Chapter 1

Match the power with the words that describe it. $$ 6^{4} $$ A. four to the sixth power B. three to the seventh power C. seven to the third power D. six to the fourth power

Evaluate the expression. $$ 9 \div 3 \cdot 2 $$

Check to see if \(a=5\) is or is not a solution of the equation. $$ a+8=13 $$

Write the sentence as an equation or an inequality. The product of 7 and a number y is 42.

State the meaning of the variable expression and name the operation. $$ 5+n $$

Make an input-output table for the function. Use 0, 1, 2, 3, 4, and 5 as values for x. $$ y=(x+3) \cdot 7 $$

SCHOOL ENROLLMENT The table shows the number of students (in millions) enrolled in school in the United States by age. Make a table showing the total number of students enrolled for each given year. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Age } & {1980} & {1985} & {1990} & {1995} & {2000} \\ \hline 14-15 \text { years old } & {7282} & {7362} & {6555} & {7651} & {8100} \\\ \hline 16-17 \text { years old } & {7129} & {6654} & {6098} & {6997} & {7600} \\\ \hline 18-19 \text { years old } & {3788} & {3716} & {4044} & {4274} & {4800} \\\ \hline \end{array} $$ Which year had the least number of students enrolled? Which had the greatest number of students enrolled?

Evaluate the variable expression when \(t=3\) \(t^{2}\)

Evaluate the expression. $$ 2 \cdot 3^{2}+5 $$

Check to see if \(a=5\) is or is not a solution of the equation. $$ 27=36-2 a $$

Write the sentence as an equation or an inequality. 20 divided by a number n is less than or equal to 2.

State the meaning of the variable expression and name the operation. $$ (8)(x) $$

Make an input-output table for the function. Use 0, 1, 2, 3, 4, and 5 as values for x. $$ y=85-15 x $$

You are one mile from your home. You can walk at a speed of 4 miles per hour. The subway comes by every 15 minutes, and you heard one come by 3 minutes ago. The subway ride takes 8 minutes. Which will get you home faster, walking or taking the subway? Explain.

SCHOOL ENROLLMENT The table shows the number of students (in millions) enrolled in school in the United States by age. Make a table showing the total number of students enrolled for each given year. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Age } & {1980} & {1985} & {1990} & {1995} & {2000} \\ \hline 14-15 \text { years old } & {7282} & {7362} & {6555} & {7651} & {8100} \\\ \hline 16-17 \text { years old } & {7129} & {6654} & {6098} & {6997} & {7600} \\\ \hline 18-19 \text { years old } & {3788} & {3716} & {4044} & {4274} & {4800} \\\ \hline \end{array} $$ Did the total enrollment increase for each 5 year period? Explain.

Evaluate the variable expression when t = 3. \(1+t^{3}\)

Evaluate the expression. $$ 2^{3} \cdot 3^{2} $$

Write the phrase as a variable expression. Let x represent the number. A number decreased by 3

Check to see if \(a=5\) is or is not a solution of the equation. $$ a-0=5 $$

Evaluate the variable expression when \(k=3\) $$ 11+k $$

Make an input-output table for the function. Use 0, 1, 2, 3, 4, and 5 as values for x. $$ y=5(15-x) $$

Kudzu is a type of Japanese vine that grows at a rate of 1 foot per day during the summer. On August \(1,\) the length of one vine was 50 feet. What was the length on July \(1 ?\) HINT: July has 31 days. Use the verbal phrases to complete the verbal model. Total length Original length Number of days Growth rate

Evaluate the variable expression when t = 3. \(4 t^{2}\)

Evaluate the variable expression when \(x=3.\) $$ x^{2}-5 $$

Write the phrase as a variable expression. Let x represent the number. Difference of 10 and a number

Check to see if \(a=5\) is or is not a solution of the equation. $$ 2 a+1=11 $$

Evaluate the variable expression when \(k=3\) $$ k-2 $$

Make an input-output table for the function. Use 0, 1, 2, 3, 4, and 5 as values for x. $$ y=2(6 x+10) $$

Kudzu is a type of Japanese vine that grows at a rate of 1 foot per day during the summer. On August \(1,\) the length of one vine was 50 feet. What was the length on July \(1 ?\) HINT: July has 31 days. Assign labels to the verbal model. Use \(x\) to represent the unknown value.

Evaluate the variable expression when t = 3. \((4 t)^{2}\)

Evaluate the variable expression when \(x=3.\) $$ x^{3}+5 x $$

Write the phrase as a variable expression. Let x represent the number. The sum of 5 and a number

Check to see if \(a=5\) is or is not a solution of the equation. $$ 6 a-5=15 $$

Evaluate the variable expression when \(k=3\) $$ 7 k $$

Kudzu is a type of Japanese vine that grows at a rate of 1 foot per day during the summer. On August \(1,\) the length of one vine was 50 feet. What was the length on July \(1 ?\) HINT: July has 31 days. Choose the algebraic model that best represents the verbal model. A. \((x+1) \cdot 31=50\) B. \(x+(1 \cdot 31)=50\) C. \(x=50 \div 1\) D. \(x+(1+31)=50\)

Draw a line graph to represent the function given by the input-output table. $$ \begin{array}{|c|c|c|c|c|c|} \hline Input\quad x & {1} & {2} & {3} & {4} & {5} & {6} \\ \hline Output \quad y & {14} & {12} & {10} & {8} & {6} & {4} \\ \hline \end{array} $$

Write the expression in exponential form. two cubed

Evaluate the variable expression when \(x=3.\) $$ x+3 x^{4} $$

Write the phrase as a variable expression. Let x represent the number. 9 more than a number

Check to see if \(a=5\) is or is not a solution of the equation. $$ 5 a+4=26 $$

Evaluate the variable expression when \(k=3\) $$ \frac{k}{33} $$

Draw a line graph to represent the function given by the input-output table. $$ \begin{array}{|c|c|c|c|c|c|} \hline Input\quad x & {1} & {2} & {3} & {4} & {5} & {6} \\ \hline Output \quad y & {8} & {11} & {14} & {17} & {20} & {23} \\ \hline \end{array} $$

The table shows the number of gallons of water needed to produce one pound of some foods. Make a bar graph of the data. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Food \((11\) b) } & {\text { Lettuce }} & {\text { Tomatoes }} & {\text { Melons }} & {\text { Broccoli }} & {\text { Corn }} \\ \hline \text { Water (gallons) } & {21} & {29} & {40} & {42} & {119} \\ \hline \end{array} $$

Write the expression in exponential form. \(p\) squared

Evaluate the variable expression when x = 3. $$ \frac{27}{x}-2+16 $$

Write the phrase as a variable expression. Let x represent the number. Product of 4 and a number

Check to see if \(a=5\) is or is not a solution of the equation. $$ 45 \div a=9 $$

Evaluate the variable expression when \(k=3\) $$ \frac{18}{k} $$

The distance \(d\) (in miles) that sound travels in air in time \(t\) (in seconds) is represented by the function \(d=0.2 t .\) Make a table of the input \(t\) and the output \(d .\) Use \(t\) values of \(0,5,10,15,20,25,\) and \(30 .\) Use your table to help you draw the graph of the function.

Kudzu is a type of Japanese vine that grows at a rate of 1 foot per day during the summer. On August \(1,\) the length of one vine was 50 feet. What was the length on July \(1 ?\) HINT: July has 31 days. Check that your answer is reasonable.