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storchak [24]
3 years ago
6

Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year

based on the tax revenue (in thousands of dollars) for the year. Using historical data, Alphaville’s planner produced the model -2x2+ 500x, while Betaville’s planner produced the model x2- 100x + 10,000. What expression gives how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue? If the tax revenue that year in each town is $75,000, how much greater is Alphaville’s budget surplus than Betaville’s that year?
Please help! I WILL MARK BRAINLIEST
Mathematics
1 answer:
kramer3 years ago
3 0

Answer:

(a)-3x^2+150x-10000

(b)-\$16,863,760,000

Step-by-step explanation:

Alphaville's Budget Surplus Model is -2x^2+ 500x

Betaville's Budget Surplus Model is x^2- 100x + 10000.

We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.

  • To do this, we subtract Betaville's Model from Alphaville's model.

-2x^2+ 500x-(x^2- 100x + 10000)\\

Opening the brackets

-2x^2+ 500x-x^2+100x - 10000\\

Collect like terms and simplify

-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000

The expression that shows how much greater Alphaville's Budget is:

-3x^2+150x-10000

(b) If the tax revenue that year in each town is $75,000

We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000

-3x^2+150x-10000\\=-3(75000)^2+150(75000)-10000\\=-\$16,863,760,000

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