Answer:
117 degrees
Step-by-step explanation:
Answer:
<em>Answer: choice D.</em>
Step-by-step explanation:
<u>Trigonometric Functions</u>
We need to recall some properties and definitions of the trigonometric functions.
![\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20%5Ctheta%3D%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
![\displaystyle \sec \theta=\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%20%5Ctheta%3D%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
We need to simplify the following expression:
![5\sin\theta\sec\theta](https://tex.z-dn.net/?f=5%5Csin%5Ctheta%5Csec%5Ctheta)
Substituting the identity for the secant:
![\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Csin%5Ctheta.%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
Operating:
![\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
Substituting the definition of the tangent:
![\displaystyle 5\sin\theta\sec\theta=5\tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Ctan%5Ctheta)
Correct choice D.
Answer: x = 5
Step-by-step explanation:
x + 2x - x + 7 = 4x - x + 2
Left side:
x + 2x = 3x
3x - x = 2x (bring down the 7)
So 2x +7
Right side:
4x - x = 3x (bring down the 2)
So 3x + 2
2x + 7 = 3x + 2
Subtract 2 from both sides (7-2 and 2-2)
2x + 5 = 3x
Subtract 2x from 3x
5 = x
Answer:
x = 74 degrees
Step-by-step explanation:
180 - 32 = 148
148 / 2 = 74
Answer:
13/18
Step-by-step explanation:
The possible 36 outcomes are as follows
1+1=2
1+2 or 2+1=3
1+3 or 2+2 or 3+1=4
1+4 or 2+3 or 3+2 or 4+1=5
The above sums are not greater than 5. They are 10 out of possible 36 outcomes
1+5 or 2+4 or 3+3 or 4+2 or 5+1=6
1+6 or 2+5 or 3+4 or 4+3 or 5+2 or 6+1=7
2+6 or 3+5 or 4+4 or 5+3 or 6+2=8
3+6 or 4+5 or 5+4 or 6+3=9
4+6 or 5+5 or 6+4 =10
5+6 or 6+5 =11
6+6=12
It is evident that 26 out of 36 outcomes will have a sum greater than 5
26/36=13/18