Question

The polynomial -3x^2 + 900x represents the budget surplus of the town of Alphaville. Betaville's surplus is represented by x^2 - 200x + 80,000. If x represents the tax revenue in thousands from both towns, enter the expression that represents the total surplus of both towns together.

a) -2x^2 + 700x - 80,000
b) -3x^2 - 200x + 80,000
c) -2x^2 + 700x + 80,000
d) -3x^2 + 700x + 80,000

Answer 1

To determine the total budget surplus of Alphaville and Betaville combined, you add the polynomial expressions of their individual surpluses. The result is the option c) -2x^2 + 700x + 80,000.

Step-by-step explanation:

To find the expression that represents the total budget surplus of both Alphaville and Betaville together, we need to add their individual budget surplus expressions. The surplus for Alphaville is given by -3x^2 + 900x, and the surplus for Betaville is given by x^2 - 200x + 80,000. Adding these two polynomials gives us:

(-3x^2 + 900x) + (x^2 - 200x + 80,000) = -3x^2 + 900x + x^2 - 200x + 80,000 = -2x^2 + 700x + 80,000.

Therefore, the correct option that represents the total surplus of both towns together is option c).