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murzikaleks [220]
3 years ago
11

An expression is shown below:

Mathematics
1 answer:
Crank3 years ago
4 0
Part A.
4m + 12 + 20m

2 (2m + 6 + 10m)

Part B.
2 (2m + 6 + 10m) = 4(m + 3 + 5m)

4m + 12 + 20m = 4m + 12 + 20m

24m + 12 = 24m + 12

My apologies...but I don't understand what you mean by algebraic properties.

Part C.
Assuming m = 2

4 (m + 3 + 5m)
4 (2 + 3 + 5 × 2)
4 (5 + 10)
4 (15)
60

4m + 12 + 20m
4 (2) + 12 + 20 (2)
8 + 12 + 40
20 + 40
60

Hope this helps!
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8 0
3 years ago
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Graph the following sequence of transformations for
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\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}
\end{array}\\\\
--------------------

\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the y-axis}

\bf \bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{  D}}\\
\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\
\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\
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with that template in mind.

\bf f(x)=\sqrt[3]{x}\qquad \boxed{-f(x+2)+4}\implies f(x)=\stackrel{A}{-1}\sqrt[3]{\stackrel{B}{1}x\stackrel{C}{+2}}\stackrel{D}{+4}\qquad 
\\\\\\
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B = 1, C = 2,  horizontal shift of C/B or 2, to the left.

D = 4, shifted upwards by 4 units.

check the picture below.

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