What is the largest integer n such that (n^2-38) / (n +1) is an integer? a. 36
b. 38
c. 72
d. 76
e. None of these

a. 36

Step-by-step explanation:

for (n^2-38)/(n+1) to be an integer, n+1 must completely divide, n^2-38.

we check with the options

option a n=36 sutisfies the above condition.

(36^2-38)/36+1 = 1258/37= 34 , which is an integer. Therefore, largest integer would be 36

77

step-by-step explanation:

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'.