6a add 21 = 27
6A - 58 = 44 Add 58 to both sides: 6A = 102 Divide both sides by 6: A = 17
Add them together: 3a+4a-a = 6a
-21 = 9a - 15 - 3a -6 = 6a -1 = a
6a - 4 = -2 Add four to both sides: 6a = 2 Divide both sides by 6: a = 1/3
12a- 6a + a = 7a Since they all have the same variable, you can simply add and subtract 12-6 = 6 6+1 = 7
P = 3a - 3q Add 3q to each side: P + 3q = 3a Double each side: 6a = 2P + 6q
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
Divide by 6a: 6a(a + 3b)
36a2 - 60a + 25 = 36a2 - 30a - 30a + 25 = 6a(6a - 5) - 5(6a - 5) = (6a - 5)(6a - 5) = (6a - 5)2
10a-37=6a+51 -6a -6a subtract 6a from both sides and the 6a's cancel 4a-37=51 +37 +37 4a=88 /4 /4 a=22
6a
18