Question

Algebra 1. Can someone please check my answers, I will medal and fan!

Answer 1

Celina had a rectangular tablecloth with dimensions x feet and 3 feet. She put lace along 4 feet of the edge of the tablecloth.

An expression is shown below:

(2x + 6) - 4

Part A: What does the expression represent? (4 points)

Part B: What does 2x + 6 represent? (3 points)

Part C: What does 2x represent? (3 points)





Question 2 (Essay Worth 10 points)

(01.07, 02.01)

Donna teaches dance in groups of five students. She rents a hall for the dance classes at $450 per month. She charges $40 per hour per student. Donna teaches four groups of students, and her net earnings per month are $4,350.

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

Part B: How many hours did each student learn dance each month? Show your work and justify each step. (5 points)





Question 3 (Essay Worth 10 points)

(03.02)

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? (5 points)




Question 4 (Essay Worth 10 points)

(03.05, 4.03)

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:

graphs of y is equal to 70 minus x and y is equal to 70 multiplied by 0.98 to the power of x


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? (2 points)

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

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

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? (4 points)




Question 5 (Essay Worth 10 points)

(03.06)

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 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. (5 points)

Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)





Question 6 (Essay Worth 10 points)

(05.02, 5.03)

The graph shows the functions f(x), p(x), and g(x):

Graph of function g of x is y is equal to 2 multiplied by 1.5 to the power of x. The straight line f of x joins ordered pairs 3, 1 and 2, minus 1 and is extended on both sides. The straight line p of x joins the ordered pairs 1, 3 and 3, 1 and is extended on both sides.

Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)

Part B: Write any two solutions for f(x). (3 points)

Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)





Question 7 (Essay Worth 10 points)

(05.06)

The coordinate plane below represents a city. Points A through F are schools in the city.

graph of coordinate plane. Point A is at 2, negative 3. Point B is at negative 3, negative 4. Point C is at negative 4, 2. Point D is at 2, 4. Point E is at 3, 1. Point F is at negative 2, 3.

Part A: Using the graph above, create a system of inequalities that only contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A. (3 points)

Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x - 1. Explain how you can identify the schools that William is allowed to attend. (2 points)