Hurry will give brainliest a truck can be rented from company a for $90 a day plus $0.30 per mile. company b charges $70 a day plus $0.80 per mile to rent the same truck. find the number of miles in a day at which the rental cost for company a and company b are the same

The rental costs for the two companies are equal at x = 40 miles.

Step-by-step explanation:

The total cost function for Company A is Ca = $90 + ($0.30/mile)x, where x is the number of miles driven during the one day of rental.

The total cost function for Company B is Cb = $70 + ($0.80)x.

Setting these two formulas = to one another and solving for x, we get:

$90 + ($0.30/mile)x = $70 + ($0.80)x

First, subtract $70 from both sides, obtaining:

$20 + ($0.30/mile)x = ($0.80)x

Subtracting ($0.30/mile)x from both sides results in:

$20 = ($0.50/mile)x

Dividing both sides by ($0.50/mile) results in

x = ($20) / ($0.50/mile) = 40 miles

The rental costs for the two companies are equal at x = 40 miles.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1