19.11.2020

Consider the line y= −2/9x-7. Find the equation of the line that is perpendicular to this line and passes through the point , (2, 3) Find the equation of the line that is parallel to this line and passes through the point , (2,3).

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09.07.2023, solved by verified expert
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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

Consider the line y= −2/9x-7. Find the equation, №18010373, 19.11.2020 10:53

so then we can say that

Consider the line y= −2/9x-7. Find the equation, №18010373, 19.11.2020 10:53

so we're really looking for the equation of a line whos slope is 9/2 and passes through (2 , 3)

Consider the line y= −2/9x-7. Find the equation, №18010373, 19.11.2020 10:53

now as far as the parallel line

keeping in mind that parallel lines have exactly the same slope, so we're really looking for the equation of a line whose slope is -2/9 and passes through (2 , 3)

Consider the line y= −2/9x-7. Find the equation, №18010373, 19.11.2020 10:53

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Mathematics
Step-by-step answer
P Answered by Master

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}{9}} x-7\qquad \impliedby \qquad \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}

so then we can say that

\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-\cfrac{2}{9}} ~\hfill \stackrel{reciprocal}{-\cfrac{9}{2}} ~\hfill \stackrel{negative~reciprocal}{-\left( -\cfrac{9}{2} \right)\implies \cfrac{9}{2}}}

so we're really looking for the equation of a line whos slope is 9/2 and passes through (2 , 3)

(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{9}{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}{3}=\stackrel{m}{\cfrac{9}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-3=\cfrac{9}{2}x-9\implies \boxed{y=\cfrac{9}{2}x-6}

now as far as the parallel line

keeping in mind that parallel lines have exactly the same slope, so we're really looking for the equation of a line whose slope is -2/9 and passes through (2 , 3)

(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{2}{9} \\\\\\ \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}{3}=\stackrel{m}{-\cfrac{2}{9}}(x-\stackrel{x_1}{2}) \\\\\\ y-3=-\cfrac{2}{9}x+\cfrac{4}{9}\implies y=-\cfrac{2}{9}x+\cfrac{4}{9}+3\implies \boxed{y=-\cfrac{2}{9}x+\cfrac{31}{9}}

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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