Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
- a² = b² +c² -2bc·cos(A)
- k² = 31² +53² -2·31·53·cos(37°)
<h3>Comparison</h3>
Comparing the two equations, we note these correspondences:
Comparing these values to the given information, we see that ...
- KN = c = 53 . . . . . . . . . . matching values 53
- NM = a = k . . . . . . . . . . . matching values k
- KM = b = n = 31 . . . . . . . matching values 31
- ∠K = ∠A = 37° . . . . . . . matching side/angle names
Abby apparently knew that ∠K = 37° and n = 31.
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<em>Additional comment</em>
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
Answer:
The country's population decreased about 5.8 % during this time period.
Step-by-step explanation:
Population in 1990 = 164 million
Population in 2010 = 155 million
Determine the percent decrease
The formula used is: 
We have :
Initial Value = 164 million (164,000,000)
New Value = 155 million (155,000,000)
Finding percent decrease
So, The country's population decreased about 5.8 % during this time period.
Quotient: The answer to a division problem
Just find 68% of 25.
0.68 * 25 = 17
So he completed 17 of his passes.
