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enyata [817]
3 years ago
10

Which algebraic properties was applied to the expression a + (b + c) = (a + b) + c?

Mathematics
1 answer:
andrew11 [14]3 years ago
5 0

Answer:

the Associative Property

Step-by-step explanation:

Notice that the ORDER doesn't change -- a, b, c on both sides.  But the GROUPING changes.

Example:

3 + (4 + 5) = (3 + 4) + 5

3 + 9 = 7 + 5

12 = 12

Subtraction does NOT behave this way!

8 - (7 - 1) = 8 - 6 = 2

(8 - 7) - 1 = 1 - 1 = 0

It matters who you associate with!  :-)

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now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4

that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.

what's the quadratic's slope? well, simple enough

\bf \left. \cfrac{dy}{dx}=2x \right|_{x=2}\implies 4\impliedby \textit{this means }
\begin{array}{llll}
mx+b\\
\uparrow \\
4
\end{array}

so we have y = 4x + b

now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means

\bf 4 = 4(2) + b\implies 4=8+b\implies 4-8=b\implies \boxed{-4=b}
\\\\\\
mx+b\implies 4x-4\\\\
-------------------------------\\\\
f(x)=
\begin{cases}
x^2&x\le 2\\
4x-4&x\ \textgreater \ 2
\end{cases}

check the picture below.

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I have a whole packet :(
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(If needed explanation ask in the comments! ty)

Hope This Helps! •v•

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