<span>(triangle) ZYB to (triangle) OWR by sss</span>
Step-by-step explanation:
you did not show us the picture or described what the shaded area is.
I assume it is the area of the circle without the inner square (as the "rectangke" is actually a square, because its sides are equally long).
so, we need to calculate the area of the circle and subtract the area of the square.
the area of the square is 3×3 = 9 cm².
the area of the circle is
pi×r²
with r being the radius.
so,
pi×4² = pi×16 = 16pi
the shaded area is then
16pi - 9 = 41.26548246... cm² ≈ 41.27 cm²
nothing of the answer options seems to be in that area, so maybe my assumption about the shaded area is wrong. or the specified answer options are mistyped. or both.
anyway, without additional information that is the best I can do.
Turn f(x) into y so the equation is y=x+2. Now switch their places so it is x=y+2. Now solve for y. The answer is y=x-2.
Check the picture below.
now, let's keep in mind that, the vertex is half-way between the focus point and the directrix, it's a "p" distance from each other.
since this horizontal parabola is opening to the left-hand-side, "p" is negative, notice in the picture, "p" is 2 units, and since it's negative, p = -2.
its vertex is half-way between those two guys, so that puts the vertex at (-5, 3)
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=7\\ p=-2 \end{cases}\implies 4(-2)[x-(-5)]=[y-7]^2 \\\\\\ -8(x+5)=(y-7)^2\implies x+5=\cfrac{(y-7)^2}{-8}\implies \boxed{x=-\cfrac{1}{8}(y-7)^2-5}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-5%5C%5C%20k%3D7%5C%5C%20p%3D-2%20%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%5Bx-%28-5%29%5D%3D%5By-7%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-8%28x%2B5%29%3D%28y-7%29%5E2%5Cimplies%20x%2B5%3D%5Ccfrac%7B%28y-7%29%5E2%7D%7B-8%7D%5Cimplies%20%5Cboxed%7Bx%3D-%5Ccfrac%7B1%7D%7B8%7D%28y-7%29%5E2-5%7D)
