Answer:
25
Step-by-step explanation:
GC and BD are 2 intersecting chords thus the measure of the angle formed is
∠DFC = 0.5( m arc CD + m arc BG ), that is
0.5(55 + BG) = 40 ( multiply both sides by 2 )
55 + BG = 80 ( subtract 55 from both sides )
BG = 25
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Answer:
Internal angle = 
Number of sides = 18
Step-by-step explanation:
Given that:
We have a regular polygon with number of sides unknown.
Measure of an exterior angle of the polygon = 
To find:
Measure of an interior angle and the number of sides of the polygon?
Solution:
Let us have a look at the relation of sum of external angles.
Sum of one internal angle and its corresponding external angle = 
Internal angle + external angle = 
Internal angle =
-
= 
Sum of all the external of a regular polygon = 
All the external angles will be equal because it is a regular polygon.
Let the number of sides = 
Therefore,

Therefore, the answers are:
Internal angle = 
Number of sides = 18
Focus of the parabola is (-5,5) and directrix is y = -1.
Let's assume a point (x,y) on parabola.
According to definition of parabola, the distance between point (x,y) and focus (-5,5) would be same as the distance between the point (x,y) and directrix y = -1.

Hence, option D is correct, i.e. f(x) = one twelfth (x + 5)2 + 2.