91Ó°ÊÓ

Find the solution sets of the given inequalities. $$ |2 x-1|>2 $$

Find a formula for \(f^{-1}(x)\) and then verify that \(f^{-1}(f(x))=x\) and \(f\left(f^{-1}(x)\right)=x\) $$ f(x)=(x-3)^{2}, x \geq 3 $$

In Problems \(35-38\), find the slope and \(y\) -intercept of each line. \(4 x+5 y=-20\)

The angle of inclination \(\alpha\) of a line is the smallest positive angle from the positive \(x\) -axis to the line \((\alpha=0\) for a horizontal line). Show that the slope \(m\) of the line is equal to \(\tan \alpha\).

change each repeating decimal to a ratio of two integers. $$ 0.217171717 \ldots $$

A 1-mile track has parallel sides and equal semicircular ends. Find a formula for the area enclosed by the track, \(A(d)\), in terms of the diameter \(d\) of the semicircles. What is the natural domain for this function?

Find a formula for \(f^{-1}(x)\) and then verify that \(f^{-1}(f(x))=x\) and \(f\left(f^{-1}(x)\right)=x\) $$ f(x)=(x-1)^{3} $$

Write an equation for the line through \((3,-3)\) that is (a) parallel to the line \(y=2 x+5\); (b) perpendicular to the line \(y=2 x+5\); (c) parallel to the line \(2 x+3 y=6\); (d) perpendicular to the line \(2 x+3 y=6\); (e) parallel to the line through \((-1,2)\) and \((3,-1)\); (f) parallel to the line \(x=8\); (g) perpendicular to the line \(x=8\).

change each repeating decimal to a ratio of two integers. $$ 2.56565656 \ldots $$

Find the solution sets of the given inequalities. $$ \left|\frac{2 x}{7}-5\right| \geq 7 $$