©Zarestky
Math 141 Quiz 2 Version B
9/10/2009
NAME:______KEY__________________________________
1.
(2 pts) What is the equation of the line that is perpendicular to the line 5x + 4 y = 3 through the
point (0, 2)?
Solve the linear equation for y to identify the slope:
5x + 4 y = 3
4 y = !5x + 3
5
3
y=! x+
4
4
The slope m = !
5
4
so the perpendicular slope m! = .
4
5
The point (0, 2) represents the y-intercept, i.e., b = 2. Use the slope-intercept form of a line.
4
y = x+2
5
2.
(3 pts) A company selling water bottles has a profit function of P(x) = 5x – 800 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 $6 each, find the break-even quantity and revenue.
The break-even occurs when profit = 0.
P ( x ) = 5x !800 = 0
5x = 800
x = 160
The break-even quantity is 160 water bottles.
The break-even revenue occurs when the break-even quantity is substituted into the revenue function.
The revenue function is R(x) = 6x. The break-even revenue is R(160) = 6*160 = $960.
3.
(2 pts) Write an equation to represent the following statement: “There are four times as many ferrets as
hedgehogs.” For full credit, define your variables.
Let f represent the number of ferrets and let h represent the number of hedgehogs.
f = 4h
For 4-6, determine whether the statement is true or false. Circle your answer. (1 pt each)
T F
4.
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.
T F
5.
Suppose that the value of a car is represented by V(t) = −3000t + 21000 where t is time in years
and V is in dollars. Then if t increases by 2 years, V will decrease by $6000.
T F
6.
The lines y = 2 and x = 2 are parallel.