There are 31 students in a math class. of those, 15 students have in-line skates, 10 have scooters, and 12 have skateboards. overall, 5 students have both in-line skates and a scooter, 3 have both a scooter and a skateboard, and 2 have both a skateboard and in-line skates. if no students have all three, how many students have only in-line skates, or only skateboards?

15 - In-line skates. 10 - Scooters. 12 - Skateboards.

5 have both skates and scooter: 15-5=10, 10-5=5.

10 - Skates. 5 - Scooters. 12 - Skateboards.

3 have both a scooter and skateboard: 5-3=2, 12-3=9.

10 - Skates. 2 - Scooters. 9 - Skateboards.

2 have skateboard and skates: 10-2=8, 9-2= 7.

Therefore, 8 students only have in-line skates and 7 have only skateboards. Hope this helped!

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.