when it comes to checking if a function is even or odd, it boils down to changing the argument, namely x = -x, and if the <u>resulting function is the same as the original</u>, then is even, if the <u>resulting function is the same as the original but negative</u>, is odd, if neither, well then neither :).
anyway, that said, let's first expand it and then plug in -x,
![\bf f(x)=(x^2-8)^2\implies f(x)=(x^2-8)(x^2-8)\implies f(x)=\stackrel{FOIL}{x^4-16x^2+64}\\\\[-0.35em]~\dotfill\\\\f(-x)=(-x)^4-16(-x)^2+64\qquad \begin{cases}(-x)(-x)(-x)(-x)=x^4\\(-x)(-x)=x^2\end{cases}\\\\\\f(-x)=x^4-16x^2+64\impliedby \stackrel{\textit{same as the original}}{Even}](https://tex.z-dn.net/?f=%20%5Cbf%20f%28x%29%3D%28x%5E2-8%29%5E2%5Cimplies%20f%28x%29%3D%28x%5E2-8%29%28x%5E2-8%29%5Cimplies%20f%28x%29%3D%5Cstackrel%7BFOIL%7D%7Bx%5E4-16x%5E2%2B64%7D%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5Cf%28-x%29%3D%28-x%29%5E4-16%28-x%29%5E2%2B64%5Cqquad%20%5Cbegin%7Bcases%7D%28-x%29%28-x%29%28-x%29%28-x%29%3Dx%5E4%5C%5C%28-x%29%28-x%29%3Dx%5E2%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5Cf%28-x%29%3Dx%5E4-16x%5E2%2B64%5Cimpliedby%20%5Cstackrel%7B%5Ctextit%7Bsame%20as%20the%20original%7D%7D%7BEven%7D%20)
C(a,b), because the x-coordinate( first coordinate) is a (seeing as it is situated directly above point B, which also has an x-coordinate of a) and the y-coordinate ( second coordinate) is b (seeing as it is situated on the same horizontal level as point D, which also has a y-coordinate of b)
the length of AC can be calculated with the theorem of Pythagoras:
length AB = a - 0 = a
length BC = b - 0 = b
seeing as the length of AC is the longest, it can be calculated by the following formula:
It is called "Pythagoras' Theorem" and can be written in one short equation:
a^2 + b^2 = c^2 (^ means to the power of by the way)
in this case, A and B are lengths AB and BC, so lenght AC can be calculated as the following:
a^2 + b^2 = (length AC)^2
length AC = √(a^2 + b^2)
Extra information: Seeing as the shape of the drawn lines is a rectangle, lines AC and BD have to be the same length, so BD is also √(a^2 + b^2). But that is also stated in the assignment!
Its a even number, and also its a whole number.
Answer:
any order where 2 is the last number in the sequence
Step-by-step explanation:
the ten-thousand place in 12,345 is 5.
ex: 3,8,9,5,2
5,9,8,3,2
8,9,5,3,2
