9514 1404 393
Answer:
Step-by-step explanation:
The Law of Cosines can be used to find the distance from the red boat to the lighthouse.
b² = l² +r² -2lr·cos(B)
b² = 18² +30² +2·18·30·cos(120°) = 1764
b = √1764 = 42
The distance from the red boat to the lighthouse is 42 miles.
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The angle at the lighthouse can be found using the law of sines.
sin(L)/l = sin(B)/b
L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°
The angle between the boats measured at the lighthouse is about 22°.
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
Answer:
Answer:
3x-x+2=4
Step-by-step explanation:
Number of boys = x
Number of girls = x plus 15% of x = 1.15x
Ratio of boys to girls x:1.15x = 1:1.15 = 20:23