A state department of public safety added 1/3 x² + 5x miles of highway to connect CoolTown and Bragville. It cost the department 3x² – 9 thousand dollars to complete each mile of interstate. Which expression shows the total cost, in thousands of dollars, of creating this highway?

To find the total cost of creating the highway, we will multiply the length of the highway (in miles) by the cost per mile.

1. The length of the highway is given by the expression:

(frac{1}{3}x^2 + 5x) miles.

2. The cost per mile is given by:

(3x^2 – 9) thousand dollars.

Now, we need to multiply these two expressions together to find the total cost:

[

text{Total Cost} = left(frac{1}{3}x^2 + 5xright) times (3x^2 – 9)

]

Let’s distribute:

1. (frac{1}{3}x^2 times 3x^2 = x^4)
2. (frac{1}{3}x^2 times (-9) = -3x^2)
3. (5x times 3x^2 = 15x^3)
4. (5x times (-9) = -45x)

Now combine these results:

[

x^4 + 15x^3 – 3x^2 – 45x

]

However, the question asks for an expression in thousands, so we can adjust the combined expression to show only the required terms related to the cost without focusing heavily on linear terms related