The answer is in the attachment
<span>Simplifying
8k + 2m = 3m + k
Reorder the terms:
8k + 2m = k + 3m
Solving
8k + 2m = k + 3m
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-1k' to each side of the equation.
8k + -1k + 2m = k + -1k + 3m
Combine like terms: 8k + -1k = 7k
7k + 2m = k + -1k + 3m
Combine like terms: k + -1k = 0
7k + 2m = 0 + 3m
7k + 2m = 3m
Add '-2m' to each side of the equation.
7k + 2m + -2m = 3m + -2m
Combine like terms: 2m + -2m = 0
7k + 0 = 3m + -2m
7k = 3m + -2m
Combine like terms: 3m + -2m = 1m
7k = 1m
Divide each side by '7'.
k = 0.1428571429m
Simplifying
k = 0.1428571429m</span>
5x + 2y = 13
x + 2y = 9
-------------------------subtract
4x = 4
x = 1
x + 2y = 9
1 + 2y = 9
2y = 8
y = 4
answer (1,4)
Answer:
The intersection of the sets A, B, and C is Bird.
Set B contains Fish, Lizard, Turtle, Bird, and Dog.
We know that
if cos x is positive
and
sin x is negative
so
the angle x belong to the IV quadrant
cos x=5/13
we know that
sin²x+cos²x=1-------> sin²x=1-cos²x------> 1-(5/13)²---> 144/169
sin x=√(144/169)-------> sin x=12/13
but remember that x is on the IV quadrant
so
sin x=-12/13
Part A) <span>cos (x/2)
cos (x/2)=(+/-)</span>√[(1+cos x)/2]
cos (x/2)=(+/-)√[(1+5/13)/2]
cos (x/2)=(+/-)√[(18/13)/2]
cos (x/2)=(+/-)√[36/13]
cos (x/2)=(+/-)6/√13-------> cos (x/2)=(+/-)6√13/13
the angle (x/2) belong to the II quadrant
so
cos (x/2)=-6√√13/13
the answer Part A) is
cos (x/2)=-6√√13/13
Part B) sin (2x)
sin (2x)=2*sin x* cos x------> 2*[-12/13]*[5/13]----> -120/169
the answer Part B) is
sin(2x)=-120/169
