Carlos began with twice as much money as david
had. after carlos gave $12 to david, carlos still had
$10 more than david. how much money did they
have combined at the start?

$102

Step-by-step explanation:

Carlos had twice as much money as david

x= david's initial money

Carlos' money = 2x

After carlos gave $12 to david, Carlos still had $10 more than david

2x-12=x+22

x=34 which means david initially had 34$

(34 x 2) carlos + 34 david = $102

check by plugging 34 back into the equation.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

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'.