91Ó°ÊÓ

In Exercises 1–4, make a conjecture about whether the relationship between \(x\) and \(y\) is linear, quadratic, or neither. Explain how you decided. $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} & {5} & {6} & {7} \\ \hline y & {-1} & {4} & {15} & {32} & {55} & {84} & {119} \\\ \hline\end{array}$$

Decide whether the relationship is an inverse variation. If it isn’t, tell what type of relationship it is. \(s=\frac{6 t}{8}\)

Hector conjectured that when you subtract an even number from an odd number, the result is odd. He tried to prove his conjecture. Hector said, "According to my proof, an odd number minus an even number is always 1 . This isn't true. What did I do wrong?" a. What did Hector do wrong? b. Give a correct proof of Hector's conjecture.

Sports A place kicker on a football team attempted three field goals during a game. All three were kicked from the opponent's 40 -yard line, which is 50 yards from the goalpost. For a field goal to count, it must clear the crossbar, which is 10 feet high. The football followed a different path through the air for each kick. These equations give the height of the kick in feet, \(h\) , for any distance from the kicker in yards, \(d .\) Each kick was aimed directly at the center of the goalpost. Kick \(1 : h=3.56 d-0.079 d^{2}\) Kick \(2 : h=1.4 d-0.0246 d^{2}\) Kick \(3 : h=2 d-0.033 d^{2}\) a. For each kick, plot enough points to draw a smooth curve. Plot all three graphs on the same axes and label them Kick \(1,\) Kick \(2,\) and Kick \(3 .\) Put distance from the kicker, from 0 to 70 yards, on the horizontal axis. Put height, from 0 to 50 feet, on the vertical axis. b. Use your graphs to estimate the maximum height of each kick. c. Use your graphs to estimate how many yards each kick traveled over the field before it struck the ground. d. To make a field goal, the football must cross over the goalpost. That means it must be at least 10 feet high when it reaches the post, which is 50 yards from the kicker. Use your graphs to estimate whether any of the kicks could have scored a field goal. Explain your reasoning.

Kiyoshi spent \(\$ 8\) at the farmer's market. She bought only mandarin oranges, which are \(\$ 0.40\) each, and nectarines, which are \(\$ 0.80\) each. a. Is the relationship between the number of mandarin oranges, m, and the number of nectarines, n, an inverse variation? Explain. b. Write an equation for the relationship between m and n.

In Exercises \(15-17\) , decide whether the conjecture is true or false. Try to give a convincing proof of the conjectures that are true. For false conjectures, give a counterexample. The square of every even number is a multiple of 4.

Rearrange each linear equation into slope-intercept form, \(y=m x+b\). \(3 y-4 x-1=8 x-2 y\)

Evaluate each expression for the given values. $$ a^{d}+a b-b^{c} \text { for } a=-3, b=-2, c=3, \text { and } d=2 $$

Write an equation of a line that is parallel to the given line. \(x=-2\)