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We appreciate your visit to To conserve water many communities have developed water restrictions The water utility charges a fee of 38 plus an additional 1 28 per hundred cubic. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additional $1.28 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $57 and $87 per month.

If \(x\) represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)

A) \(57 \leq 1.28x + 38 \leq 87\); To stay within the range, the usage should be between 14.8 and 38.3 HCF.

B) \(57 \leq 1.28x - 38 \leq 87\); To stay within the range, the usage should be between 74.2 and 97.7 HCF.

C) \(57 \leq 1.28x + 38 \leq 87\); To stay within the range, the usage should be between 14.8 and 38.3 HCF.

D) \(57 \leq 1.28x + 38 \leq 87\); To stay within the range, the usage should be between 14.8 and 67.9 HCF.

Answer :

Using a linear function, the correct option regarding the situation is given by:

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The bill is modeled by a linear function, with an intercept of $38 and a slope of $1.28, hence it is given by:

C(x) = 1.28x + 38

The bill should be between $57 and $87 dollars per month, hence:

57 <= C(x) <= 87.

The values of x are:

C(x) >= 57

1.28x + 38 >= 57

x >= 19/1.28

x >= 14.8.

C(x) >= 87

1.28x + 38 >= 87

x >= 49/1.28

x >= 38.3.

Hence option C is correct.

More can be learned about linear functions at https://brainly.com/question/24808124

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