©Zarestky
Math 141 Quiz 2 Version A
9/10/2009
NAME:____________KEY____________________________
1.
(2 pts) What is the equation of the line that is perpendicular to the line 3x + 2 y = 5 through the
point (0, 4)?
Solve the linear equation for y to identify the slope:
3x + 2 y = 5
2 y = !3x + 5
3
5
y=! x+
2
2
The slope m = !
3
2
so the perpendicular slope m! = .
2
3
The point (0, 4) represents the y-intercept, i.e., b = 4. Use the slope-intercept form of a line.
2
y = x+4
3
2.
(3 pts) A company selling water bottles has a profit function of P(x) = 3x – 900 where x is the
number of water bottles made and sold and profit is given in dollars. If the company sells the water
bottles for $4 each, find the break-even quantity and revenue.
The break-even occurs when profit = 0.
P ( x ) = 3x !900 = 0
3x = 900
x = 300
The break-even quantity is 300 water bottles.
The break-even revenue occurs when the break-even quantity is substituted into the revenue function.
The revenue function is R(x) = 4x. The break-even revenue is R(300) = 4*300 = $1200.
3.
(2 pts) Write an equation to represent the following statement: “There are three times as many parrots as
macaws.” For full credit, define your variables.
Let p represent the number of parrots and let m represent the number of macaws.
p = 3m
For 4-6, determine whether the statement is true or false. Circle your answer. (1 pt each)
T F
4.
The lines x = 3 and y = 3 are parallel.
T F
5.
Suppose that the value of a car is represented by V(t) = −2000t + 16000 where t is time in years
and V is in dollars. Then if t increases by 2 years, V will decrease by $4000.
T F
6.
If the value of the correlation coefficient r is close to −1 for a data set, the least-squares line is
not a good model for the data.