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Thank you for visiting 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 is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

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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Rewritten by : Jeany

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