91Ó°ÊÓ

Write each English sentence as an equation in two variables Then graph the equation. The \(y\) -value is three decreased by the square of the \(x\) -value.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.

Solve each absolute value equation or indicate that the equation has no solution. $$ |x+1|+6=2 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. (graph cannot copy for a,b,c,d,e,f) $$y=x^{\frac{1}{3}}+2 x^{\frac{1}{6}}-3$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I find the hardest part in solving a word problem is writing the equation that models the verbal conditions.

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$

Solve each equation. $$ \text { Solve for } A: r=\sqrt{\frac{A}{4 \pi}} $$

A basketball player's hang time is the time spent in the air when shooting a basket. The formula $$t=\frac{\sqrt{d}}{2}$$ models hang time, \(t,\) in seconds, in terms of the vertical distance of a player's jump, \(d,\) in feet. (image cannot copy) If hang time for a shot by a professional basketball player is 0.85 second, what is the vertical distance of the jump, rounded to the nearest tenth of a foot?

Suppose you are an algebra teacher grading the following solution on an examination: $$\begin{aligned}-3(x-6) &=2-x \\\\-3 x-18 &=2-x \\\\-2 x-18 &=2 \\\\-2 x &=-16 \\\x &=8\end{aligned}$$ You should note that 8 checks, so the solution set is \(\\{8\\}\) The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points, how many points should you give the student? Justify your position.

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y=5 x^{2}+3 x \text { and } y=2 $$