Let a be a rational number and b be an irrational number. a + b = c, assume c is rational

a + b - a = c - a, subtract a from both sides

b = c - a, which means that b is rational. But this contradicts the initial assumption.
The above proof shows that the sum of an irrational and rational number is always . Explain.

the answer is 15% decrease

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'.

hiking down a winding trail.

step-by-step explanation:

1010: 3030

is it i think