Answer:
What is it you need help with for this question? Please provide all information in your question so we can know exactly how to help you. Thank you!
Find the midpoint:
m= x1+x2/2; y1+y2/2
m= 9+-1/2; 8+-2/2
m= 8/2; 6/2
m= (4,3)
(4,3) is your answer.
I hope this helps!
~kaikers
Answer:
1: 80 (Vertical angles congruent)
2: 70 (Vertical angles congruent)
3:
4: 110 (Straight angle w/ angle 2, 180-70 {known variable})
5: 90 (Right angle)
6: 90 (Right angle)
7: 20 (180-90-70 (unmarked angle opposite 4)
9:
10:
Answer:
![\sqrt{119+120 i}=\pm (12.24+i 4.90)](https://tex.z-dn.net/?f=%5Csqrt%7B119%2B120%20i%7D%3D%5Cpm%20%2812.24%2Bi%204.90%29)
Step-by-step explanation:
Given
z = 119 + 120 i
Let ![\sqrt{119+120 i}=p+iq](https://tex.z-dn.net/?f=%5Csqrt%7B119%2B120%20i%7D%3Dp%2Biq)
Squaring both sides
![119+120 i=p^2-q^2+2ipq](https://tex.z-dn.net/?f=119%2B120%20i%3Dp%5E2-q%5E2%2B2ipq)
Comparing real and imaginary part
Re(LHS)=Re(RHS)
...........................(1)
comparing Im(LHS)=Im(RHS)
120=2pq
![q=\frac{60}{p}](https://tex.z-dn.net/?f=q%3D%5Cfrac%7B60%7D%7Bp%7D)
Substitute q in 1
![119=p^2-(\frac{60}{p})^2](https://tex.z-dn.net/?f=119%3Dp%5E2-%28%5Cfrac%7B60%7D%7Bp%7D%29%5E2)
![p^4-119p^2-(68)^2=0](https://tex.z-dn.net/?f=p%5E4-119p%5E2-%2868%29%5E2%3D0)
Let ![x=p^2](https://tex.z-dn.net/?f=x%3Dp%5E2)
![x^2-119x-4624=0](https://tex.z-dn.net/?f=x%5E2-119x-4624%3D0)
![x=\dfrac{119\pm \sqrt{119^2+4\times 4624}}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B119%5Cpm%20%5Csqrt%7B119%5E2%2B4%5Ctimes%204624%7D%7D%7B2%7D)
![x=\frac{119\pm 180.71}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B119%5Cpm%20180.71%7D%7B2%7D)
we take only Positive value because ![p^2=x](https://tex.z-dn.net/?f=p%5E2%3Dx)
x=149.85
![p^2=149.85](https://tex.z-dn.net/?f=p%5E2%3D149.85)
thus ![p=\pm 12.24](https://tex.z-dn.net/?f=p%3D%5Cpm%2012.24)
![q=\pm 4.90](https://tex.z-dn.net/?f=q%3D%5Cpm%204.90)
thus,
![\sqrt{119+120 i}=\pm (12.24+i 4.90)](https://tex.z-dn.net/?f=%5Csqrt%7B119%2B120%20i%7D%3D%5Cpm%20%2812.24%2Bi%204.90%29)
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