91Ó°ÊÓ

List six whole numbers that satisfy the inequality \(n-2>5.\)

Solve each equation by backtracking. (Backtrack mentally if you can.) Check your solutions. $$ 2(n-5)=7 $$

Solve the systems of equations in Exercises \(8-11\) by elimination, and check your solutions. Give the following information: \(\cdot\) which variable you eliminated \(\cdot\) whether you added or subtracted equations \(\bullet\) the solution $$ \begin{array}{l}{9 s+2 t=3} \\ {4 s+2 t=8}\end{array} $$

Economics A manager of a rock group wants to estimate, based on past experience, how many tickets will be sold in advance of the next concert and how many tickets will be sold at the door on the night of the concert. At a recent concert, the \(1,000\) -seat hall was full. Tickets bought in advance cost \(\$ 30\) , tickets sold at the door cost \(\$ 40\) , and total ticket sales were \(\$ 38,000\) . a. Write a system of two equations to represent this information. b. On one set of axes, draw graphs for the equations. c. Use your graphs to estimate the number of advance sales and the number of door sales made that night. d. Check that your estimates fit the conditions by substituting them into both equations.

Recall that the absolute value of a number is its distance from 0 on the number line. You can solve equations involving absolute values. For example, the solutions of the equation \(|x|=8\) are the two numbers that are a distance of 8 from 0 on the number line, 8 and \(-8 .\) Solve each equation. $$ \begin{array}{ll}{\text { a. }|a|=2.5} & {\text { b. }|2 b+3|=8} \\ {\text { c. }|9-3 c|=6} & {\text { d. } \frac{15 d 1}{25}=1} \\ {\text { e. }|-3 e|=15} & {\text { f. } 20+|2.5 f|=80}\end{array} $$

Recall that for linear equations, first differences are constant; and that for quadratic equations, second differences are constant. Determine whether the relationship in each table could be linear, quadratic, or neither. $$ \begin{array}{|c|c|}\hline x & {y} \\ \hline-3 & {0} \\ {-2} & {-0.5} \\\ {-1} & {-1} \\ {0} & {-1.5} \\ {1} & {-2} \\ {2} & {-2.5} \\\ \hline\end{array} $$

Consider the inequality \(x^{3} \leq 27.\) a. Express the solution of \(x^{3} \leq 27\) as an inequality. b. Graph the solution on a number line.

Write \(64,256,\) and \(1,024\) using integer exponents and the same base.

Rewrite each expression as simply as you can. $$\left(a^{m}\right)^{n} \cdot\left(b^{3}\right)^{0}$$