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Answer :
Final answer:
The total cost of creating the highway can be found by multiplying the cost per mile by the total number of miles added. The expression that represents the total cost is 39x^4 - 102x^3 - 45x^2.
Explanation:
The total cost, in thousands of dollars, of creating the highway can be calculated by multiplying the cost per mile by the total number of miles added. The cost per mile is given by the expression 3x^2 - 9x.
To find the total cost, we need to multiply this expression by the number of miles added, which is 13x^2 + 5x.
Therefore, the expression that represents the total cost is (3x^2 - 9x)(13x^2 + 5x). To simplify this expression, we can use the distributive property:
(3x^2 - 9x)(13x^2 + 5x) = 39x^4 + 15x^3 - 117x^3 - 45x^2
Simplifying further, we combine like terms:
39x^4 + 15x^3 - 117x^3 - 45x^2 = 39x^4 - 102x^3 - 45x^2
Therefore, the correct expression that represents the total cost, in thousands of dollars, of creating the highway is 39x^4 - 102x^3 - 45x^2. So the answer is:
D) 39x^4 - 102x^3 - 45x^2
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