Solve the Problem $T ( x )$ For a Home with a Taxable Value Thousand Dollars

question 191

Multiple Choice

Solve the problem.
-The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 29 mil. A city within the county also imposes a flat fee of $101 per
Home. a. Write a function representing the total amount of property tax $T ( x )$ for a home with a taxable value thousand dollars.
b. Write an equation for $T ^ { - 1 } ( x )$ .
c. What does the inverse function represent in the context of this problem?

• A) a. \(T ( x ) = 29 x + 101\)
• b. \(T ^ { - 1 } ( x ) = \frac { x - 101 } { 29 }\)
• c. \(T ^ { - 1 } ( x )\) represents the amount of property tax paid based on \(x\) thousand dollars of taxable value of the home.
• B) a. \(T ( x ) = 101 x + 29\)
• b. \(T ^ { - 1 } ( x ) = \frac { x - 29 } { 101 }\)
• c. \(T ^ { - 1 } ( x )\) represents the amount of property tax paid based on \(x\) thousand dollars of taxable value of the home.
• C) a. \(T ( x ) = 101 x + 29\)
• b. \(T ^ { - 1 } ( x ) = \frac { x - 29 } { 101 }\)
• c. \(T ^ { - 1 } ( x )\) represents the taxable value of a home (in \(\$ 1000\) ) based on \(x\) dollars of property tax paid on the home.
• D) a. \(T ( x ) = 29 x + 101\)
• b. \(T ^ { - 1 } ( x ) = \frac { x - 101 } { 29 }\)
• c. \(T ^ { - 1 } ( x )\) represents the taxable value of a home (in \(\$ 1000\) ) based on \(x\) dollars of property tax paid on the home. x

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Optimal Quantity

The amount of a good or service that yields the maximum benefit or utility to the consumer or producer.

Marginal Cost

The cost of producing one additional unit of a good or service, important in making decisions about production levels and pricing.

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Goods or services that are non-excludable and non-rivalrous, meaning they can be used by many without diminishing availability to others.

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A product or service that is consumed by an individual without its benefits being available to others who have not paid for it, characterized by excludability and rivalry.