Answer:
A) y = 8.63 x
B) $224.38
Step-by-step explanation:
The the average monthly cost = (147.98+152.17+165.63)/3 = $155.26
So, For 18 employees the average monthly cost = $155.26
Let the equation that can be used to estimate y, the average monthly cost, in dollars, to buy lunch for x employees. ⇒ y = mx
For x = 18 , y = $155.26
So, m = y/x = $155.26/18 ≈ $8.63
∴ y = 8.63 x
To find the total cost for 26 employees.
∴ x = 26
∴ y = 8.63 * 26 = 224.38
The total cost of a monthly lunch for 26 employees = $224.38
Answer:
3a - 21
Step-by-step explanation:
3 ( a - 7 )
= 3 ( a ) + 3 ( - 7 )
= 3a - 21
The answer is 4/5 all you do is rise over run
Option A
![\cos 3 x=\cos x-4 \cos x \sin ^{2} x](https://tex.z-dn.net/?f=%5Ccos%203%20x%3D%5Ccos%20x-4%20%5Ccos%20x%20%5Csin%20%5E%7B2%7D%20x)
<em><u>Solution:</u></em>
Given that we have to rewrite with only sin x and cos x
Given is cos 3x
![cos 3x = cos(x + 2x)](https://tex.z-dn.net/?f=cos%203x%20%3D%20cos%28x%20%2B%202x%29)
We know that,
![\cos (a+b)=\cos a \cos b-\sin a \sin b](https://tex.z-dn.net/?f=%5Ccos%20%28a%2Bb%29%3D%5Ccos%20a%20%5Ccos%20b-%5Csin%20a%20%5Csin%20b)
Therefore,
---- eqn 1
We know that,
![\sin 2 x=2 \sin x \cos x](https://tex.z-dn.net/?f=%5Csin%202%20x%3D2%20%5Csin%20x%20%5Ccos%20x)
![\cos 2 x=\cos ^{2} x-\sin ^{2} x](https://tex.z-dn.net/?f=%5Ccos%202%20x%3D%5Ccos%20%5E%7B2%7D%20x-%5Csin%20%5E%7B2%7D%20x)
Substituting these values in eqn 1
-------- eqn 2
We know that,
![\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x](https://tex.z-dn.net/?f=%5Ccos%20%5E%7B2%7D%20x-%5Csin%20%5E%7B2%7D%20x%3D1-2%20%5Csin%20%5E%7B2%7D%20x)
Applying this in above eqn 2, we get
![\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)](https://tex.z-dn.net/?f=%5Ccos%20%28x%2B2%20x%29%3D%5Ccos%20x%5Cleft%281-2%20%5Csin%20%5E%7B2%7D%20x%5Cright%29-%5Csin%20x%282%20%5Csin%20x%20%5Ccos%20x%29)
![\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Ccos%20%28x%2B2%20x%29%3D%5Ccos%20x-2%20%5Csin%20%5E%7B2%7D%20x%20%5Ccos%20x-2%20%5Csin%20%5E%7B2%7D%20x%20%5Ccos%20x%5C%5C%5C%5C%26%5Ccos%20%28x%2B2%20x%29%3D%5Ccos%20x-4%20%5Csin%20%5E%7B2%7D%20x%20%5Ccos%20x%5Cend%7Baligned%7D)
![\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x](https://tex.z-dn.net/?f=%5Ccos%20%28x%2B2%20x%29%3D%5Ccos%20x-4%20%5Ccos%20x%20%5Csin%20%5E%7B2%7D%20x)
Therefore,
![\cos 3 x=\cos x-4 \cos x \sin ^{2} x](https://tex.z-dn.net/?f=%5Ccos%203%20x%3D%5Ccos%20x-4%20%5Ccos%20x%20%5Csin%20%5E%7B2%7D%20x)
Option A is correct