Write 4.135 as a fraction

Mathematics

2 answers:

Nuetrik [128]3 years ago

8 0

Answer:

Step-by-step explanation:

827/200

marshall27 [118]3 years ago

5 0

The answer is 827/200

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Write an absolute value equation for the graph shown below

BabaBlast [244]

So, hmmm keeping in mind that, an absolute value expression is in effect a piece-wise function, let's find its "slopes", the negarive slope on the left-side and the positive slope on the right side, and let's use the vertex point as our first point

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$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 0}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
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\\\\\\
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\\\\\\
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now, what is the slope of a line that passes through (2, -1) and (4,7)

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{7-(-1)}{4-2}\implies \cfrac{7+1}{2}\implies 4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=4(x-2)
\\\\\\
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since an absolute value expression is just a piece-wise with a +/- versions, then we can just combine those two.

$\bf \begin{cases}
y+1=-4(x-2)\\
y+1=4(x-2)
\end{cases}\implies y+1=\pm 4(x-2)
\\\\\\
y+1=|4(x-2)|\implies y=|4(x-2)|-1$

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