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nordsb [41]
1 year ago
5

What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equat

ion? y= -2/5 x-1
Mathematics
1 answer:
tino4ka555 [31]1 year ago
3 0

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-1\qquad \impliedby \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

\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}

so we're really looking for the equation of a line whose slope is 5/2 and it passes through (-2 , 14)

(\stackrel{x_1}{-2}~,~\stackrel{y_1}{14})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \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-\stackrel{y_1}{14}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -14= \cfrac{5}{2} (x +2) \\\\\\ y-14=\cfrac{5}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{5}{2}x+19 \end{array}}

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Teacher will have 3 bottles of glue after he combines

<em><u>Solution:</u></em>

Given that,

The art teacher has 7 bottles of glue that are each 2/5 full

He combines them so he will have fewer bottles

<em><u>To find: bottles of glue does he have after he combines them</u></em>

From given,

Total bottles = 7

Each is 2/5 full

Therefore, multiply 7 with 2/5 to get total bottles of glues he will have after combining

Number\ of\ bottles\ of\ glues = 7 \times \frac{2}{5}\\\\Number\ of\ bottles\ of\ glues = \frac{14}{5} = 2.8 \approx 3

Thus teacher will have 3 bottles of glue after he combines

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3 years ago
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75.2

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klasskru [66]

Answer:

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Answer:

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drek231 [11]
<u>Define x:</u>
Let one of the numbers be x.
The other number is x + 2

<u>Construct equation:</u>
<span>twice the smaller is 16 more than the larger
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<u>Solve x:</u>
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Answer: The two numbers are -14 and -12
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