X=1 because, −2.8x+5.6<8.4
Answer:
![r=\frac{5}{2}\sqrt{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5%7D%7B2%7D%5Csqrt%7B2%7D)
Step-by-step explanation:
<u>Triangles And Circles</u>
If a right triangle is inscribed in a circle (or the circle is circumscribed around the right triangle), then the hypotenuse of the triangle is the diameter of the circle.
The right triangle has both legs of known lengths, thus the hypotenuse (the diameter of the circle is):
![d^2=5^2+5^2](https://tex.z-dn.net/?f=d%5E2%3D5%5E2%2B5%5E2)
![d^2=25+25=50](https://tex.z-dn.net/?f=d%5E2%3D25%2B25%3D50)
![d=\sqrt{50}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B50%7D)
Since 50=2*25:
![d=5\sqrt{2}](https://tex.z-dn.net/?f=d%3D5%5Csqrt%7B2%7D)
Thus the radius of the circle is:
![r=\frac{d}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bd%7D%7B2%7D)
![r=\frac{5\sqrt{2}}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B2%7D)
![\boxed{r=\frac{5}{2}\sqrt{2}}](https://tex.z-dn.net/?f=%5Cboxed%7Br%3D%5Cfrac%7B5%7D%7B2%7D%5Csqrt%7B2%7D%7D)
We need to know how many weeks there are is a year , we know a year is 365 days and a week is 7 days so we do this to get the number of weeks 365÷7=52 weeks and 1 day , then we do 52÷6 to know the number of times she will pay : she will pay 8 times in a year for a total of 8x156=1248$ and she will also have an additional 4 weeks and one day with nothing to do (she cannot pay one more time as she still did not finish her 9th period)