IJKL is a rectangle, so opposite sides have the same length:
• IJ = KL ⇒ 6y - 6 = 2x + 20
• JK = IL ⇒ 3x + 21 = 6y
Substitute the second equation into the first and solve for x :
6y - 6 = 2x + 20
(3x + 21) - 6 = 2x + 20
3x + 15 = 2x + 20
x = 5
Solve for y :
3x + 21 = 6y
15 + 21 = 6y
36 = 6y
y = 6
if the diameter is 10, its radius is half that, or 5.
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5 \end{cases}\implies V=\cfrac{4\pi (5)^3}{3}\implies V=\cfrac{500\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill V\approx 523.599~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20sphere%7D%5C%5C%5C%5C%20V%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D5%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B4%5Cpi%20%285%29%5E3%7D%7B3%7D%5Cimplies%20V%3D%5Ccfrac%7B500%5Cpi%20%7D%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20V%5Capprox%20523.599~%5Chfill)
1) Correct.
2) The y-intercept is when x=0, so it is (0,5).
Answer:
Step-by-step explanation:
The domain includes all x values, and here, it is [-2, 4].
