91Ó°ÊÓ

plot the points in the Cartesian plane. $$ (-5,3),(1,-1),(-2,-4),(2,0),(1,-6) $$

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ (-3,2),(3,-2) $$

Plot the points and find the slope of the line passing through the pair of points. $$ \left(\frac{2}{3}, \frac{5}{2}\right),\left(\frac{1}{4},-\frac{5}{6}\right) $$

Break-Even Analysis You are setting up a part-time business with an initial investment of \(\$ 15,000\). The unit cost of the product is \(\$ 11.80,\) and the selling price is \(\$ 19.30 .\) (a) Find equations for the total cost \(C\) and total revenue \(R\) for \(x\) units. (b) Find the break-even point by finding the point of intersection of the cost and revenue equations. (c) How many units would yield a profit of \(\$ 1000 ?\)

Write an equation of the line with \(y\) -intercept at \(-10\) and parallel to all horizontal lines.

You deposit \(\$ 2000\) in an account that is compounded quarterly at an annual rate of \(r\) (in decimal form). The balance \(A\) after 10 years is \(A=2000\left(1+\frac{r}{4}\right)^{40}\). Does the limit of \(A\) exist as the interest rate approaches \(6 \% ?\) If so, what is the limit?

A company invests \(98,000 for equipment to produce a new product. Each unit of the product costs \)12.30 and is sold for \(17.98. Let be the number of units produced and sold. (a) Write the total cost \)C\( as a function of \)x .\( (b) Write the revenue \)R\( as a function of \)x .\( (c) Write the profit \)P\( as a function of \)x .$

MAKE A DECISION: REVENUE For groups of 80 or more people, a charter bus company determines the rate \(r\) (in dollars per person) according to the formula \(r=15-0.05(n-80), \quad n \geq 80\) where \(n\) is the number of people. (a) Express the revenue \(R\) for the bus company as a function of \(n .\) (b) Complete the table. (c) Criticize the formula for the rate. Would you use this formula? Explain your reasoning.

Break-Even Point Define the break-even point for a business marketing a new product. Give examples of a linear cost equation and a linear revenue equation for which the break-even point is \(10,000\) units.

Sketch the graph of the equation. Use a graphing utility to verify your result. $$ x+2 y+6=0 $$