91Ó°ÊÓ

While traveling on the Pennsylvania Turnpike, you pass milepost 326 near Valley Forge, then milepost 351 near Philadelphia. How many miles do you travel during that time period?

In Exercises 73-78, identify the terms. Then identify the coefficients of the variable terms of the expression. $$ 7 x+4 $$

In Exercises 73-78, identify the terms. Then identify the coefficients of the variable terms of the expression. $$ \sqrt{3} x^{2}-8 x-11 $$

In Exercises 73-78, identify the terms. Then identify the coefficients of the variable terms of the expression. $$ 3 x^{4}-\frac{x^{2}}{4} $$

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line. \((-3.9,-1.4)\) Line $$ \begin{aligned} &4 x-2 y=3 \\ &x+y=7 \\ &3 x+4 y=7 \\ &5 x+3 y=0 \\ &y=-3 \\ &y=1 \\ &x=4 \\ &x=-2 \\ &x-y=4 \\ &6 x+2 y=9 \end{aligned} $$

The total numbers \(f\) (in billions) of miles traveled by motor vehicles in the United States from 1995 through 2002 are shown in the table. The time (in years) is given by \(t\), with \(t=5\) corresponding to 1995 . (Source: U.S. Federal Highway Administration) $$ \begin{array}{|c|c|} \hline 0 \text { Year, } t & \text { Miles traveled, } f(t) \\ \hline 5 & 2423 \\ 6 & 2486 \\ 7 & 2562 \\ 8 & 2632 \\ 9 & 2691 \\ 10 & 2747 \\ 11 & 2797 \\ 12 & 2856 \\ \hline \end{array} $$ (a) Does \(f^{-1}\) exist? (b) If \(f^{-1}\) exists, what does it mean in the context of the problem? (c) If \(f^{-1}\) exists, find \(f^{-1}\) (2632). (d) If the table was extended to 2003 and if the total number of miles traveled by motor vehicles for that year was 2747 billion, would \(f^{-1}\) exist? Explain.

In Exercises 79-84, evaluate the expression for each value of \(x\). (If not possible, state the reason.) \(\frac{x+1}{x-1}\) (a) \(x=1\) (b) \(x=-1\)

You need a total of 50 pounds of two types of ground beef costing \(\$ 1.25\) and \(\$ 1.60\) per pound, respectively. A model for the total cost \(y\) of the two types of beef is $$ y=1.25 x+1.60(50-x) $$ where \(x\) is the number of pounds of the less expensive ground beef. (a) Find the inverse function of the cost function. What does each variable represent in the inverse function? (b) Use the context of the problem to determine the domain of the inverse function. (c) Determine the number of pounds of the less expensive ground beef purchased when the total cost is \(\$ 73\).

(a) use the position equation \(s=-16 t^{2}+v_{0} t+s_{0}\) to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from \(t_{1}\) to \(t_{2}\), (d) interpret your answer to part (c) in the context of the problem, (e) find the equation of the secant line through \(t_{1}\) and \(t_{2}\), and (f) graph the secant line in the same viewing window as your position function. An object is thrown upward from a height of 6 feet at a velocity of 64 feet per second. $$ t_{1}=0, t_{2}=3 $$

Sales The following are the slopes of lines representing annual sales \(y\) in terms of time \(x\) in years. Use the slopes to interpret any change in annual sales for a one-year increase in time. (a) The line has a slope of \(m=135\). (b) The line has a slope of \(m=0\). (c) The line has a slope of \(m=-40\).