Irene's mean score on 5 tests is 88%. What is
the lowest score she can get on her next test
to raise her mean test score to 91%?

The least score she can get on her next test is 455 points.

Step-by-step explanation: From the available information, her current mean score is 88%, and that was achieved from a total of 5 tests. Hence, her mean score was computed as follows;

Mean = (Summation of data)/observed data

Where the observed data is 5 and the mean is 88. Therefore the mean can now be expressed as,

88 = Summation of data/5

By cross multiplication we now have

88 x 5 = Summation of data

440 = Summation of data.

So, if she wants to raise her mean score on her next test to 91%, her least possible score would be derived as

91 = (Summation of data)/5

By cross multiplication we now have

91 x5 = Summation of data

455 = Summation of data

Therefore, on her next test, she must score at least 455 points.

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'.