91Ó°ÊÓ

Solve each three-part inequality analytically. Support your answer graphically. $$-3 \leq \frac{x-4}{5}<4$$

Solve each three-part inequality analytically. Support your answer graphically. $$1<\frac{4 x-5}{-2}<9$$

Solve each problem. Prove that the midpoint \(M\) of the line segment joining endpoints \(P\left(x_{1}, y_{1}\right)\) and $Q\left(x_{2}, y_{2}\right) has coordinates $$ \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) $$ by showing that the distance between P and M is equal to the distance between M and Q and that the sum of these distances is equal to the distance between P and Q.

Solve each three-part inequality analytically. Support your answer graphically. $$-\frac{1}{2}

Solve each three-part inequality analytically. Support your answer graphically. $$-\frac{3}{4}<2 x-1<\frac{3}{4}$$

Solve each three-part inequality analytically. Support your answer graphically.. $$-4 \leq \frac{1}{2} x-5 \leq 4$$

Solve each three-part inequality analytically. Support your answer graphically. $$-2<\frac{x-4}{6}<2$$

Solve each three-part inequality analytically. Support your answer graphically. $$\sqrt{2} \leq \frac{2 x+1}{3} \leq \sqrt{5}$$

Solve each three-part inequality analytically. Support your answer graphically. $$\pi \leq 5-4 x<7 \pi$$

Amtrak Passengers In 2008 Amtrak had 28.7 million passengers, and in 2012 it had a record 31.2 million passengers. (a) Find a linear function \(P(x)=a x+b\) that models the number of passengers in millions \(x\) years after 2008 (b) Interpret the slope of the graph of \(y=P(x)\) (c) Use \(P(x)\) to estimate the number of passengers in 2014 (d) Assuming trends continue, predict when Amtrak might have 35 million passengers.