Answer:
15 miles
Step-by-step explanation:
Let's say the dock is at the origin on a coordinate plane and each unit is 1 mile. If the boat travels 9 mile due north, that means that we move up from the origin (0, 0) 9 units to point A (0, 9). Now, this boat moves 12 miles due west, so we will go 12 units to the left of (0, 9) to point B (-12, 9). See the attached drawing (sorry for the crudeness).
Notice that this is a right triangle with legs of 9 and 12. That means the distance from the boat to the dock is just the hypotenuse, so use the Pythagorean Theorem: distance = 
Thus, the answer is 15 miles.
Hope this helps!
Answer:
Step-by-step explanation:
50a³b = 2⋅5²a³b
8ab = 2³ab
GCF = 2ab
50a³b - 8ab = 2ab(5²a² - 2²)
5²a² - 2² = (5a - 2)(5a + 2)
Answer:
sin 105 = sin (45 + 60) = sin 45 cos 60 + cos 45 sin 60, or
= (1 / √2)(1 / 2) + (1 / √2)(√3 / 2)
1 + √3
= -------------
2√2
Step-by-step explanation:
This is complicated because I’m typing on a phone, but
24:30 simplified is 4:5
30:54 simplified is 5:9
10:5 simplified is 2:1
5:15 simplified is 1:3
32:72 simplified is 4:9
72:104 simplified is 9:13
56:7 simplified is 8:1
7:63 simplified is 1:9