Sorry, it's late, and I'm a bad explainer.
The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.
A straight line is also 180°.
(2x - 12) + ? = 180
30 + x + ? = 180
If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)
2x - 12 = 30 + x
x = 42
Now you plug 42 into the exterior angle equation
2(42) - 12 = 84 - 12 = 72°
Answer:
cosФ = 
, sinФ = 
, tanФ = -8, secФ = 
, cscФ = 
, cotФ = 
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
- cosФ =
- sinФ =
- tanФ =
- secФ =
- cscФ =
- cotФ =
- Where r =
(the length of the terminal side from the origin to point (x, y)
- You should find the quadrant of (x, y) to adjust the sign of each function
∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r =
∵ x = 1 and y = -8
∴ r = 
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ =
∴ cosФ =
∵ sinФ =
∴ sinФ =
∵ tanФ =
∴ tanФ = 
= -8
∵ secФ =
∴ secФ = 
=
∵ cscФ =
∴ cscФ =
∵ cotФ =
∴ cotФ =
Find the prime factorization
45=3*3*5
60=2*2*3*5
GCF=3*5=15
45=3*15
60=4*15
remember
ab+ac=a(b+c) so
45+60=15(3)+15(4)=15(3+4)=15(7)=105
Let us name the players A,Dave,Zack,Paul,E and F
For the first position there are two candidades ( Zack / Paul )
For the second position there is only one candidate i.e. Dave
For the third place there will be 4 candidates (out of Zack and Paul - 1 as one of them is already taken for the first position and A, E and F total-4)
For the fourth place there will be 3 candidates ( out of the four available candidates in the 3rd place, one will be taken up for 3rd place )
For the fifth place there will be 2 candidates
Finally, for the last place there will be only one candidate left.
On multiplying the no. of available cadidates, we get 2 * 1 * 4 * 3 * 2 * 1 = 48 i.e. option (A)
Please mention minor spelling mistakes
For the second question:
Let the no of dotted marbles be 'x' and no of striped marbles be 'y'
then the equation will become as follows
(y+6)/x = 3
and
(x+6)/y = (2/3)
On solving the equations, we will get x = 10 and y = 24
Total balls = 10+24+6 = 40 (option E)
Answer 3 will be ) For the first edge, he can choose 3 paths
For the second edge he can choose 2 paths for each path of its first edge's path
For the third , he is bounded to move on the paths created by the first and the second edges hence 1 path for each path created by the first and the second edge together
It will be multiplication of all the possibilities of the paths of the three edges differently.........
i.e. 3 * 2 * 1 = 6
