91Ó°ÊÓ

Four solutions of the equation \(y=a x^{3}+b x^{2}+c x+d\) are given. Use a system of four equations in four variables to find the constants \(a, b, c,\) and \(d\) and write the equation. $$(-2,-39),(-1,-12),(1,-6), \text { and }(3,16)$$

Find two different row-echelon forms of $$ \left[\begin{array}{ll} 1 & 5 \\ 3 & 2 \end{array}\right] $$

Golden Harvest Foods makes jumbo biscuits and regular biscuits. The oven can cook at most 200 biscuits per day. Each jumbo biscuit requires 2 oz of flour, each regular biscuit requires 1 oz of flour, and there is 300 oz of flour available. The income from each jumbo biscuit is \(\$ 0.80\) and from each regular biscuit is 0.50 dollar . Assume that all that are made are sold. How many of each size biscuit should be made in order to maximize income? What is the maximum income?

Francisco is planning to invest up to 40,000 dollar in corporate and municipal bonds. The least he is allowed to invest in corporate bonds is 6000 dollar, and he does not want to invest more than 22,000 dollar in corporate bonds. He also does not want to invest more than 30,000 dollar in municipal bonds. The interest is \(3 \%\) on corporate bonds and \(4 \frac{1}{4} \%\) on municipal bonds. This is simple interest for one year. How much should he invest in each type of bond in order to maximize his income? What is the maximum income?

Nancy jogs and walks to campus each day. She averages \(4 \mathrm{km} / \mathrm{h}\) walking and \(8 \mathrm{km} / \mathrm{h}\) jogging. The distance from home to the campus is \(6 \mathrm{km},\) and she makes the trip in 1 hr. How far does she jog on each trip?

Graph the system of inequalities. $$\begin{aligned} &y \geq x^{2}-2\\\ &y \leq 2-x^{2} \end{aligned}$$

Graph the inequality. $$|x|+|y| \leq 1$$