21x + 28 = 156 - 2
21x = 154 - 28
21x/21 = 126/21
X = 6
Since
lies in quadrant II and
lies in quadrant IV, we expect
,
, and
.
Recall the Pythagorean identities,
![\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x](https://tex.z-dn.net/?f=%5Csin%5E2x%2B%5Ccos%5E2x%3D1%5Ciff1%2B%5Ccot%5E2x%3D%5Ccsc%5E2x%5Ciff%5Ctan%5E2x%2B1%3D%5Csec%5E2x)
It follows that
![\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}](https://tex.z-dn.net/?f=%5Csec%5Calpha%3D%5Cdfrac1%7B%5Ccos%5Calpha%7D%3D-%5Csqrt%7B%5Ctan%5E2%5Calpha%2B1%7D%3D-%5Cdfrac%7B13%7D5%5Cimplies%5Ccos%5Calpha%3D-%5Cdfrac5%7B13%7D)
![\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}](https://tex.z-dn.net/?f=%5Csin%5Calpha%3D%5Csqrt%7B1-%5Ccos%5E2%5Calpha%7D%3D%5Cdfrac%7B12%7D%7B13%7D)
![\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45](https://tex.z-dn.net/?f=%5Csin%5Cbeta%3D-%5Csqrt%7B1-%5Ccos%5E2%5Cbeta%7D%3D-%5Cdfrac45)
Recall the angle sum identity for sine:
![\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%2B%5Cbeta%29%3D%5Csin%5Calpha%5Ccos%5Cbeta%2B%5Csin%5Cbeta%5Ccos%5Calpha)
So we have
![\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%2B%5Cbeta%29%3D%5Cdfrac%7B12%7D%7B13%7D%5Cdfrac35%2B%5Cleft%28-%5Cdfrac45%5Cright%29%5Cleft%28-%5Cdfrac5%7B13%7D%5Cright%29%3D%5Cboxed%7B%5Cdfrac%7B56%7D%7B65%7D%7D)
Answer:
On average, 3161 people visited the park each day in August.
Step-by-step explanation:
To find how many people visited the park each day in august, we divide the total number of visitors during the months of august by the number of days that there are in August.
We have that:
97.991 people visited the park in august
There are 31 days in August.
97991/31 = 3161
On average, 3161 people visited the park each day in August.
Answer:
-A clothing store claims that 45% of its customers prefer skinny jeans over regular jeans. They concluded this from a survey which asked 120 randomly selected teenage customers which style they prefer.
-A report by a company that manufactures hair brushes says 56% of people who buy their brushes own only one hair brush. The conclusion comes from a survey of 500 males who bought the company's brush.
Please give me brainliest, I really need it.