Harry bought a package of blueberries to put in his muffins. tha package he bought had 64 blueberries inside. he plans on making 17 muffins with 6 blueberries in each each. how many more berries will he need?

38

Step-by-step explanation:

He will need 38 because,

17 muffins x 6 blueberries = 102 blueberries

he already has 64, so to find the remaining amount he needs

102 blueberries - 64 blueberries = 38 blueberries

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

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'.