91Ó°ÊÓ

Rationalize the denominator. $$\frac{3}{2-\sqrt{5}}$$

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$\left|\frac{x+1}{2}\right| \geq 4$$

Tangent Line to a Circle (a) Find an equation for the line tangent to the circle \(x^{2}+y^{2}=25\) at the point \((3,-4) .\) (See the figure.) (b) At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?

Factor the expression by grouping terms. $$3 x^{3}-x^{2}+6 x-2$$

Discriminant Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation. $$x^{2}+r x-s=0 \quad(s>0)$$

Global Warming Some scientists believe that the average surface temperature of the world has been rising steadily. The average surface temperature can be modeled by $$T=0.02 t+15.0$$ where \(T\) is temperature in \(^{\circ} \mathrm{C}\) and \(t\) is years since \(1950 .\) (a) What do the slope and \(T\) -intercept represent? (b) Use the equation to predict the average global surface temperature in 2050 .

Factor the expression by grouping terms. $$5 x^{3}+x^{2}+5 x+1$$

Write the number indicated in each statement in scientific notation. (a) A light-year, the distance that light travels in one year, is about \(5,900,000,000,000 \mathrm{mi}\) (b) The diameter of an electron is about \(0.0000000000004 \mathrm{cm}\) (c) A drop of water contains more than 33 billion billion molecules.

Find all real solutions of the equation. $$\frac{x^{2}}{x+100}=50$$

Rationalize the denominator. $$\frac{2}{\sqrt{2}+\sqrt{7}}$$