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Vesnalui [34]
3 years ago
7

Find the equation of the following line and graph. Through (3,-10) perpendicular to 5x-y=9

Mathematics
1 answer:
enot [183]3 years ago
7 0

bearing in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of 5x -  y = 9 then.

\bf 5x-y=9\implies -y=-5x+9\implies y=\stackrel{\stackrel{m}{\downarrow }}{5}x-9\leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{5\implies \cfrac{5}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{5}}\qquad \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}

so then, we're really looking for the equation of a line whose slope is -1/5 and runs through (3,-10).

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-10})~\hspace{10em} slope = m\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-10)=-\cfrac{1}{5}(x-3)\implies y+10=-\cfrac{1}{5}x+\cfrac{3}{5} \\\\\\ y=-\cfrac{1}{5}x+\cfrac{3}{5}-10\implies y=-\cfrac{1}{5}x+\cfrac{53}{5}

and it looks like the one in the picture below.

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An elementary school is offering 2 language classes: one in Spanish (S) and one in French (F). Given that P(S) = 50%, P(F) = 40%
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Step-by-step explanation:

We are given that an elementary school is offering 2 language classes ;

 <em>Spanish Language is denoted by S and French language is denoted by F.</em>

Also we are given, P(S) = 0.5 {Probability of students taking Spanish language}

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<em>We know that,  </em>P(A\bigcup B)<em>  = </em>P(A) + P(B) -<em> </em>P(A\bigcap B)<em />

So, P(S\bigcap F) = P(S) + P(F) - P(S\bigcup F) = 0.5 + 0.4 - 0.7 = 0.2

P(S\bigcap F) means Probability of students taking  both Spanish and French Language.

Also, P(S)' = 1 - P(S) = 1 - 0.5 = 0.5

         P(F)' = 1 - P(F) = 1 - 0.4 = 0.6

        P(S'\bigcap F') = 1 -  P(S\bigcup F) = 1 - 0.7 = 0.3

(a) Probability that a randomly selected student is taking Spanish given that he or she is taking French is given by P(S/F);

  P(S/F) = \frac{P(S\bigcap F)}{P(F)} = \frac{0.2}{0.4} = 0.5

(b) Probability that a randomly selected student is not taking French given that he or she is not taking Spanish is given by P(F'/S');

   P(F'/S') = \frac{P(S'\bigcap F')}{P(S')} = \frac{1- P(S\bigcup F)}{1-P(S)} = \frac{0.3}{0.5} = 0.6 .

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