Bret had a rectangular piece of plywood with dimensions x feet and 10 feet. He put a frame along 15 feet of the edge of the plywood.

An expression is shown below:

(2x + 20) – 15

Part A: What does the expression represent?

Part B: What does 2x + 20 represent?

Part C: What does 2x represent?

<object:standard:macc.912.a-ced.1.1, macc.912.a-rei.1.1,=”” macc.912.a-rei.2.3=””>Tara teaches ballet in groups of two students. She rents a room for the ballet classes at $350 per month. She charges $50 per hour per student. Tara teaches five groups of students, and her net earnings per month are $3,150.

Part A: If each student learns ballet for the same number of hours, write an equation that can be used to calculate the number of hours each student learns ballet in a month. (5 points)

Part B: How many hours did each student learn ballet each month? Show your work and justify each step of your work.

<object:standard:macc.912.f-if.1.1, macc.912.f-if.1.2=””>The table below shows the cube roots of different numbers:

Number (x) |
8 | 27 | 64 | 125 |

Cube root (y) |
2 | 3 | 4 | 5 |

Part A: Does the table represent y as a function of x? Justify your answer. (5 points)

Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below:

f(x) = 10 + 20x

What is the value of f(100), and what does f(100) represent?

<object:standard:macc.912.f-if.2.4, macc.912.f-if.2.5,=”” macc.912.f-if.2.6=””>The graph below shows the distance (y) in kilometers of two cars from their destination at different times (x) in minutes. The table shows the values plotted on the graph:

Time (in minutes) x |
0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |

Car 1 (in km) y |
70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |

Car 2 (in km) y |
70 | 57.19511 | 46.73256 | 38.18388 | 31.199 | 25.4919 | 20.82871 | 17.01861 |

Part A: What does the x-intercept of the function for car 1 represent?

Part B: What does the y-intercept of the function for car 2 represent?

Part C: What is the domain of the functions for car 1 and car 2?

Part D: What is the average rate of change from x = 30 to x = 40 for the function representing the motion for car 2? What does the value of this average rate of change represent?

<object:standard:macc.912.a-ced.1.1, macc.912.a-rei.1.1,=”” macc.912.a-rei.2.3=””>

<object:standard:macc.912.a-ced.1.2, macc.912.f-bf.1.1,=”” macc.912.f-bf.1.1a,=”” macc.912.f-if.3.7,=”” macc.912.f-if.3.7a=””>Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 54 km/h. After four hours, the velocity of the car is 58 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used.

Part B: How can you graph the equation obtained in Part A for the first six hours?

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