Answer:
![\large\boxed{a=4\sqrt5,\ b=8\sqrt5,\ f=8}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Ba%3D4%5Csqrt5%2C%5C%20b%3D8%5Csqrt5%2C%5C%20f%3D8%7D)
Step-by-step explanation:
ΔBDC and ΔCDA are similar (AA). Therefore the sides are in proportion:
![\dfrac{BD}{DC}=\dfrac{DC}{DA}](https://tex.z-dn.net/?f=%5Cdfrac%7BBD%7D%7BDC%7D%3D%5Cdfrac%7BDC%7D%7BDA%7D)
We have:
BD = 4, DA = 16 and DC = f. Substitute:
<em>cross multiply</em>
![f^2=(4)(16)\\\\f^2=64\to f=\sqrt{64}\\\\\boxed{f=8}](https://tex.z-dn.net/?f=f%5E2%3D%284%29%2816%29%5C%5C%5C%5Cf%5E2%3D64%5Cto%20f%3D%5Csqrt%7B64%7D%5C%5C%5C%5C%5Cboxed%7Bf%3D8%7D)
We can use the Pythagorean theorem:
![leg^2+leg^2=hypotenuse^2](https://tex.z-dn.net/?f=leg%5E2%2Bleg%5E2%3Dhypotenuse%5E2)
ΔBDC:
leg = 4, leg = 8, hypotenuse = a. Substitute:
![a^2=4^2+8^2\\\\a^2=16+64\\\\a^2=80\to a=\sqrt{80}\\\\a=\sqrt{16\cdot5}\\\\a=\sqrt{16}\cdot\sqrt5\\\\\boxed{a=4\sqrt5}](https://tex.z-dn.net/?f=a%5E2%3D4%5E2%2B8%5E2%5C%5C%5C%5Ca%5E2%3D16%2B64%5C%5C%5C%5Ca%5E2%3D80%5Cto%20a%3D%5Csqrt%7B80%7D%5C%5C%5C%5Ca%3D%5Csqrt%7B16%5Ccdot5%7D%5C%5C%5C%5Ca%3D%5Csqrt%7B16%7D%5Ccdot%5Csqrt5%5C%5C%5C%5C%5Cboxed%7Ba%3D4%5Csqrt5%7D)
ΔCDA:
leg = 8, leg = 16, hypotenuse = b. Substitute:
![b^2=8^2+16^2\\\\b^2=64+256\\\\b^2=320\to b=\sqrt{320}\\\\b=\sqrt{16\cdot4\cdot5}\\\\b=\sqrt{16}\cdot\sqrt4\cdot\sqrt5\\\\b=4\cdot2\cdot\sqrt5\\\\\boxed{b=8\sqrt5}](https://tex.z-dn.net/?f=b%5E2%3D8%5E2%2B16%5E2%5C%5C%5C%5Cb%5E2%3D64%2B256%5C%5C%5C%5Cb%5E2%3D320%5Cto%20b%3D%5Csqrt%7B320%7D%5C%5C%5C%5Cb%3D%5Csqrt%7B16%5Ccdot4%5Ccdot5%7D%5C%5C%5C%5Cb%3D%5Csqrt%7B16%7D%5Ccdot%5Csqrt4%5Ccdot%5Csqrt5%5C%5C%5C%5Cb%3D4%5Ccdot2%5Ccdot%5Csqrt5%5C%5C%5C%5C%5Cboxed%7Bb%3D8%5Csqrt5%7D)
So she works 9 hours in total subtract 1 which is 8 16.25x8=530 Answer: 530
(5) (-2) would be the denominator, it’s always the last two numbers ,,
Two planes may intersect, be parallel, or coincide .
If two planes intersect, then the set of common points is a line that lies in both planes. Two parallel planes can not intersect.
The intersection of two planes that do not coincide (if it exists) is always a line.
If an intersection of the planes does not exist, the planes are said to be parallel.