Chapter 1

Simplify. $$ \frac{8-3(-2)}{2-5(-4)} $$

The area of a plane figure is a measure of the amount of surface of the figure. Find the area of each figure. (The area of a triangle is \(\frac{1}{2}\) the product of its base and height. The area of a rectangle is the product of its length and width. Recall that area is measured in square units IMAGE CANNOT COPY!

The expression \(\frac{I}{P T}\) represents the rate of interest being charged if a loan of \(P\) dollars for \(T\) years required \(I\) dollars in interest to be paid. Find the interest rate if a \(\$ 650\) loan for 3 years to buy a used IBM personal computer requires \(\$ 126.75\) in interest to be paid.

Simplify. $$ \frac{-3-2(-9)}{-15-3(-4)} $$

The expression \(\frac{d}{t}\) represents the average speed \(r\) in miles per hour if a distance of \(d\) miles is traveled in \(t\) hours. Find the rate to the nearest whole number if the distance between Dallas, Texas, and Kaw City, Oklahoma, is 432 miles, and it takes Peter Callac 8.5 hours to drive the distance.

Simplify. $$ \frac{-4-8(-2)}{-9-2(-3)} $$

Verizon long-distance service offers a "Talk to the World Plan," which offers lower rates on international phone calls to Verizon subscribers. This plan charges \(\$ 3.00\) per month, plus \(\$ 0.12\) per minute for calls to Japan. The expression \(3.00+\) \(0.12 m\) represents the long-distance charge for a call to Japan last month by a Verizon customer enrolled in this plan. Find the monthly bill for the customer whose only call to Japan lasted 84 minutes.

Simplify. $$ \frac{|5-9|+|10-15|}{|2(-3)|} $$

In forensics, the density of a substance is used to help identify it. The expression \(\frac{M}{V}\) represents the density of an object with a mass of \(M\) grams and a volume of \(V\) milliliters. Find the density of an object having a mass of 29.76 grams and a volume of 12 milliters.

Simplify. $$ \frac{|-3+6|+|-2+7|}{|-2 \cdot 2|} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ 3 x+2 y $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ 4 x+5 y $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ 2 x^{2}-y^{2} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ x^{2}-2 y^{2} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ x^{3}+3 y $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ y^{3}+3 x $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ \frac{2 x-5}{y-2} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ \frac{2 y-12}{x-4} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ \frac{-3-y}{x-4} $$

If \(x=-5\) and \(y=-3,\) evaluate each expression. $$ \frac{4-2 x}{y+3} $$

At the end of the third quarter of 2006 . General Motors reported a net loss of \(\$ 115\) million. If this continued, what would General Motor's income be after four more quarters?

Decide whether the given number is a solution of the given equation. Is 7 a solution of \(-5 x=-35 ?\)

Decide whether the given number is a solution of the given equation. Is \(-4\) a solution of \(2 x=x-1 ?\)

Decide whether the given number is a solution of the given equation. Is \(-20\) a solution of \(\frac{x}{10}=2 ?\)

Decide whether the given number is a solution of the given equation. Is \(-3\) a solution of \(\frac{45}{x}=-15 ?\)

Decide whether the given number is a solution of the given equation. Is 5 a solution of \(-3 x-5=-20 ?\)

Decide whether the given number is a solution of the given equation. Is \(-4\) a solution of \(2 x+4=x+8 ?\)

Explain why the product of an even number of negative numbers is a positive number.

If \(a\) and \(b\) are any real numbers, is the statement \(a \cdot b=b \cdot a\) always true? Why or why not?

Find any real numbers that are their own reciprocal.

Explain why 0 has no reciprocal.

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ \frac{q}{r \cdot t} $$

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ q^{2} \cdot r \cdot t $$

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ q+t $$

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ t+r $$

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ t(q+r) $$

If \(q\) is a negative number, \(r\) is a negative number, and t is a positive number, determine whether each expression simplifies to a positive or negative number. If it is not possible to determine, state so. $$ r(q-t) $$

Write each of the following as an expression and evaluate. The sum of \(-2\) and the quotient of \(-15\) and 3

Write each of the following as an expression and evaluate. The sum of 1 and the product of \(-8\) and \(-5\)

Write each of the following as an expression and evaluate. Twice the sum of \(-5\) and \(-3\)

Write each of the following as an expression and evaluate. 7 subtracted from the quotient of 0 and 5