Analyze Manda’s work. Is she correct? If not, what was her mistake?

Yes, she is correct.
In step 2, she needed to multiply both sides by 10.
In step 3, she did not subtract one x from the left side.
In step 4, she did not simplify her fraction.

1. x=0.27272727273
2. 100x=27.2727272
3. 100x= 27
4. x=27/100

Step-by-step explanation: step 3 is the answer

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'.

30005

yes ok