A car rental offers two options for renting a car. Plan A costs $200 per week plus $0.35 for each mile driven during that week. Plan B costs $180 per week plus $0.55 for each mile driven that week. How many miles of driving would result in both plans costing the same amount for that week

100 miles

Step-by-step explanation:

Two plans are being offered for the renting of cars.

Plan A:

Cost per week = $200

Cost for each mile = $0.35

Plan B:

Cost per week = $180

Cost for each mile = $0.55

To find:

Number of miles for which the cost is same ?

Solution:

Let the number of miles driven so that the cost becomes the same = miles

First of all, let us find the cost for each plan as per miles.

Cost as per plan A = Cost per week + Cost for miles = $200 + $0.35

Cost as per plan B = Cost per week + Cost for miles = $180 + $0.55

Now, putting both the costs equal to find the value of :

Therefore, after 100 miles the cost from each plan will be the same.

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