Chapter 1

Climate Change During the past 50 years, the average rate of change in temperature in Antarctica has been \(0.9^{\circ} \mathrm{F}\) per decade. (a) Write a function \(W\) that calculates the increase in temperature after \(x\) years during this time period. (b) Evaluate \(W(15)\) and interpret the result.

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$0.6 x-2(0.5 x+0.2) \leq 0.4-0.3 x$$

Find (a) the distance between P and Q and (b) the coordinates of the midpoint M of the segment joining P and Q. $$P(13 x,-23 x), Q(6 x, x), \quad x>0$$

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$-0.9 x-(0.5+0.1 x)>-0.3 x-0.5$$

Find (a) the distance between P and Q and (b) the coordinates of the midpoint M of the segment joining P and Q. $$P(12 y,-3 y), Q(20 y, 12 y), \quad y>0$$

Suppose that P is an endpoint of a segment PQ and M is the midpoint of \(P Q .\) Find the coordinates of endpoint Q. $$P(7,-4), M(8,5)$$

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$-\frac{1}{2} x+0.7 x-5>0$$

Suppose that P is an endpoint of a segment PQ and M is the midpoint of $P Q . Find the coordinates of endpoint Q. $$P(13,5), M(-2,-4)$$

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$\frac{3}{4} x-0.2 x-6 \leq 0$$

Suppose that P is an endpoint of a segment PQ and M is the midpoint of $P Q . Find the coordinates of endpoint Q. $$P(5.64,8.21), M(-4.04,1.60)$$

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$-4(3 x+2) \geq-2(6 x+1)$$

Suppose that P is an endpoint of a segment PQ and M is the midpoint of $P Q . Find the coordinates of endpoint Q. $$P(-10.32,8.55), M(1.55,-2.75)$$

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$8(4-3 x) \geq 6(6-4 x)$$

Solve each three-part inequality analytically. Support your answer graphically. $$4 \leq 2 x+2 \leq 10$$

Solve each problem. Triangles can be classified by their sides. (a) An isosceles triangle has at least two sides of equal length. Determine whether the triangle with vertices (0,0),(3,4), and (7,1) is isosceles. (b) An equilateral triangle has all sides of equal length. Determine whether the triangle with vertices (-1,-1), (2,3) , and (-4,3) is equilateral. (c) Determine whether a triangle having vertices (-1,0) (1,0) and (0, \sqrt{3}) is isosceles, equilateral, or neither. (d) Determine whether a triangle having vertices (-3,3) (-2,5) and (-1,3) is isosceles, equilateral, or neither.

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

Solve each problem. At 9: 00 A.M., Car A is traveling north at 50 mph and is located 50 miles south of Car \(B\). Car B is traveling west at 20 mph. (a) Let (0,0) be the initial coordinates of Car B in the xy-plane, where units are in miles. Plot the locations of each car at 9: 00 A.M. and at 11: 00 A.M. (b) Find the distance between the cars at 11: 00 A.M.

Solve each three-part inequality analytically. Support your answer graphically. $$-10>3 x+2>-16$$

Solve each problem. Two ships leave the same harbor at the same time. The first ship heads north at 20 mph and the second ship heads west at 15 mph. (a) Draw a sketch depicting their positions after t hours. (b) Write an expression that gives the distance between the ships after t hours.

Solve each three-part inequality analytically. Support your answer graphically. $$4>6 x+5>-1$$

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

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. $$1<\frac{4 x-5}{-2}<9$$

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.

Error Tolerances Suppose that an aluminum can is manufactured so that its radius \(r\) can vary from 0.99 inches to 1.01 inches. What range of values is possible for the circumference \(C\) of the can? Express your answer by using a threepart inequality.

Error Tolerances Suppose that a square picture frame has sides that vary between 9.9 inches and 10.1 inches. What range of values is possible for the perimeter \(P\) of the picture frame? Express your answer by using a threepart inequality.