Let's call the midpoint of GF M.
MF = 16/2 = 8
KF = 25.89
MK = sqrt(25.89^2 - 8^2)
MK = 24.62
MKF = 8 * 24.62 / 2 = 98.48 square units for one triangle
There are 20 of those triangles that make up the decagon.
Therefore the total area = 20(98.48) = 1969.6 which would be option C
Answer:
Minor arc BC - 130° (arc at which inscribed angle is subtended)
The major arc BC - 230°
Step-by-step explanation:
Angle BDC is inscribed angle subtended on the arc BC.
The measure of the angle BDC is 65°.
The Central Angle Theorem states that the central angle from two chosen points B and C on the circle is always twice the inscribed angle from those two points.
By the central angle theorem, the measure of central angle BOC (O is the center of the circle) has the measure of

Hence, the minor arc BC has the same measure as the central angle BOC that is 130°.
The major arc BC has the measure

Time taken to collect 12 different state quarters is 2.5 months.
Now , we need to find time taken to collect all 50 state quarters.
Let , time required is x.
So,

Therefore, time required is 10.7 months.
Hence, this is the required solution.
Hello from MrBillDoesMath!
Answer: -3 and 2
Discussion:
The equation to solve is:
6/m + 2 = (m+3)/(m-1)
Multiple both sides by m * (m-1).
6/m * (m*(m-1)) + 2 m (m-1) = (m+3)/(m-1) * (m(m-1))
Simplify:
6 (m-1) + 2 m (m-1) = (m+3)*m =>
6m -6 + 2m^2 - 2m = m^2 + 3m =>
2m^2 +4m - 6 = m^2 + 3m. Subtract m^2 and 3m from both sides
m^2 + m - 6 = 0. Factor this equation.
(m +3) ( m-2) = 0 so the solution set is -3 and 2
Thank you,
MrB