Avillage parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. the village plans to increase the length by 30%.
a. what will be the new length of the parking lot?
b. how much greater is the new area?
c. if each cars needs about 288 square feet in a parking lot, will the new parking lot be able to fit 20 more cars than the original parking lot? explain.

A: 234 feet

B: 6,480 feet^2

C: No, it is able to fit 22 cars, and 22 is not 20.

Step-by-step explanation:

A:

To get a percentage increase, you multiply whatever you're increasing by 1.%(see that it's 1 point percent, 1 "." %)

So to get the new length, we multiply 180 * 1.30  to get a new length of 234 feet.

B:

To find the old area, we multiply our width * our old length

120 * 180 = 21,600

To find the new area, we multiply our width * our new length

120 * 234 = 28,080

To find how much greater the new area is, we subtract the old area from the new area

28,080-21,600 = 6,480

So the new area is 6,480 feet^2 greater than the old area.

C:

Let's start by seeing how many cars that the new area can fit in the first place. To do this, we'll divide our new area by 288.

28,080/288 = 97.5

We round this down instead of up because we cannot fit 0.5 of a car.

Now we check if 97 is 20 more than 75

97 - 75 = 22

So, here's the weird thing now. The question asks if the parking lot is able to fit "20 more cars," which is technically false, because it can fit 22. But if you believe the problem actually meant "20 cars or more," then the answer would be true. It's up to your own interpretation of the question at this point, but going by just what the question was asking, the answer is false.

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