Answer:
140
Step-by-step explanation:
Solve 40% of 350.
The region(s) represent the intersection of Set A and Set B (A∩B) is region II
<h3>How to determine which region(s) represent the intersection of Set A and Set B (A∩B)?</h3>
The complete question is added as an attachment
The universal set is given as:
Set U
While the subsets are:
The intersection of set A and set B is the region that is common in set A and set B
From the attached figure, we have the region that is common in set A and set B to be region II
This means that
The intersection of set A and set B is the region II
Hence, the region(s) represent the intersection of Set A and Set B (A∩B) is region II
Read more about sets at:
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Answer:
See explanation
Step-by-step explanation:
Simplify left and right parts separately.
<u>Left part:</u>
![\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ctan%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ccot%20%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B%5Csin%5E2A%2B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B%5Ccos%5E2A%2B%5Csin%5EA%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
<u>Right part:</u>
![\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Csin%5E2A-%5Csin%5E4A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%281-%5Csin%5E2A%29%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
Since simplified left and right parts are the same, then the equality is true.
Answer:
Step-by-step explanation:
The interior angles of a heptagon add up to 5*180 = 900
So
x + 143 + 116 + 135 + 135 + 116 + 155 = 900 Add up the known angles
x + 800 = 900 Subtract 800 from both sides
x + 800 - 800 = 900 - 800 Combine
x = 100
Answer:
C. 5units
Step-by-step explanation: