Ashley Is an assistant for a football team called the Silver Stripes. Last night, they played a rainy game against the Lucky Elephants. Ashley kept track of the yards gained or lost each quarter. She noticed that one out of every three yards lost by the Stripes were due to the slippery conditions of the rainy game. Define units for the total yards lost and the yards lost due to slippery conditions. 1. If the Stripes lost 48 yards on one play, how many of these yards were lost due to the slippery conditions? 2. If the Stripes lost thirty-six yards in back- to-back plays, how many of these yards were lost due to the slippery conditions? 3. If Ashley attributes 7 yards lost in the

Suppose that the price \( p \), in dollars, and the number of sales, \( x \), of a certain item follow the equation \( 4 p+3 x+2 p x=46 \). Suppose also that \( p \) and \( x \) are both functions of time, measure in days. Find the rate at which \( x \) is changing when \( x=2, p=5 \), and \( \frac{d p}{d t}=1.5 \). The rate at which \( x \) is changing is \( \square \) sale(s) per day. (Round to the nearest hundredth as needed.)

1. Halla, en cada caso, el valor de las funciones trigo- nométricas a partir de \( P(x, y) \). \( \begin{array}{ll}\text { a. }\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) & \text { b. }\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \\ \text { c. }\left(\frac{2}{3},-\frac{\sqrt{5}}{3}\right) & \text { d. }\left(\frac{3}{5}, \frac{4}{5}\right)\end{array} \)

Find the rate of change of total revenue, cost, and profit with respect to time. Assume that \( R(x) \) and \( C(x) \) are in dollars. \[ R(x)=50 x-0.5 x^{2}, C(x)=3 x+5 \text {, when } x=40 \text { and } \frac{d x}{d t}=15 \text { units per day } \] The rate of change of total revenue is \( \$ \square \) per day.

For the function below, (a) find the vertex; (b) find the axis of symmetry, (c) determine whether there is a maximum or a minimum value and find that value; and (d) graph the function \( f(x)=2 x^{2}+6 x+2 \) (a) The vertex is (Type an ordered pair, using integers or fractions.)

Graph this system of equations: \[ \begin{array}{l}2 x=4 \\ y-2(x+2)\end{array} \] How many solutions are there to this system of equations? No solutions ane solution Infinite solutions