Answer:
You greatest common factor is
![3t^{2}](https://tex.z-dn.net/?f=3t%5E%7B2%7D)
Step-by-step explanation:
You need to find a number and letter which goes into both monomials.
,![3t^{2}](https://tex.z-dn.net/?f=3t%5E%7B2%7D)
Split both monomials up, into each integer and letter.
INTERGERS: 6, 3
LETTER t:
,![t^{2}](https://tex.z-dn.net/?f=t%5E%7B2%7D)
LETTER z: ![z^{5}](https://tex.z-dn.net/?f=z%5E%7B5%7D)
3 goes into 6 and 3.
goes into
and
.
Nothing goes into
and 0.
You greatest common factor is
![3t^{2}](https://tex.z-dn.net/?f=3t%5E%7B2%7D)
Therefore
![3t^{2} (tz^{5} , 1) = 3t^{3}z^{5} ,3t^{2}](https://tex.z-dn.net/?f=3t%5E%7B2%7D%20%28tz%5E%7B5%7D%20%2C%201%29%20%3D%203t%5E%7B3%7Dz%5E%7B5%7D%20%2C3t%5E%7B2%7D)
Answer:
Step-by-step explanation:
So this gives us a few clues. The numbers all have an equal value between them, and the fourth and fifth are 27 and 32 respectively. So how much is between these two?
5, so since you add five to go from fourth to fifth, you subtract to go backwards. So then the third is 27-5 = 22 and so on, can you figure it out from there? just subtract 5 however many more times is needed.
If he attempted 45 passes, find how many passes he completed. Round to the nearest whole number of necessary.
Answer: Thus you found the rate of the slower bus. It is 67 miles per hour.
Then the rate of the faster bus is 67 + 18 = 85 mph.
Step-by-step explanation:
ANSWER
![\tan(x + y) = - \frac{63}{16}](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%3D%20%20-%20%20%5Cfrac%7B63%7D%7B16%7D%20)
EXPLANATION
We were given that,
![\csc(x) = \frac{5}{3}](https://tex.z-dn.net/?f=%20%20%5Ccsc%28x%29%20%20%3D%20%20%5Cfrac%7B5%7D%7B3%7D%20)
This implies that,
![\sin(x) = \frac{3}{5}](https://tex.z-dn.net/?f=%20%5Csin%28x%29%20%20%3D%20%20%5Cfrac%7B3%7D%7B5%7D%20)
We use the Pythagorean identity
![\sin^{2} (x) + \cos^{2} (x)= 1](https://tex.z-dn.net/?f=%20%5Csin%5E%7B2%7D%20%28x%29%20%20%2B%20%20%5Ccos%5E%7B2%7D%20%28x%29%3D%201)
to get,
![\cos(x) = \sqrt{1 - ( { \frac{3}{5} })^{2}} = \frac{4}{5}](https://tex.z-dn.net/?f=%20%5Ccos%28x%29%20%20%3D%20%20%5Csqrt%7B1%20-%20%28%20%7B%20%5Cfrac%7B3%7D%7B5%7D%20%7D%29%5E%7B2%7D%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%20)
We were also given that,
![\cos(y) = \frac{5}{13}](https://tex.z-dn.net/?f=%20%5Ccos%28y%29%20%20%3D%20%20%5Cfrac%7B5%7D%7B13%7D%20)
This means that,
![\sin(y) = \sqrt{1 - {( \frac{5}{13}) }^{2} } = \frac{12}{13}](https://tex.z-dn.net/?f=%20%5Csin%28y%29%20%20%3D%20%20%5Csqrt%7B1%20-%20%20%7B%28%20%5Cfrac%7B5%7D%7B13%7D%29%20%7D%5E%7B2%7D%20%7D%20%20%3D%20%20%5Cfrac%7B12%7D%7B13%7D%20)
This is because,
![0 < \: x \: < \frac{\pi}{2}](https://tex.z-dn.net/?f=0%20%3C%20%20%5C%3A%20x%20%5C%3A%20%20%3C%20%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20)
![0 < \: y \: < \frac{\pi}{2}](https://tex.z-dn.net/?f=0%20%3C%20%20%5C%3A%20y%20%5C%3A%20%20%3C%20%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20)
This angles are in the first quadrant so we pick the positive values.
![\tan(x + y) = \frac{ \sin(x + y) }{ \cos(x + y) }](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%20%3D%20%20%5Cfrac%7B%20%5Csin%28x%20%2B%20y%29%20%7D%7B%20%5Ccos%28x%20%2B%20y%29%20%7D%20)
![\tan(x + y) = \frac{ \sin(x ) \cos(y) + \sin(y) \cos(x) }{ \cos(x) \cos(y) - \sin(x) \sin(y) }](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%20%3D%20%20%5Cfrac%7B%20%5Csin%28x%20%29%20%5Ccos%28y%29%20%20%20%2B%20%20%5Csin%28y%29%20%20%5Ccos%28x%29%20%7D%7B%20%5Ccos%28x%29%20%5Ccos%28y%29%20%20-%20%20%5Csin%28x%29%20%20%5Csin%28y%29%20%7D%20)
![\tan(x + y) = \frac{ \frac{3}{5} \times \frac{5}{13} + \frac{12}{13} \times \frac{4}{5} }{ \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13} }](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%20%3D%20%20%5Cfrac%7B%20%20%5Cfrac%7B3%7D%7B5%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B13%7D%20%20%2B%20%20%20%5Cfrac%7B12%7D%7B13%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B4%7D%7B5%7D%20%20%7D%7B%20%20%5Cfrac%7B4%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B13%7D%20%20%20-%20%20%20%5Cfrac%7B3%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B12%7D%7B13%7D%20%20%7D%20)
![\tan(x + y) = - \frac{63}{16}](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%3D%20%20-%20%20%5Cfrac%7B63%7D%7B16%7D%20)
The correct answer is D