36 and 48
a = b+12
a+b = 84
(b+12) + b =84
2b +12 = 84
2b = 72
b= 36
a = b + 12
a = 36 + 12
a = 48
8 is b because a circle is 360.
Answer:
$2.64
Step-by-step explanation:
Selling them at 5 cents each ($0.05), he could sell 1 dozen buttons for
12 * $0.05 = $0.60
As he bought them at $0.38 per dozen, the profit per dozen would be
$0.60 - $0.38 = $0.22
As 12 dozen is 1 gross, the profit per gross would be
12 * $0.22 = $2.64
Step-by-step explanation:

We start with Left hand side
We know that csc(x) = 1/ sin(x)
So csc(2x) is replaced by 1/sin(2x)

Also we use identity
sin(2x) = 2 sin(x) cos(x)

4 divide by 2 is 2
Now we multiply top and bottom by sin(x) because we need tan(x) in our answer



We know that sinx/ cosx = tan(x)
Also 1/ sin(x)= csc(x)
so it becomes 2csc^2(x) tan(x) , Right hand side
Hence verified
(2/7)^2 x (7/9)^2
((2^2)/(7^2)) x ((7^2)/(9^2))
(4/49) x (49/81)
*Cross multiply*
(4/81)