91Ó°ÊÓ

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\sqrt{1+\left(x^{3}-\frac{1}{4 x^{3}}\right)^{2}}$$

Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts and test for symmetry. $$x=y^{3}$$

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$\frac{1}{2}|x| \geq 1$$

Evaluate each expression. (a) \(\left|\frac{-6}{24}\right|\) (b) \(\left|\frac{7-12}{12-7}\right|\)

Factor the expression by grouping terms. $$x^{5}+x^{4}+x+1$$

Find all real solutions of the quadratic equation. $$3 x^{2}+2 x+2=0$$

Temperature Scales \(\quad\) The relationship between the Fahrenheit \((F)\) and Celsius (C) temperature scales is given by the equation \(F=\frac{9}{5} C+32\) (a) Complete the table to compare the two scales at the given values. (b) Find the temperature at which the scales agree. I Hint: Suppose that \(a\) is the temperature at which the scales agree. Set \(F=a \text { and } C=a . \text { Then solve for } a .]\) $$\begin{array}{|c|c|} \hline C & F \\ \hline-30^{\circ} & \\ -20^{\circ} & \\ -10^{\circ} & \\ 0^{\circ} & \\ & 50^{\circ} \\ & 68^{\circ} \\ & 86^{\circ} \\ \hline \end{array}$$

Factor the expression completely. Begin by factoring out the lowest power of each common factor. $$x^{5 / 2}-x^{1 / 2}$$

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$|x-5| \leq 3$$

Find all real solutions of the quadratic equation. $$25 x^{2}+70 x+49=0$$