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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

Respuesta :

Answer:

(a)[tex]-3x^2+150x-10000[/tex]

(b)[tex]-\$16,863,760,000[/tex]

Step-by-step explanation:

Alphaville's Budget Surplus Model is [tex]-2x^2+ 500x[/tex]

Betaville's Budget Surplus Model is [tex]x^2- 100x + 10000.[/tex]

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.

[tex]-2x^2+ 500x-(x^2- 100x + 10000)\\[/tex]

Opening the brackets

[tex]-2x^2+ 500x-x^2+100x - 10000\\[/tex]

Collect like terms and simplify

[tex]-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000[/tex]

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

[tex]-3x^2+150x-10000[/tex]

(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

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

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