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To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars 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.) 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 37.6 HCF. 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 58.2 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 38.2 and 78.7 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 58.9 and 78.7 HCF.

Sagot :

Using a linear function, we have that:

  • The inequality is: 54 ≤ C(x) ≤ 82.
  • To stay within the range, the usage should be between 17.7 and 37.6 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.

For the cost function, we have that:

  • The fee of $29 is the intercept.
  • The cost of $1.41 per HCF is the slope.

Hence the function is:

C(x) = 29 + 1.41x.

The recommended monthly bill for a household is between $54 and $82 dollars per month, hence the inequality is given by:

54 ≤ C(x) ≤ 82.

The bounds of the range will be found as follows:

29 + 1.41x = 54

x = (54 - 29)/1.41

x = 17.7.

29 + 1.41x = 82

x = (82 - 29)/1.41

x = 37.6.

Hence the correct option is:

To stay within the range, the usage should be between 17.7 and 37.6 HCF.

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

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