Area and Linear Models

The area of a rectangular sandbox is (8x + 40) feet. What are the possible dimensions of the sandbox? Select all possible answers.

• 5(x + 8)

• 8(x + 5)

• 2(4x + 20)

• 4(2x + 10)

A sidewalk has an area that can be represented by the expression (8x + 24) feet. What are the possible dimensions of the sidewalk? Select all correct answers.

• 8(x + 3)

• 4(2x + 6)

• 2(4x + 12)

• 1(8x + 24)

The area of a rectangular pool is (15x – 9) square units. What are the dimensions of the pool?

• 5(3x - 3)

• 3(5x - 3)

• 3(14x)

• 3(15x)

The table below shows the number of hours 7 students studied for a math test and the grade each student earned on the test. How does Amanda’s test score compare to the score predicted using the linear best-fit model of data for a student who studied 3.50 hours?

• Amanda scored about 5 points lower than the score predicted for a student who studied 3.50 hours.

• Amanda scored about 5 points higher than the score predicted for a student who studied 3.50 hours.

• Amanda scored about 2 points lower than the score predicted for a student who studied 3.50 hours.

• Amanda scored about 2 points higher than the score predicted for a student who studied 3.50 hours.

Students in a group of chess teams submitted data about hours of team practice and the number of matches the team won.  The graph shows the results of the data.  Based on the linear regressions equation y = 3.14x + 3.52, if a team practices 4.5 hours per week next year, which is the best prediction of the number of chess matches a team could expect to win?  

• about 24

• about 12

• about 8

• about 18

• A

• B

• C

• D

• A

• B

• C

• D

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage.  If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

• C = 0.20x + 15

• C =15 (0.20x)

• C = 15 + x + 0.20

• C = 0.20 + 15x

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. What equation best represents how much his tenants will now have to pay?

• y = 425x + 600

• y = 425 + 600x

• y = 400x + 625

• y = 400 + 625x

Conner has $25,000 in his bank account. Every month he spends $1,500. He does not add money to the account.

Write a linear model that shows how much money will be in the account after x months.

• y=25000x-1500

• y=25000+1500

• y=1500x+25000

• y=-1500x+25000