91Ó°ÊÓ

Evaluate each expression. (a) ||\(-6|-|-||4\) (b) \(\frac{-1}{|-1|}\)

Flea Market The manager of a weekend flea market knows from past experience that if she charges \(x\) dollars for a rental space at the flea market, then the number \(y\) of spaces she can rent is given by the equation \(y=200-4 x\) (a) Sketch a graph of this linear equation. (Remember that the rental charge per space and the number of spaces rented must both be nonnegative quantities.) (b) What do the slope, the \(y\) -intercept, and the \(x\) -intercept of the graph represent?

Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts and test for symmetry. $$y=-\sqrt{4-x^{2}}$$

Factor the expression by grouping terms. $$-9 x^{3}-3 x^{2}+3 x+1$$

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$|3 x|<15$$

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. $$\left(x^{-5} y^{3} z^{10}\right)^{-3 / 5}$$

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\frac{(x+h)^{3}-7(x+h)-\left(x^{3}-7 x\right)}{h}$$

Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 4 h to deliver all the flyers, and it takes Lynn 1 h longer than it takes Kay. Working together, they can deliver all the flyers in 40 \% of the time it takes Kay working alone. How long does it take Kay to deliver all the flyers alone?

Find all real solutions of the quadratic equation. $$x^{2}-\sqrt{5} x+1=0$$

Factor the expression by grouping terms. $$x^{3}+x^{2}+x+1$$