C because once you round it up
sin(2<em>x</em>) - sin(<em>x</em>) = 0
Expand the first term using the double angle identity:
2 sin(<em>x</em>) cos(<em>x</em>) - sin(<em>x</em>) = 0
Factor out sin(<em>x</em>) :
sin(<em>x</em>) (2 cos(<em>x</em>) - 1) = 0
This leaves you with 2 cases that can be solved separately:
sin(<em>x</em>) = 0 or 2 cos(<em>x</em>) - 1 = 0
sin(<em>x</em>) = 0 or cos(<em>x</em>) = 1/2
[<em>x</em> = 2<em>nπ</em> or <em>x</em> = <em>π</em> + 2<em>nπ</em>] or [<em>x</em> = <em>π</em>/6 + 2<em>nπ</em> or <em>x</em> = 5<em>π</em>/6 + 2<em>nπ</em>]
(where <em>n</em> is any integer)
Let g = graph paper and r = ruler
1st equation: 5g + 30r = 40
2nd equation: 12g + 20r = 44
Multiply the 2nd equation by -1.5 to cancel out the r's
2nd equation: 12g + 20r = 44 x -1.5 = -18g - 30r = -66
Now add the 1st equation to that:
-18g + 5g = -13g
30r -30r = 0
40 -66 = -26
The new equation becomes -13g = -26
Divide both sides by -13
g = -26 / -13
g = 2
This means each pack of graph paper cost $2.
Now replace g with 2 in the first equation to solve for the cost of a rule:
5(2) + 30r = 40
Simplify:
10 + 30r = 40
Subtract 10 from each side:
30r = 30
Divide both sides by 30:
r = 30 / 30
r = 1
Each rule cost $1.
How are you? Ok so It probably B but I’m not sure so just wait a few minutes till someone else answers because I’m not sure
