Chapter 4

Determine whether the ordered pair is a solution of the equation. (Lesson 4.2) $$ 5 x+6 y=-1,(1,-1) $$

Determine whether the graphs of the two equations are parallel lines. Explain your answer. $$line\quad a: y=x+8 line\quad b: x-y=-1$$

Rewrite the equation so that \(y\) is a function of \(x\). $$-8 x+2 y=10$$

Find the least common denominator (LCD) of each pair of fractions. Then rewrite each pair with their LCD. (Skills Review p.762). $$ \frac{12}{13}, \frac{5}{26} $$

In Exercises 49–51, Mary Gordon is training for a triathlon. Like most triathletes she regularly trains in two of the three events every day. On Saturday she expects to burn about 800 calories during her workout by running and swimming. $$Running: 7.1 calories per minute \quad Swimming: 10.1 calories per minute \quad Bicycling: 6.2 calories per minute$$ If Mary Gordon spends 45 minutes running, about how many minutes will she have to spend swimming to burn 800 calories?

ABSOLUTE VALUE Evaluate the expression. $$ \left|\frac{-2}{3}\right| $$

In Exercises \(52-54,\) use the following information. The number of people who worked for the railroads in the United States each year from 1989 to 1995 can be modeled by the equation \(y=-6.6 x+229,\) where \(x\) represents the number of years since 1989 and \(y\) represents the number of railroad employees (in thousands). Find the \(y\) -intercept of the line. What does it represent?

Determine whether the ordered pair is a solution of the equation. (Lesson 4.2) $$ -4 x-3 y=-8,(-4,2) $$

Determine whether the graphs of the two equations are parallel lines. Explain your answer. $$line\quad a: 2 x-5 y=-3 line\quad b: 5 x+2 y=6$$

Rewrite the equation so that \(y\) is a function of \(x\). $$-3 x+6 y=12$$

Find the least common denominator (LCD) of each pair of fractions. Then rewrite each pair with their LCD. (Skills Review p.762). $$ \frac{7}{18}, \frac{2}{15} $$

In Exercises 52 and 53, use the table showing the boiling point of water (in degrees Fahrenheit) for various altitudes (in feet). $$ \begin{array}{|c|c|c|c|c|c|c|} \hline \text { Altitude } & {0} & {500} & {1000} & {1500} & {2000} & {2500} \\\ \hline \text { Boiling Point } & {212.0} & {211.1} & {210.2} & {209.3} & {208.5} & {207.6} \\ \hline \end{array} $$ Make a graph that shows the boiling point of water and the altitude. Use the horizontal axis to represent the altitude.

SOLVING EQUATIONS Solve the equation. $$ 3 x-6=0 $$

Determine whether the relation is a function. If it is a function, give the domain and range. $$ (-2,-2),(0,0),(1,1),(2,2) $$

In Exercises \(52-54,\) use the following information. The number of people who worked for the railroads in the United States each year from 1989 to 1995 can be modeled by the equation \(y=-6.6 x+229,\) where \(x\) represents the number of years since 1989 and \(y\) represents the number of railroad employees (in thousands). About how many people worked for the railroads in \(1995 ?\)

Determine whether the ordered pair is a solution of the equation. (Lesson 4.2) $$ 3 x+4 y=36,(4,6) $$

Determine whether the graphs of the two equations are parallel lines. Explain your answer. $$line\quad a: y+6 x-8=0 line\quad b: 2 y=12 x-4$$

Rewrite the equation so that \(y\) is a function of \(x\). $$x+\frac{2}{5} y=-1$$

Find the least common denominator (LCD) of each pair of fractions. Then rewrite each pair with their LCD. (Skills Review p.762). $$ \frac{3}{20}, \frac{7}{15} $$

use the table showing the boiling point of water (in degrees Fahrenheit) for various altitudes (in feet). $$ \begin{array}{|c|c|c|c|c|c|c|} \hline \text { Altitude } & {0} & {500} & {1000} & {1500} & {2000} & {2500} \\\ \hline \text { Boiling Point } & {212.0} & {211.1} & {210.2} & {209.3} & {208.5} & {207.6} \\ \hline \end{array} $$ Describe the relationship between the altitude and the boiling point of water.

SOLVING EQUATIONS Solve the equation. $$ 6 x+5=35 $$

Determine whether the ordered pair is a solution of the equation. (Lesson 4.2) $$ 5 x-3 y=47,(2,9) $$

Determine whether the graphs of the two equations are parallel lines. Explain your answer. $$line\quad a: 3 y-4 x=3 line\quad b: 3 y=-4 x+9$$

Determine whether the equation is true or false. $$ 1.3-2.7=1.4 $$

In Exercises \(54-56,\) use the following information. An Internet service provider estimates that the number of households \(h\) (in millions) with Internet access can be modeled by the equation \(h=6.76 t+14.9\) where \(t\) represents the number of years since 1996. Make a table of values. Use \(0 \leq t \leq 6\) for \(1996-2002\)

SOLVING EQUATIONS Solve the equation. $$ x+1=-3 $$

Find the \(x\) -intercept of the graph of the equation \(3 x+y=-9\) A. \(-3\) B. 3 C. 9 D. -9

Find the number with the given prime factorization. (Skills Review p. 761) $$ 2 \cdot 3 \cdot 11 $$

Determine whether the equation is true or false. $$ \frac{1.8}{1.8}-1=0 $$

SOLVING EQUATIONS Solve the equation. $$ a-3=-2 $$

Find the \(y\) -intercept of the graph of the equation \(2 x-3 y=12\). F. -4 G. -1 H. 4 J. 3

Find the number with the given prime factorization. (Skills Review p. 761) $$ 3 \cdot 5 \cdot 7 $$

Use the following information. Snow fell for 9 hours at a rate of \(\frac{1}{2}\) inch per hour. Before the snowstorm began, there were already 6 inches of snow on the ground. The equation \(y=\frac{1}{2} x+6\) models the depth y (in inches) of snow on the ground after x hours. What is the slope of\(y=\frac{1}{2} x+6 ?\)What is the y-intercept?

Determine whether the equation is true or false. $$ \left(\frac{2.7}{0.3}+1\right) \div 10=0 $$

Use the following information. An Internet service provider estimates that the number of households \(h\) (in millions) with Internet access can be modeled by the equation \(h=6.76 t+14.9\) where \(t\) represents the number of years since 1996. What does the graph mean in the context of the real-life situation?

SOLVING EQUATIONS Solve the equation. $$ \frac{1}{2} x-1=-1 $$

Find the difference. $$ 5-9 $$

Find the number with the given prime factorization. (Skills Review p. 761) $$ 2^{3} \cdot 7 $$

Use the following information. Snow fell for 9 hours at a rate of \(\frac{1}{2}\) inch per hour. Before the snowstorm began, there were already 6 inches of snow on the ground. The equation \(y=\frac{1}{2} x+6\) models the depth y (in inches) of snow on the ground after x hours. Explain what the slope and y-intercept represent in the snowstorm model.

Determine whether the equation is true or false. $$ 14.4+0.14=2.88 $$

Which ordered pair is a solution of \(-3 x+y=-5 ?\) $$ (A)(8,-16) $$ $$ (B)(8,-29) $$ $$ (C)(8,-64) $$ $$ (D)(8,19) $$

SOLVING EQUATIONS Solve the equation. $$ \frac{1}{5} r+3=4 $$

Find the difference. $$ 17-(-6) $$

Find the number with the given prime factorization. (Skills Review p. 761) $$ 5^{3} \cdot 7 \cdot 11 $$

Determine whether the equation is true or false. $$ (7.8)(1.5)+4.6=16.3 $$

Rewrite the equation \(-2 x+5 y=10\) in function form. $$ (F)y=2 x+2 $$ $$ (G)y=2 x+5 $$ $$ (H)y=\frac{2}{5} x+2 $$ $$ (J)y=\frac{2}{5} x+5 $$

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form. $$ 7 \frac{4}{9}-4 \frac{1}{9} $$

It takes 4.25 years for starlight to travel 25 trillion miles. Let t be the number of years and let f(t) be trillions of miles traveled. Write a linear function f(t) that expresses the distance traveled as a function of time.

Find the difference. $$ |8|-13 $$

Use the following information.You have \(\$50\) in your savings account at the beginning of the year. Each month you save \(\$30\). Assuming no interest is paid, the equation s = 30m + 50 models the amount of money s (in dollars) in your savings account after m months. Explain what the y-intercept and slope represent in this model.