Do you know works in a building that is 130 feet tall. She's outside, looking up at the building at an angle of 37° from her feet to the top of the building.

17.6 feet

Step-by-step explanation:

If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.

Let x be the distance between the building and Diana,

Tan theta = opposite / adjacent side

then tan 37 = 130/x

Let y be  distance between the building and Diana after moving forward,

now find the distance by subtracting to find how much closer she is to the building

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

it's d

step-by-step explanation: