Octagon, stop sign.
Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.
So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,
area = 8(1/2)(9.9)(12) = 475.2
Answer: 475.2
Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.
The area of the right triangle with long leg 12, short leg x,
tan 22.5 = x/12 or
x = 12 tan 22.5
Twice that is what we're told is 9.9; let's check:
2x = 24 tan 22.5 = 9.941125496954282
The area of the little right triangle is
(1/2) 12 × 12 tan 22.5
and there are 16 of these
16 (1/2) 12 × 12 tan 22.5 ≈ 477.174
Pyramid's apex is constructed by isosceles triangles. If we slice it from its apex-from the vertex, in the cross section we'll obtain a triangle, This triangle is also going to be an isosceles triangle.
Answer:
b = - 0.432
Step-by-step explanation:
It takes 200 seconds to produce the first widget. And by the 400th widget, it takes only 15 seconds.
Now, the formula that gives the time to make the nth widget is given by
and we have to evaluate the constant b from the above-given conditions.
So, 
⇒ 
Taking log on both sides
b log (400) = log (0.075)
⇒ b = - 0.432 (Answer)
To solve this
problem, we must remember that the sum of interior angle of a polygon is:
Sum of
interior angles = (n – 2) * 180˚
So, we can say
that:
Sum of
interior angles = angle A + angle B + angle C + angle D = (4 – 2) * 180˚
Where,
angle C + angle
D = 110 + 70 = 180˚
Therefore
substituting this value:
angle A + angle
B + 180˚ = 2 * 108˚
angle A + angle
B = 360˚ - 180˚
angle A + angle
B = 180˚ (answer)
Hence we can
also conclude that,
<span>angle A + angle
B = angle C + angle D</span>
Answer:
The right option is C) 21.75
Step-by-step explanation:
we have given,
Number of shares = 75
Cost of each share = $24.13
Total cost of shares = 75×24.13 = $1809.75
since the company paid annual dividends of $0.29 per share.
Total annual dividends company paid = 75×0.29 = $21.75
Hence the right option is C) 21.75