Answer:
m∠SBE = 26°,
= 126°
Step-by-step explanation:
The arc of a circle is a portion of the circumference of the circle. For a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.
Central angle is an angle whose vertex is on the center of the circle and endpoints on the circumference of the circle. If the endpoints of the central angle are are also the endpoints for the angle's intercepted arc, then both angles are congruent.
Also, the angle at the center is twice the angle at the circumference.
Angle at center =
= 52° (central angle is congruent with angle that intercept the arc)
2 * m∠SBE = central angle (angle at the center is twice the angle at the circumference)
2 * m∠SBE = 52
m∠SBE = 26°
2 * m∠BEO = central angle (angle at the center is twice the angle at the circumference)
2 * 63 = central angle
central angle = 126°
Angle at center =
= 126° (central angle is congruent with angle that intercept the arc)
Answer:
7x
Step-by-step explanation:
4x−6+3x+6
=4x+−6+3x+6
Combine Like Terms:
=4x+−6+3x+6
=(4x+3x)+(−6+6)
=7x
No but it could be. It would be a harder way though. I prefer doing it without reversing it.
Answer:
1) Solving -5x+y we get: ![\mathbf{-8-41i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-8-41i%7D)
2) Solving -x . y we get: ![\mathbf{-29-53i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-29-53i%7D)
3) Solving x . 2y we get: ![\mathbf{58+106i}](https://tex.z-dn.net/?f=%5Cmathbf%7B58%2B106i%7D)
4) Solving 2x - 3y we get: ![\mathbf{-15+19i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-15%2B19i%7D)
Step-by-step explanation:
We are given:
![x = 3 + 8i\\y = 7 - i](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%208i%5C%5Cy%20%3D%207%20-%20i)
We need to find:
1) -5x+y
Solving:
Simply put values of x and y and add them.
![-5x+y\\=-5(3+8i)+7-i\\=-15-40i+7-i\\=-15+7-40i-i\\=-8-41i](https://tex.z-dn.net/?f=-5x%2By%5C%5C%3D-5%283%2B8i%29%2B7-i%5C%5C%3D-15-40i%2B7-i%5C%5C%3D-15%2B7-40i-i%5C%5C%3D-8-41i)
So, Solving -5x+y we get: ![\mathbf{-8-41i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-8-41i%7D)
2) -x . y
Simply put values of x and y and multiply them.
![-x\:.\:y\\=-(3+8i)\:.\:(7-i)\\=-3-8i\:.\:(7-i)\\=-3(7-i)-8i(7-i)\\=-21+3i-56i+8i^2\\We\:know\:that\:i^2=-1\\=-21+3i-56i+8(-1)\\=-21+3i-56i-8\\=-21-8+3i-56i\\=-29-53i](https://tex.z-dn.net/?f=-x%5C%3A.%5C%3Ay%5C%5C%3D-%283%2B8i%29%5C%3A.%5C%3A%287-i%29%5C%5C%3D-3-8i%5C%3A.%5C%3A%287-i%29%5C%5C%3D-3%287-i%29-8i%287-i%29%5C%5C%3D-21%2B3i-56i%2B8i%5E2%5C%5CWe%5C%3Aknow%5C%3Athat%5C%3Ai%5E2%3D-1%5C%5C%3D-21%2B3i-56i%2B8%28-1%29%5C%5C%3D-21%2B3i-56i-8%5C%5C%3D-21-8%2B3i-56i%5C%5C%3D-29-53i)
So, Solving -x . y we get: ![\mathbf{-29-53i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-29-53i%7D)
3) x . 2y
Simply put values of x and y and multiply them.
![x\:.\:2y\\=(3+8i)\:.\:2(7-i)\\=2(3+8i)\:.\:(7-i)\\=2(3(7-i)+8i(7-i)\\=2(21-3i+56i-8i^2)\\We\:know\:i^2=-1\\=2(21-3i+56i-8(-1))\\=2(21-3i+56i+8)\\=2(21+8-3i+56i)\\=2(29+53i)\\=58+106i](https://tex.z-dn.net/?f=x%5C%3A.%5C%3A2y%5C%5C%3D%283%2B8i%29%5C%3A.%5C%3A2%287-i%29%5C%5C%3D2%283%2B8i%29%5C%3A.%5C%3A%287-i%29%5C%5C%3D2%283%287-i%29%2B8i%287-i%29%5C%5C%3D2%2821-3i%2B56i-8i%5E2%29%5C%5CWe%5C%3Aknow%5C%3Ai%5E2%3D-1%5C%5C%3D2%2821-3i%2B56i-8%28-1%29%29%5C%5C%3D2%2821-3i%2B56i%2B8%29%5C%5C%3D2%2821%2B8-3i%2B56i%29%5C%5C%3D2%2829%2B53i%29%5C%5C%3D58%2B106i)
So, Solving x . 2y we get: ![\mathbf{58+106i}](https://tex.z-dn.net/?f=%5Cmathbf%7B58%2B106i%7D)
4) 2x-3y
![2x-3y\\=2(3+8i)-3(7-i)\\=6+16i-21+3i\\=6-21+16i+3i\\=-15+19i](https://tex.z-dn.net/?f=2x-3y%5C%5C%3D2%283%2B8i%29-3%287-i%29%5C%5C%3D6%2B16i-21%2B3i%5C%5C%3D6-21%2B16i%2B3i%5C%5C%3D-15%2B19i)
So, Solving 2x - 3y we get: ![\mathbf{-15+19i}](https://tex.z-dn.net/?f=%5Cmathbf%7B-15%2B19i%7D)
Answer:
343 square root 1000
Step-by-step explanation:
See Image below:)