with the following properties.
A. Passes through the points (2,3) and (4,-1).
B. Passes through the point (-4,2) and has slope -2/5.
Problem 7
The graphs of several lines are shown below. decide which of the statements are true and which are false and explain your reasoning.
A. The slope of line II is greater than the slope of line I.
B. The y-intercept of lines I and II are equal.
C. The x-coordinate of the x-intercept of line I is greater than the x-coordinate of the x intercept of line III.
D. Lines I and II are perpendicular.
Problem 8
Solve the following inequalities, write the solution in interval notation, and sketch the solution set on a number line.
A. 3x - 5 > 2
B. 5 - 2x > 1
C. -10 < 6 - 2x < 10
Problem 9
Susan earned 75% and 81% on the first two exams. If she wants the average, x, of the first three exams to be at least 80%, what are the possible scores that she can get on her exam? Write your answer in interval notation.
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