91Ó°ÊÓ

Solve each equation and inequality analytically. Use interval notation to write the solution set for each inequality. (a) \(5-3 x=x+1\) (b) \(5-3 x \leq x+1\) (c) \(5-3 x \geq x+1\)

Find the length of the unknown side of the right triangle. In each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. $$a=9, b=10 ; \text { find } c$$

Sketch by hand the graph of the line passing through the given point and having the given slope. Label Through \((-3,0),\) undefined slope}, 2\right)$$,

Find the length of the unknown side of the right triangle. In each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. $$b=\sqrt{13}, c=\sqrt{29} ; \text { find } a$$

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(9-(x+1)<0\) (b) \(9-(x+1) \geq 0\)

Find the length of the unknown side of the right triangle. In each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. $$b=\sqrt{7}, c=\sqrt{11} ; \text { find } a$$

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(6+3(1-x) \geq 0\) (b) \(6+3(1-x)<0\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(2 x-3>x+2\) (b) \(2 x-3 \leq x+2\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(5-3 x \leq-11+x\) (b) \(5-3 x>-11+x\)

Rainfall By noon, 3 inches of rain had fallen during a storm. Rain continued to fall at a rate of \(\frac{1}{4}\) inch per hour. (a) Find a formula for a linear function \(f\) that models the amount of rainfall \(x\) hours past noon. (b) Find the total amount of rainfall by 2: 30 P.M.