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Lostsunrise [7]
1 year ago
5

What is the slope of a line perpendicular to the line whose equation is 2x+3y=21. Fully simplify your answer.

Mathematics
1 answer:
erastova [34]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

2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\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}

therefore then

\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}

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Arrange the pairs of points in increasing order of the slopes of the lines joining them. (15, 30) and (20, 40)
gavmur [86]

Answer: m1 = 0.5

M2= 0.375

M3 = 2.25

M4 = 3.0

M5 = 13.5

M6 = 0.285

M7 = 7.0

Step-by-step explanation:

(20,40)-(15,30)=(5,10), m1=5/10=0.5

(18,48)-(12,32)=(6,16), m2=3/8=0.375

(72,32)-(27,12)=(45,20), m3=9/4=2.25

(60,20)-(45,15)=(15,5), m4=3.0

(243,18)-(27,2)=(216,16), m5=27/2=13.5

(24,84)-(18,63)=(6,21), m6=2/7=0.285...

(84,12)-(63,9)=(21,3), m7=7.0

4 0
3 years ago
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Cloud [144]

i cant read it clearly


4 0
3 years ago
Please help as soon as possible!
AnnZ [28]

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (8, 4)

m = \frac{4-6}{8-3} = - \frac{2}{5}, hence

y = - \frac{2}{5} x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 4), then

4 = - \frac{16}{5} + c ⇒ c = 4 + \frac{16}{5} = \frac{36}{5}

y = - \frac{2}{5} x + \frac{36}{5} ← equation of line

6 0
2 years ago
Read 2 more answers
Who can help me with this plzz
Brrunno [24]
.04d + 20. 

This is because even with no miles they charge 20 more and then 4 cents more for any additional mile. 
6 0
3 years ago
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours. Daryl plans to be gone at least
lubasha [3.4K]

The inequality equation will be -5x + 20 < -10.

<h3>What is inequality?</h3>

Inequality is defined as an equation that does not contain an equal sign.

The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.

Daryl plans to be gone at least 6 hours, and he has a plant outside.

If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving will be

The inequality equation will be

-5x + 20 < -10

where x is the number of hours.

Then we have

-10 < -5x + 20

5x > 30

   x > 6 hours

More about the inequality link is given below.

brainly.com/question/19491153

#SPJ1

5 0
1 year ago
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