28.03.2021

A school system is reducing the amount dumpster loads of removed each week dumpster loads of waste removed in there were 30 dumpster loads removed Assume that the reduction in the amount of waste week islinear an equation in function form to show the amount of trash removed each week

. 5

Faq

Mathematics
Step-by-step answer
P Answered by PhD

 y = -3x + 60

Step-by-step 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

Mathematics
Step-by-step answer
P Answered by PhD

 y = -3x + 60

Step-by-step 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

Mathematics
Step-by-step answer
P Answered by PhD
Let x be the number of weeks and y be the amount of waste. The linear equation may be expressed as,
                                        y = mx + b
where m and b are the slope and y - intercept, respectively. Substituting the corresponding values,
   (Week 5)                     40 = 5m + b
   (Week 10)                   30 = 10m + b
Solving for m and b gives the values as m = -2 and b =50. Thus, the equation is 
                                       y = -2x + 50
The answer is letter C. 
Mathematics
Step-by-step answer
P Answered by Specialist
The answer would be C because you are subtracting 3 by a number(x) because you are REMOVING garbage. And if you remove the x from 3x and replace it with the number of weeks, you'll get the number of loads dumped. For example -3(5)+60. Follow your order of operations. Multiply first to get -15. Then add that to 60. You will get 45, which is the correct answer because in the problem, the number of loads are 45. Or how about this, -3(10)+60. Multiply first to get -30, then add positive 60 to get 30 overall. Since 30 is the number of loads removed in the problem, your answer is correct, thus, making the correct equation C.
Mathematics
Step-by-step answer
P Answered by PhD

y = -3x + 60, D: x ≥ 0, r: y ≥ 0

Step-by-step explanation:

1. Find the slope (x-axis is the week number, y-axis is the # of dump loads)

Slope equation: (y₁ - y₂)/(x₁ - x₂), where two points are (x₁, y₁) and (x₂, y₂)

Plug in: (45 - 30)/(5 - 10)

Subtract: 15/(-5)

Divide: -3, representing the number of dumps removed/week

2. Find the y-intercept (when x = 0)

Since we found that 3 dumps are removed per week, we can find that at week 0, there were 60 dump loads.

3. Construct equation

Point-intercept equation: y = mx + b, where m = slope, b = y-intercept

Plug in: y = -3x + 60 (with the domain of x ≥ 0 and the range of y ≥ 0)

Mathematics
Step-by-step answer
P Answered by PhD
Since it is given that the reduction in the amount of waste each week is linear, it is conclusive that these data are also in arithmetic sequence. First, determine the common difference (d)
                                 d = (a10 - a5) / (10 - 5)
Subsituting the known values,
                                d = (30 - 40) / 5 = -2
To determine any term (at) of the arithmetic sequence,
                            at = a1 + (n - 1) x d 
Solve for a1 by using either the given a5 or a10,
                            40 = a1 + (5 -1) x -2     ; a1 = 48
The equation becomes, 
                                 at = 48 + -2(n -1)
                               

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