Answer:
To find the area of the wood deck only, we need to subtract the area of the pool from the overall area of the pool deck.
Overall area of the pool deck = 3w^2 + 12.5w - 5.2
Area of the pool = 0.6w^2 - 1.4w + 2.9
So, the area of the wood deck only can be represented by the polynomial:
aw^2 + bw + c = (3w^2 + 12.5w - 5.2) - (0.6w^2 - 1.4w + 2.9)
Simplifying the expression inside parentheses:
aw^2 + bw + c = 3w^2 + 12.5w - 5.2 - 0.6w^2 + 1.4w - 2.9
Combining like terms:
aw^2 + bw + c = (3 - 0.6)w^2 + (12.5 + 1.4)w + (-5.2 - 2.9)
Simplifying further:
aw^2 + bw + c = 2.4w^2 + 13.9w - 8.1
So, the correct values of a and b are:
a = 2.4
b = 13.9
Step-by-step explanation: hope this helps <3