1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is
, so the measure of arc DF is

The inscribed angle theorem tells us that the central angle subtended by arc DF,
, has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

so the measure of arc DF is also 64 degrees. So we have

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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

Answer:
My family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.
Step-by-step explanation:
Since I am taking a trip at the same time as another family, and my family traveled 1,900 miles in 2 days, while their family traveled 2,700 miles in 3 days, to determine who is traveling faster the following calculation must be performed:
1,900 / 2 = 950
2,700 / 3 = 900
Thus, my family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.
Answer:
C
Step-by-step explanation:
given a triangle with 2 sides and the angle between them given, then the area (A) is calculated as
A =
bc sinA
the 2 sides are b = 4, c = 6 and ∠ A = 35° , then
A =
× 4 × 6 × sin35° = 12 × sin35° ≈ 6.9 m² ( to the nearest tenth )
(a-b)(a+b) because when you reverse the sum you do axa and ax-b xx