Chapter 3

Point \(A\) is a point on the number line halfway between \(-9\) and \(3 .\) Point \(B\) is a point halfway between \(A\) and the graph of 1 on the number line. Point \(B\) is the graph of what number?

The boiling point of oxygen is \(-182.962^{\circ} \mathrm{C}\). Oxygen's melting point is \(-218.4^{\circ} \mathrm{C} .\) What is the difference between the boiling point and the melting point of oxygen?

Determine whether each statement is always true, sometimes true, or never true. Assume that \(a\) and \(b\) are integers. If \(a>0\) and \(b>0,\) then \(a-b>0\)

Determine whether the statement is true or false. a. Every integer is a rational number. b. Every whole number is an integer. c. Every integer is a positive number. d. Every rational number is an integer.

Determine whether each statement is always true, sometimes true, or never true. Assume that \(a\) and \(b\) are integers. If \(a>0\) and \(b<0,\) then \(a-b>0\)

Place the correct symbol, \(<\) or \(>,\) between the numbers. $$-\frac{3}{4} \quad-0.7$$

Find the temperature after a rise of \(9^{\circ} \mathrm{C}\) from \(-6^{\circ} \mathrm{C}\)

Given any two different rational numbers, is it always possible to find a rational number between them? If so, explain how. If not, give an example of two different rational numbers for which there is no rational number between them.

Temperature The table at the right shows the average temperatures at different cruising altitudes for airplanes. Use the table for Exercise. $$\begin{array}{|l|l|} \hline \text{CruisingAltitude}&\text{Average Temperature} \\ \hline 12,000 \mathrm{ft} & 16^{\circ} \\ \hline 20,000 \mathrm{ft} & -12^{\circ} \\ \hline 30,000 \mathrm{ft} & -48^{\circ} \\ \hline 40,000 \mathrm{ft} & -70^{\circ} \\ \hline 50,000 \mathrm{ft} & -70^{\circ} \\ \hline \end{array}$$ What is the difference between the average temperatures at \(12,000\) ft and at \(40,000\) ft?

Temperature The table at the right shows the average temperatures at different cruising altitudes for airplanes. Use the table for Exercise. $$\begin{array}{|l|l|} \hline \text{CruisingAltitude}&\text{Average Temperature} \\ \hline 12,000 \mathrm{ft} & 16^{\circ} \\ \hline 20,000 \mathrm{ft} & -12^{\circ} \\ \hline 30,000 \mathrm{ft} & -48^{\circ} \\ \hline 40,000 \mathrm{ft} & -70^{\circ} \\ \hline 50,000 \mathrm{ft} & -70^{\circ} \\ \hline \end{array}$$ How much colder is the average temperature at \(30,000\) ft than at \(20,000\) ft?

Golf Use the equation \(S=N-P,\) where \(S\) is a golfer's score relative to par in a tournament, \(N\) is the number of strokes made by the golfer, and \(P\) is par, to find a golfer's score relative to par when the golfer made 49 strokes and par is 52 .

Golf Use the equation \(S=N-P,\) where \(S\) is a golfer's score relative to par in a tournament, \(N\) is the number of strokes made by the golfer, and \(P\) is par, to find a golfer's score relative to par when the golfer made 196 strokes and par is 208 .

Mathematics The distance \(d\) between point \(a\) and point \(b\) on the number line is given by the formula \(d=|a-b| .\) Find \(d\) when \(a=6\) and \(b=-15\)

Mathematics The distance \(d\) between point \(a\) and point \(b\) on the number line is given by the formula \(d=|a-b| .\) Find \(d\) when \(a=7\) and \(b=-12\)

Mathematics Given the list of numbers at the right, find the largest difference that can be obtained by subtracting one number in the list from a different number in the list. $$5,-2,-9,11,14$$

A Make up three addition problems such that each problem involves one positive and one negative addend, and each problem has the sum - 3. Then describe a strategy for writing these problems.

Make up three subtraction problems such that each problem involves a negative number minus a negative number, and each problem has a difference of \(-8 .\) Then describe a strategy for writing these problems.