Suppose a is an irrational number and b/c is a rational number. Can their sum be rational? Explain your

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

4 0

Answer:

it can but doesnt always have to be because it can be a commplex decimal and not a fractionn

Step-by-step explanation:

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What is the equation of the perpendicular to y=2/3x+1 that passes through the point (12,-6)

postnew [5]

Well, first off let's check what is the slope of y = 2/3x+1.... .hmmmmm, notice $\bf y=\stackrel{slope}{\cfrac{2}{3}}x+1$ , since the equation is already in slope-intercept form, we can see it has a slope of 2/3.

well then, a line perpendicular to that one, will have a negative reciprocal to it.

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
slope=\cfrac{2}{{{ 3}}}\qquad negative\implies -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}$

so, we're really looking for the equation of a line whose slope is -3/2 and goes through 12, -6.

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 12}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-6)=-\cfrac{3}{2}(x-12)
\\\\\\
y+6=-\cfrac{3}{2}x+18\implies y=-\cfrac{3}{2}x+12$