Chapter 2

A 170 -pound person uses 5.3 calories per minute when bicycling at a speed of \(5.5 \mathrm{mph}\). How long must a person ride a bike at this speed in order to use at least 200 calories? Round up to the nearest minute. (Source: Same as Exercise 67)

Write each phrase as an algebraic expression. Use \(x\) for the unknown number. Three times a number

Must the percents in a circle graph have a sum of \(100 \%\) ? Why or why not?

Find each multiplicative inverse or reciprocal. $$ -\frac{3}{5} $$

\(12=3 j-4\)

The average temperature on the planet Jupiter is \(-227^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius. Round to the nearest degree.

Evaluate each expression for the given values. See Section \(1.8 .\) \(2 W+2 L ; \quad W=7\) and \(L=10\)

Evaluate each expression. $$ 3^{4} $$

Write each phrase as an algebraic expression. Use \(x\) for the unknown number. The sum of -3 and twice a number

Perform each indicated operation and simplify. $$ \frac{3 x}{3} $$

\(10-3 x-6-9 x=7\)

Write each percent as a decimal. $$ 32 \% $$

Evaluate each expression for the given values. See Section 1.8 \(\frac{1}{2} B h ; \quad B=14\) and \(h=22\)

Evaluate each expression. $$ 4^{3} $$

Write each phrase as an algebraic expression. Use \(x\) for the unknown number. The difference of 8 and twice a number

Perform each indicated operation and simplify. $$ \frac{-2 y}{-2} $$

\(12 x+30+8 x-6=10\)

Write each percent as a decimal. $$ 8 \% $$

Evaluate each expression. $$ 1^{8} $$

Write each phrase as an algebraic expression. Use \(x\) for the unknown number. The product of 9 and the sum of a number and 20

Perform each indicated operation and simplify. $$ -5\left(-\frac{1}{5} y\right) $$

\(z-5 z=7 z-9-z\)

Write each percent as a decimal. $$ 200 \% $$

Evaluate each expression for the given values. See Section 1.8 \(r \cdot t ; \quad r=15\) and \(t=2\)

Evaluate each expression. $$ 0^{7} $$

Write each phrase as an algebraic expression. Use \(x\) for the unknown number. The quotient of -12 and the difference of a number and 3

Perform each indicated operation and simplify. $$ 7\left(\frac{1}{7} r\right) $$

\(t-6 t=-13+t-3 t\)

Write each percent as a decimal. $$ 0.5 \% $$

A golden rectangle is a rectangle whose length is approximately 1.6 times its width. The early Greeks thought that a rectangle with these dimensions was the most pleasing to the eye and examples of the golden rectangle are found in many early works of art. For example, the Parthenon in Athens contains many examples of golden rectangles. Mike Hallahan would like to plant a rectangular garden in the shape of a golden rectangle. If he has 78 feet of fencing available, find the dimensions of the garden.

Evaluate each expression. $$ \left(\frac{7}{8}\right)^{2} $$

a. Solve: \(\quad x+3=x+3\) b. If you simplify an equation (such as the one in part a) and get a true statement such as \(3=3\) or \(0=0\), what can you conclude about the solution(s) of the original equation? C. On your own, construct an equation for which every real number is a solution.

Perform each indicated operation and simplify. $$ \frac{3}{5}\left(\frac{5}{3} x\right) $$

\(-x-\frac{4}{5}=x+\frac{1}{2}+\frac{2}{5}\)

Write each decimal as a percent. $$ 0.17 $$

Dr. Dorothy Smith gave the students in her geometry class at the University of New Orleans the following question. Is it possible to construct a triangle such that the second angle of the triangle has a measure that is twice the measure of the first angle and the measure of the third angle is 5 times the measure of the first? If so, find the measure of each angle. (Hint: Recall that the sum of the measures of the angles of a triangle is \(180^{\circ} .\) )

Evaluate each expression. $$ \left(\frac{2}{3}\right)^{3} $$

a. Solve: \(\quad x+3=x+5\) b. If you simplify an equation (such as the one in part a) and get a false statement such as \(3=5\) or \(10=17,\) what can you conclude about the solution(s) of the original equation? C. On your own, construct an equation that has no solution.

Perform each indicated operation and simplify. $$ \frac{9}{2}\left(\frac{2}{9} x\right) $$

\(x+\frac{3}{7}=-x+\frac{1}{3}+\frac{4}{7}\)

Write each decimal as a percent. $$ 0.03 $$

Only male crickets chirp. They chirp at different rates depending on their species and the temperature of their environment. Suppose a certain species is currently chirping at a rate of 90 chirps per minute. At this rate, how many chirps occur in one hour? In one 24 -hour day? In one year?

Match each equation in the first column with its solution in the second column. Items in the second column may be used more than once. a. all real numbers b. no solution C. 0 $$ 5 x+1=5 x+1 $$

Write two terms whose sum is \(-3 x\).

\(-15+37=-2(x+5)\)

Write each decimal as a percent. $$ 7.2 $$

The human eye blinks once every 5 seconds on average. How many times does the average eye blink in one hour? In one 16 -hour day while awake? In one year while awake?

Match each equation in the first column with its solution in the second column. Items in the second column may be used more than once. a. all real numbers b. no solution C. 0 $$ 3 x+1=3 x+2 $$

Write four terms whose sum is \(2 y-6\).

\(-19+74=-5(x+3)\)