A decagon has 10 sides.
It it is regular you can build 10 isosceles triangles from the center of the decagon to the 10 sides.
Each triangle has a common vertex where the angle of each triangle is 360° / 10 = 36°.
So each time that you rotate the decagon a multiple of 36° around the center you get an image that coincides with the original decagon.
If the letters are given clockwise:
- when you rotate 36° counter clockwise, the point A' (the image of A) will coincide with the point J.
- when you rotate 72° (2 times 36°) counter clockwise, the point A' will land on I.
- when you rotate 108° (3 times 36°) counter clockwise, the point A' will land on H.
- when you rotate 144° (4 times 36°) counter clockwise, the point A' will land on G.
- when you rotate 180° (5 times 36°) counter clockwise, the point A' will land on I.
- when you rotate 216° (6 times 36°) counter clockwise, the point A' will land on E.
- whn you rotate 252° (7 times 36°) counterclockwise, the point A' will coincide with D.
Add other 36° each time and A' will coincide successively with C, B and the same A.
As you know that sum of complementary angles equal 90°
so,
7x + 11x = 90
18x = 90
x = 90/18
x =5
so,
option A is the correct one.
Answer:
Step-by-step explanation:
The given quadratic equation is
2x^2+3x-8 = 0
To find the roots of the equation. We will apply the general formula for quadratic equations
x = -b ± √b^2 - 4ac]/2a
from the equation,
a = 2
b = 3
c = -8
It becomes
x = [- 3 ± √3^2 - 4(2 × -8)]/2×2
x = - 3 ± √9 - 4(- 16)]/2×2
x = [- 3 ± √9 + 64]/2×2
x = [- 3 ± √73]/4
x = [- 3 ± 8.544]/4
x = (-3 + 8.544) /4 or x = (-3 - 8.544) / 4
x = 5.544/4 or - 11.544/4
x = 1.386 or x = - 2.886
The positive solution is 1.39 rounded up to the nearest hundredth
To solve 16x18, you may split it up into a smaller increment you understand. Like 16x2, which equals 32. (18/2 is 9) multiply 32 by 9. you get your answer 288.
