Answer:
4
Step-by-step explanation:
Yeah if you don't know this one... you're... special.
Answer:
y = -2/3x - 11/3
Step-by-step explanation:
Answer:
k = -8
Step-by-step explanation:
The location of P is ...
P = (2A+B)/3 = (2·2+5, 2·1-8)/3 = (3, -2)
Putting this point into the equation for the line, we have ...
2(3) -(-2) +k = 0
8 +k = 0
k = -8
Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
The trig function sine, often abbreviated as "sin" (pronounced the same way as "sine"), is essentially the ratio or fraction of the opposite side and the hypotenuse. See the attached image for a reference.
The leg opposite angle B is side AC. Note how B is not present in the sequence "AC". Visually, we are as far away as possible from point B. This side is 16 units long. So AC = 16
The hypotenuse is the longest side of the right triangle. Always always always. This longest side is opposite the largest angle (90 degrees). Therefore the hypotenuse is BC = 17.46
In summary so far, we have,
opposite side = AC = 16
hypotenuse BC = 17.46
Let's use those values to compute sin(B)
sin(Angle) = opposite/hypotenuse
sin(B) = AC/BC
sin(B) = 16/17.46
sin(B) = 0.916 (this is approximate)
sin(B) =
0.92 (rounding to nearest hundredth)
This points to the
final answer of choice A) 0.92--------------------------------
Edit: Sorry nearly forgot about the reference image. I attached it just now.