Question

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. f(x) = −2x + 40 f(x) = 2x + 40 f(x) = −2x + 50 f(x) = 2x + 50

Answer 1

To find the equation in function form for the amount of trash removed each week, we can use the given information about the reduction in waste.

We are told that the reduction in waste each week is linear. So, we can assume that the amount of trash removed follows a linear equation in the form of f(x) = mx + b, where x represents the week number, f(x) represents the amount of trash removed, m represents the slope of the line, and b represents the y-intercept.

From the given information, we can determine the slope (m) of the line. The slope is calculated as the change in y divided by the change in x. In this case, the change in y is 30 (the amount of trash removed in week 10) minus 40 (the amount of trash removed in week 5), which gives us -10. The change in x is 10 (week 10) minus 5 (week 5), which gives us 5.

Therefore, the slope (m) is -10/5, which simplifies to -2.

Now, we need to determine the y-intercept (b). We can substitute the values of one of the given points (week 5, 40 dumpster loads) into the equation and solve for b:

f(5) = -2(5) + b

40 = -10 + b

40 + 10 = b

b = 50

So, the equation in function form to show the amount of trash removed each week is:

f(x) = -2x + 50

Therefore, the correct answer is: f(x) = -2x + 50.

Explanation:

Answer 2

So the answer to this question is the third one

Explanation:

For the answer to the question above,

let x = number of weeks let y = amount of waste.

The linear equation may be expressed as,y = mx + b

m and b are the slope and y - intercept, respectively. Substituting the corresponding values,

(Week 5) 45 = 5m + b

(Week 10) 30 = 10m + b

Solving for m and b gives the values as m = -3 and b = 60. Thus, the equation is

y = -3x + 60