Answer:
k=4
Step-by-step explanation:
Answer:
True.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:
6² + 13² = 14.32²
36 + 169 = 205.062
205 = 205 (rounded), so True.
Answer:
Option A: ![\frac{1}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B27%7D)
Step-by-step explanation:
The first step to solve this exercise is to find the scale factor from the radius of the small sphere to the radius of the large sphere. This is:
![radius\ scale\ factor=\frac{6.2}{18.6}\\\\radius\ scale\ factor=\frac{1}{3}](https://tex.z-dn.net/?f=radius%5C%20scale%5C%20factor%3D%5Cfrac%7B6.2%7D%7B18.6%7D%5C%5C%5C%5Cradius%5C%20scale%5C%20factor%3D%5Cfrac%7B1%7D%7B3%7D)
The second step is to find the scale factor from the volume of the small sphere to the volume of the large sphere. By definition, this will be:
![volume\ scale\ factor=(radius\ scale\ factor)^3](https://tex.z-dn.net/?f=volume%5C%20scale%5C%20factor%3D%28radius%5C%20scale%5C%20factor%29%5E3)
Therefore, you must substitute the radius scale factor into the equation and then you must evaluate in order to find the volume scale factor. This is: ![volume\ scale\ factor=(\frac{1}{3})^3\\\\volume\ scale\ factor=\frac{1}{3}*\frac{1}{3}*\frac{1}{3}\\\\volume\ scale\ factor=\frac{1}{27}](https://tex.z-dn.net/?f=volume%5C%20scale%5C%20factor%3D%28%5Cfrac%7B1%7D%7B3%7D%29%5E3%5C%5C%5C%5Cvolume%5C%20scale%5C%20factor%3D%5Cfrac%7B1%7D%7B3%7D%2A%5Cfrac%7B1%7D%7B3%7D%2A%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5Cvolume%5C%20scale%5C%20factor%3D%5Cfrac%7B1%7D%7B27%7D)
Then, the volume of the small sphere is
times the volume of the large sphere.
ANSWER
The point is
![(-9,8).](https://tex.z-dn.net/?f=%28-9%2C8%29.)
EXPLANATION
When two nonparallel lines are drawn on the same plane, they will intersect at a unique point. This point represents the solution to the two systems of equations represented by the lines.
The vertical line
![x = - 9](https://tex.z-dn.net/?f=x%20%3D%20-%209)
and the horizontal line
![y = 8](https://tex.z-dn.net/?f=y%20%3D%208)
will intersect at
![(-9,8).](https://tex.z-dn.net/?f=%28-9%2C8%29.)
This is the unique solution to the two equations.
See graph.