Answer: 
Step-by-step explanation:
Given
Complex number is 
Its conjugate is obtained by changing the sign of the original number i.e. 
The product of the two numbers is
![\Rightarrow (2-i5)(2+i5)=2^2-(5i)^2\quad \quad [(x+y)(x-y)=x^2-y^2]\\\\\Rightarrow (2-i5)(2+i5)=4-25i^2\\\\\Rightarrow (2-i5)(2+i5)=4+25=29](https://tex.z-dn.net/?f=%5CRightarrow%20%282-i5%29%282%2Bi5%29%3D2%5E2-%285i%29%5E2%5Cquad%20%5Cquad%20%5B%28x%2By%29%28x-y%29%3Dx%5E2-y%5E2%5D%5C%5C%5C%5C%5CRightarrow%20%282-i5%29%282%2Bi5%29%3D4-25i%5E2%5C%5C%5C%5C%5CRightarrow%20%282-i5%29%282%2Bi5%29%3D4%2B25%3D29)
Problem 1
x = measure of angle N
2x = measure of angle M, twice as large as N
3(2x) = 6x = measure of angle O, three times as large as M
The three angles add to 180 which is true of any triangle.
M+N+O = 180
x+2x+6x = 180
9x = 180
x = 180/9
x = 20 is the measure of angle N
Use this x value to find that 2x = 2*20 = 40 and 6x = 6*20 = 120 to represent the measures of angles M and O in that order.
<h3>Answers:</h3>
- Angle M = 40 degrees
- Angle N = 20 degrees
- Angle O = 120 degrees
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Problem 2
n = number of sides
S = sum of the interior angles of a polygon with n sides
S = 180(n-2)
2700 = 180(n-2)
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
<h3>Answer: 17 sides</h3>
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Problem 3
x = smaller acute angle
3x = larger acute angle, three times as large
For any right triangle, the two acute angles always add to 90.
x+3x = 90
4x = 90
x = 90/4
x = 22.5
This leads to 3x = 3*22.5 = 67.5
<h3>Answers:</h3>
- Smaller acute angle = 22.5 degrees
- Larger acute angle = 67.5 degrees
Your answer is 1,024. Hope this helps!
Work:
-4 x 8 = -32
-32 x -32 = 1,024
Answer:
a
Step-by-step explanation:
