Answer:
B). 1 1/2 tubs per minute.
Step-by-step explanation:
In 1/4 minute the faucet filling 3/8 of a bath.
So in 1 minute the rate of filling = 3/8 / 1/4
= 3/8 * 4
= 12/8
= 1 1/2 tubs per minute.
Answer:
y < -2x - 4
Step-by-step explanation:
This is a guessing game. You just have to plug and chugg to find your answer.
Look at the table they gave you and plug in the x and y value into the given equations and see if they're true or not.
For example, I used the point x=-2 and y=1 from the table.
I plug that into y < -2x - 4 and got a false statement:
y < -2x - 4
(1) < -2(-2) - 4
1 < 4 - 4
1 < 0
this is false because one cannot be less than zero. Therefore this equation is the wrong one.
If you tried to plug in x=-2 and y=1 into the other 3 equations you'll see that they'll be correct.
Multiply the amount of flowers in each arrangement by 4
I can't help more without the amount of flowers in each arrangement
Its 15 degrees in celsius
Answer:
See below.
Step-by-step explanation:
![\cot(x-\frac{\pi}{2})=-\tan(x)](https://tex.z-dn.net/?f=%5Ccot%28x-%5Cfrac%7B%5Cpi%7D%7B2%7D%29%3D-%5Ctan%28x%29)
Convert the cotangent to cosine over sine:
![\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos%28x-%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%7D%7B%5Csin%28x-%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D%20%3D-%5Ctan%28x%29)
Use the cofunction identities. The cofunction identities are:
![\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)](https://tex.z-dn.net/?f=%5Csin%28x%29%3D%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%29%5C%5C%5Ccos%28x%29%3D%5Csin%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%29)
To convert this, factor out a negative one from the cosine and sine.
![\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos%28-%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%20%29%29%7D%7B%5Csin%28-%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%29%29%7D%20%3D-%5Ctan%28x%29)
Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:
![\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos%28%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%20%29%29%7D%7B-%5Csin%28%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%29%29%7D%20%3D-%5Ctan%28x%29%5C%5C-%5Cfrac%7B%5Csin%28x%29%7D%7B%5Ccos%28x%29%7D%20%3D-%5Ctan%28x%29%5C%5C-%5Ctan%28x%29%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D-%5Ctan%28x%29)