91Ó°ÊÓ

The given equation is either linear or equivalent to a linear equation. Solve the equation. $$5 t-13=12-5 t$$

Write an equation that expresses the statement. \(A\) is jointly proportional to the square roots of \(x\) and \(y\).

Simplify the rational expression. $$\frac{x^{2}-x-2}{x^{2}-1}$$

Express the given quantity in terms of the indicated variable. The time (in hours) it takes to travel a given distance at \(55 \mathrm{mi} / \mathrm{h} ; d=\) given distance (in \(\mathrm{mi}\) )

Evaluate each expression. (a) \(5^{4} \cdot 5^{-2}\) (b) \(\frac{10^{7}}{10^{4}}\) (c) \(\frac{3}{3^{-2}}\)

A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$(6,-2),(-6,2)$$

Evaluate each expression. (a) \(\left(\frac{5}{3}\right)^{0} 2^{-1}\) (b) \(\frac{2^{-3}}{3^{0}}\) (c) \(\left(\frac{1}{4}\right)^{-2}\)

Express the statement as an equation. Use the given information to find the constant of proportionality. \(y\) is directly proportional to \(x .\) If \(x=6,\) then \(y=42\).

Express the given quantity in terms of the indicated variable. The concentration (in oz/gal) of salt in a mixture of 3 gals of brine containing 25 oz of salt to which some pure water has been added; \( x=\) volume of pure water added (in gal)

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$2 x+1<0$$