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
Probability that first student prefers mechanical pen = 0.30
P(first student does not and second student does) = 0.70 * 0.3 = 0.21)
P( selecting 2 or fweer) = 0.30+ 0.21) = 0.51 or 51%
Answer:
Step-by-step explanation:
Factoring will reveal the solution. So we divide the equation by the greatest common factor of the terms and use that factor as the coefficient. In this case the greatest common factor is just x.
2x^2+5x
x(2x+5) so the equation will equal zero when either of those expressions is zero because zero times anything is zero. x=0 and x=-5/2
Answer:
5.0
Step-by-step explanation:
Using Pythagorean Theorem:
a² + b² = c²
where a =? b= 12 in and c = 13 in
a² + (12)² = (13)²
a² + 144 = 169
a² = 169 - 144
a² = 25
a = √25 = 5
∴ a = 5.0
Pythagoras Theorem is usually applied when finding one missing side of a right-angle triangle.
