Heidy is standing on a 40-foot cliff overlooking a river. The angle of depression to the near side of the river is 64°, and the angle of depression to the far side is 35°. How wide is the river, to the nearest tenth of a foot?

Width of the river =57 feet

Step-by-step explanation:

Width of the river = length AC

Hence Tan 55 = AC/ 40

AC = Tan 55 x 40 = 57.12592026968ft

Hence width of the river = 57.12592026968 feet  ≅ 57 feet

37.6 feet

Step-by-step explanation:

Please kindly see the attached for explanation

12.5 feet

step-by-step explanation:

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