In the science lab, Wanda Ngo measures the following values of $x$ and $y$ :\

$$\begin{array}{ll}\frac{x}{11} & \frac{y}{341} \\ 18 & 411 \\ 23 & 471\end{array}$$

Wanda wants to know whether the function could be linear. Tell her the answer, and how you decided. If it is linear, find the particular equation. If it is not linear, assume it is quadratic and find the particular equation.

Solve the equation .
$2 x^2-15 x=0$

Solve the equation .\

$$3 x^2-7 x=0$$

Dee Side has a pig that presently weighs 200 pounds. She could sell it now for a price of $\$ 1.40$ a pound.
a. What is the worth of the pig now?
b. The pig is gaining 5 pounds a week. Write an equation for its weight as a function of weeks. What kind of function is this?
c. The price per pound is dropping 2 cents a week. Write an equation for price per pound as a function of weeks. What kind of function is this?
d. Write an equation for the total worth of the pig as a function of weeks. What kind of function is this?
e. Predict the worth of the pig after 8 weeks, 16 weeks, and 24 weeks.
f. When should Dee sell the pig to get the maximum amount of money for it?
g. Sketch the graph of worth versus time in a reasonable domain.

Plot the graph accurately by making a table of values of $x$ and $y$. You may use different scales on the two axes, if necessary, to make the graphs have reasonable proportions.
$y=-3 x^2+5 x-10$

a. Solve the equation.
b. Check one of the solutions.\

$$3 x(x+5)+2 x^2=8 x-11$$

Use the discriminant to tell whether or not the indicated function ever has the given values of $y$ (for real values of $x$ ).
$y=-3 x^2+5 x+1 ; \quad y=4, \quad y=-3$.

a. Solve the equation.
b. Check one of the solutions.
$x^2+5 x+50=3 x-15$

Solve: $8 x-10=3 x$

Your nose, windpipe, and so forth, hold about a pint of air. So when you breathe in, the first pint of air to reach your lungs is the air you have breathed before. If you breathe more than a pint, the rest of the air reaching your lungs is fresh air. The maximum amount you can inhale in any one breath is about 4 pints.
a. Sketch a graph of $f$, the pints of fresh air reaching the lungs, as a function of $a$, the total pints of air breathed in. Explain why the function is linear, and tell its slope and $a$-intercept.
b. Write the particular equation expressing $f$ in terms of $a$.
c. What percent of the air reaching your lungs is fresh air if you inhale 1 pint? or 2 pints? 3 pints? 4 pints?
d. Plot the graph of the percent of fresh air reaching the lungs as a function of pints of air breathed in. Is the function linear? Justify your answer.
e. What would happen to you if you breathed very shallow breaths, less than a pint, for a long period of time?

Solve: $8 x-13=47$

Use the discriminant to tell whether or not the indicated function ever has the given values of $y$ (for real values of $x$ ).
$y=5 x^2-8 x+6 ; \quad y=3, \quad y=-4$.

Multiply: $\left(\frac{3}{11}\right)\left(\frac{22}{7}\right)$

What special name is given to the domain in a linear programming problem?