91Ó°ÊÓ

Yes or No? If No, give a reason. (a) When you add the same number to each side of an equation, do you always get an equivalent equation? (b) When you multiply each side of an equation by the same nonzero number, do you always get an equivalent equation? (c) When you square each side of an equation, do you always get an equivalent equation?

(a) When we multiply two powers with the same base, we ________________ the exponents. So \(3^{4} \cdot 3^{5}=\) ________________ . (b) When we divide two powers with the same base, we _________________the exponents. So \(\frac{3^{5}}{3^{2}}=\) __________________ .

The graph of the equation \((x-1)^{2}+(y-2)^{2}=9\) is a circle with center (_____ , _____) and radius __________.

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = ? Exponential expression = \(10^{-3 / 2}\)

Sketch the region given by the set. (a) \(\\{(x, y) | y<3\\}\) (b) \(\\{(x, y) | x=-4\\}\)

Constants of Proportionality Express the statement as an equation. Use the given information to find the constant of proportionality. A is directly proportional to \(x\) and inversely proportional to \(t\) If \(x=7\) and \(t=3,\) then \(A=42\).

Linear Inequalities Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$-\frac{1}{2} \leq \frac{4-3 x}{5} \leq \frac{1}{4}$$

Third Law of planetary motion states that the square of the period \(T\) of a planet (the time it takes for the planet to make a complete revolution about the sun) is directly proportional to the cube of its average distance \(d\) from the sun. (a) Express Kepler's Third Law as an equation. (b) Find the constant of proportionality by using the fact that for our planet the period is about 365 days and the average distance is about 93 million miles. (c) The planet Neptune is about \(2.79 \times 10^{9} \mathrm{mi}\) from the sun. Find the period of Neptune.

Solving by Factoring Find all real solutions of the equation by factoring. $$x^{2}+x-12=0$$

The period of a pendulum (the time elapsed during one complete swing of the pendulum) varies directly with the square root of the length of the pendulum. (a) Express this relationship by writing an equation. (b) To double the period, how would we have to change the length \(l ?\) (IMAGES CANNOT COPY)