Please indicate exponentiation using " ^ " Thanks.
f(x)=x2+14x+40 => <span>f(x)=x^2+14x+40
Next, complete the square:
</span>f(x)=x^2+14x+ 49 - 49 +40 = (x+7)^2 - 9
Write this in the form y = (x+7)^2 - 9 or y + 9 = (x+7)^2
Comparing this result to y = a(x-h)^2 + k, we see that h = -7 and k=-9
In vertex form, the equation is y + 9 = (x+7)^2 and the vertex is at (-7, -9).
Check the picture below.
now, we have a triangle with all three sides, thus we can use Heron's Area Formula on the triangle.
![\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=10\\ b=26.695\\ c=22\\ s=29.3475 \end{cases} \\\\\\ A=\sqrt{29.3475(29.3475-10)(29.3475-26.695)(29.3475-22)} \\\\\\ A=\sqrt{29.3475(19.3475)(2.6525)(7.3475)}\implies A\approx \sqrt{11066.007} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 105.195~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BHeron%27s%20area%20formula%7D%20%5C%5C%5C%5C%20A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5Cqquad%20%5Cbegin%7Bcases%7D%20s%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D10%5C%5C%20b%3D26.695%5C%5C%20c%3D22%5C%5C%20s%3D29.3475%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B29.3475%2829.3475-10%29%2829.3475-26.695%29%2829.3475-22%29%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B29.3475%2819.3475%29%282.6525%29%287.3475%29%7D%5Cimplies%20A%5Capprox%20%5Csqrt%7B11066.007%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20A%5Capprox%20105.195~%5Chfill)
Answer:
Step-by-step explanation:
Polygons (shapes made of straight lines) where no angle is greater than 180 degrees. If even one angle is greater than 180 then it is a concave polygon.
Answer:
25.5
Step-by-step explanation:
first find the area od the rectangle than the triangle.
to find the area count the number of squares and use A=b*h
than do the same for the triangle using A=.5*b*h
15=3*5
10.5=.5*3*7
10.5+15=25.5
Answer: 62
Step-by-step explanation:
See picture for more information
