The total money is $2,178
Answer:
option B
![\frac{31}{50}-\frac{4}{25} i](https://tex.z-dn.net/?f=%5Cfrac%7B31%7D%7B50%7D-%5Cfrac%7B4%7D%7B25%7D%20i)
Step-by-step explanation:
Given in the question a complex fraction
<h3>Step1</h3>
To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.
![\frac{5+4i}{6+8i}(\frac{6-8i}{6-8i})](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B4i%7D%7B6%2B8i%7D%28%5Cfrac%7B6-8i%7D%7B6-8i%7D%29)
<h3>Step2</h3>
Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
![\frac{30+24i-40i-32i²}{36-64i^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B30%2B24i-40i-32i%C2%B2%7D%7B36-64i%5E%7B2%7D%20%7D)
<h3>Step3</h3>
Simplify the powers of i, specifically remember that i² = –1.
![\frac{62-16i}{36+64}](https://tex.z-dn.net/?f=%5Cfrac%7B62-16i%7D%7B36%2B64%7D)
<h3>Step4</h3>
![\frac{62}{100}-\frac{16i}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B62%7D%7B100%7D-%5Cfrac%7B16i%7D%7B100%7D)
<h3>Step5</h3>
simply
![\frac{31}{50}-\frac{4}{25}i](https://tex.z-dn.net/?f=%5Cfrac%7B31%7D%7B50%7D-%5Cfrac%7B4%7D%7B25%7Di)
Answer:
Commutative property
Step-by-step explanation:
Hope that helps!
Answer:
or 38
Step-by-step explanation:
If Q is the midpoint of Line PR, then lines PQ and QR add up to equal Line PR. We then get
![PQ=6x+25\\QR=16-3x\\PQ+QR=PR\\6x+25+16-3x=PR\\3x+41=PR\\](https://tex.z-dn.net/?f=PQ%3D6x%2B25%5C%5CQR%3D16-3x%5C%5CPQ%2BQR%3DPR%5C%5C6x%2B25%2B16-3x%3DPR%5C%5C3x%2B41%3DPR%5C%5C)
If you want to know the exact number that PR is, we can do additional steps where PQ = QR.
![PQ=6x+25\\QR=16-3x\\PQ=QR\\6x+25=16-3x\\9x+25=16\\9x=-9\\x=-1\\\\3x+41=PR\\3(-1)+41=PR\\-3+41=PR\\38=PR\\PR=38](https://tex.z-dn.net/?f=PQ%3D6x%2B25%5C%5CQR%3D16-3x%5C%5CPQ%3DQR%5C%5C6x%2B25%3D16-3x%5C%5C9x%2B25%3D16%5C%5C9x%3D-9%5C%5Cx%3D-1%5C%5C%5C%5C3x%2B41%3DPR%5C%5C3%28-1%29%2B41%3DPR%5C%5C-3%2B41%3DPR%5C%5C38%3DPR%5C%5CPR%3D38)