A man travels at 42 degrees northwest, and ends up 8.5 miles west of his starting point. How far did he travel?

The man traveled 12.70 miles.

Step-by-step explanation:

We can find the distance traveled by the man knowing:

: the distance at the west = 8.5 miles

: the northwest angle = 42°

Then by using the following trigonometric identity we have:

Therefore, the man traveled 12.70 miles.

I hope it helps you!                                    

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.