Alright so turn 3/4 into a decimal.
3/4 =.75
We need to set up an equation. To do that are need to give boys and girls their own variables.
Girls= X
And since there is 3/4 as many boys
Boys=. 75X
Now we know the sum of boys and girls equals 35
X+.75X=35
X+.75X=1.75X
Now we have 1.75X=35
Divide by 1.75 and get
20=X
Now plug 20 into the equations got from before.
Boys =. 75*X = 20 *. 75 = 15
Girls = X =20
Your Answer:
15 boys
20 girls
You can check
20+15=35
15/20=3/4
Answer:
x = 
Step-by-step explanation:
x^2 + 8^2 = 9
Simplify the 8^2
x^2 + 64 = 9
Subtract 64 from both sides
x^2 = -55
Take the square root from both sides
x = +/- 
Simplify
x =
Hope this helps!
Answer:
<u>r=6</u>
Step-by-step explanation:
3 = r/2
6 = r
<h3>
Answer: 70.9%</h3>
Work Shown:
56/79 = 0.70886 approximately
Move the decimal point 2 spots to the right to go from 0.70886 to 70.886%
That rounds to 70.9%
It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
