Question

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

Answer 1

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

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