17 Jan The area of a rectangle is modeled by

A college student is moving into a campus dormitory. The student rents a moving truck for $19.95 plus $0.99 per mile. Before returning the truck, the student fills the tank with gasoline, which costs $65.32. The total cost is $144.67. Using a linear equation, explain the process to find how many miles the student drove the truck.

A hairdresser is deciding where to open her own studio. If the hairdresser chooses location A, she will pay $1,200 per month in rent and will charge $45 per haircut. If she chooses location B, she will pay $1,800 per month in rent and will charge $60 per haircut. Using linear equations, explain the process to find how many haircuts she would have to give in one month to make the same profit at either location

Experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By 2010, the estimated world tiger population was 3,200. The table below shows the estimated world tiger population for selected years from 1970 through 2010.

Year

Wild Tiger Population

1970

37,500

1980

28,000

1990

12,500

2000

6,300

2010

3,200

The polynomial function.png”> models the population of wild tigers, where.png”> represents the number of years since 1970.

a) Using the websitehttps://www.desmos.com/calculator, graph the polynomial using the settings 0 to 40 (step 5) for the x-axis and 0 to 40000 (step 5000) for the y-axis. Do not use commas in any of the numbers.Share the graph by exporting and downloading the image. Include the graph as part of your solution.

b) Find and interpret the function’s value at 40. Does this overestimate or underestimate the actual data shown in the table? By how much?

c) Find and interpret the function’s value at 10. Does this overestimate or underestimate the actual data shown in the table? By how much?

d) Based on the graph alone, what is the lowest population of wild tigers and in what year does this take place?

As a teacher, you assigned this problem to your class: “Factor the trinomial.png”>.” You received four different answers from your students. Provide appropriate feedback to these students explaining in detail their mistakes (if any).

a) .png”>

b) .png”>

c) .png”>

d) .png”>

The area of a rectangle is modeled by the polynomial.png”> square units. The width of the rectangle is modeled by the polynomial.png”> units. Showing all work, write a polynomial that represents the length of the rectangle.

A projectile is fired straight up with an initial velocity of 80 feet per second. Its height in feet after.png”> seconds is.png”>.

a) Explaining the process and showing all work, how long will it take for the projectile to hit the ground?

b) Explaining the process and showing all work, at what time(s) will the projectile be 96 feet in the air? What does this tell you about the projectile?