The function f(t) = 750t + 20,000 models the number of movie theaters in the United States t years after 1985. Use this equation to predict the year in which the United States will have 35,000 movie theaters.

Given:

The function models the number of movie theaters in the United States t years after 1985.

To find:

The year in which the United States will have 35,000 movie theaters.

Solution:

We have,

Putting f(t)=35000, we get

Divide both sides by 750.

It means, United States will have 35,000 movie theaters 20 years after 1985.

Therefore, United States will have 35,000 movie theaters is 2005.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.