Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
= 
(2sin20°cos20°)cos40°cos80°
= 
(2sin40°cos40°)cos80°
= (sin80°cos80° )
= 
(2sin80°cos80° )
= . sin160°
= . sin(180 - 20)°
= . sin20°
= 
= right side , thus proven
Answer:
16
Step-by-step explanation:
To solve a quadratic equation by using the completing the square method, the coefficient of the square term i.e x² must be one (1).
Therefore, we would have to first make the coefficient of x² to be equal to 1.
4x² + 24x + 8 = 32
We would simplify the equation;
4x² + 24x = 32 - 8
4x² + 24x = 24
Divide all through by 4;
x² + 8x = 24
The value to be added = (8/2)² = 4² = 16
x² + 8x + 16 = 8 + 16
x² + 4x + 4x + 16 = 24
x(x + 4) + 4(x + 4) = 24
(x + 4)² = 24
Taking the square root of both sides;
x + 4 = ± 4.9
x = -4 ± 4.9
x = -4 + 4.9 = 0.9
or
x = -4 - 4.9 = - 8.9
<em>Therefore, 16 must be added to solve the quadratic equation by completing the square method. </em>
1 and one - twelfth
because 12gies 3 times in 37
6²+8²=c²
36+64=c²
c²=100
c=10
G divides each median in the ratio of 2 to 1 (the longer side goes from G to the angle)
triangle AMN is similar to triangle ABC (why?)
AMN is a scaled version of ABC (by a factor of ⅔)
its area should be scaled by (⅔)^2
