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PIT_PIT [208]
3 years ago
13

Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 1 , − 1 ) (−1,−1) and ( 9 , 7 ) (9,7

)
Mathematics
2 answers:
SIZIF [17.4K]3 years ago
5 0

Answer:

y = - \frac{5}{4} x + 8

Step-by-step explanation:

The perpendicular bisector intersects the line segment at its midpoint and is perpendicular to it.

Using the midpoint formula

M = ( \frac{x_{}+x_{2}  }{2}, \frac{y_{1}+y_{2}  }{2} )

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (9, 7)

midpoint = ( \frac{-1+9}{2}, \frac{-1+7}{2} ) = ( \frac{8}{2}, \frac{6}{2} ) = (4, 3 )

Calculate the slope using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (9, 7)

m = \frac{7-(-1)}{9-(-1)} = \frac{7+1}{9+1} = \frac{8}{10} = \frac{4}{5}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{4}{5} } = - \frac{5}{4} , then

y = - \frac{5}{4} x + c ← is the partial equation

To find c substitute (4, 3) into the partial equation

3 = - 5 + c ⇒ c = 3 + 5 = 8

y = - \frac{5}{4} x + 8 ← equation of perpendicular bisector

Hunter-Best [27]3 years ago
3 0

Answer:

Place the compass at one end of line segment.

Adjust the compass to slightly longer than half the line segment length.

Draw arcs above and below the line.

Keeping the same compass width, draw arcs from other end of line.

Place ruler where the arcs cross, and draw the line segment.

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The weight of a piece of raw silk that is 100 yards long by 1.25 yards wide (standard width) is about 38 pounds. The weight of a
butalik [34]

The total weight of the two pieces together is 6 pounds.

<h3>How much would the two pieces weigh together?</h3>

A piece of raw silk that is 100 yards long by 1.25 yards wide weights 38lb.

Then, a piece that is 12.5 yards long (and still 1.25 yards wide) will weight:

M = (12.5/100)*38lb = 4.75 lb

And a piece of habotai silk that is 100 yards long by 1.25 yards wide weights 12lb.

Then, a piece that is 12.5 yards long will weigh:

M' = (12.5/100)*12lb = 1.5 lb

If we add these two, we get a total weight of:

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The total weight of the two pieces together is 6 pounds.

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5 0
1 year ago
What is .84 divided by .02<br> please help me because i really really REALLY need help on this
KatRina [158]

Hello There!

.84 ÷ .02 ≈ 42

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3 0
3 years ago
I'm struggling fr now, pls can you help me answer these questions using the y= mx+ c method thanks!
Phoenix [80]

Answer:

Examination of the equation shows (graph):

x = 0, y = .5

Then .5 = c      gives us the value of c giving

y = m x + .5    is our equation

Using y = 0, x = -1 gives

o = -1 * m + .5

m = .5

y = .5 x + .5    for the final equation

Check:

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4 0
2 years ago
Solve using long division <br> Please
madreJ [45]

1. Solution,\frac{2x^3+4x^2-5}{x+3}:\quad 2x^2-2x+6-\frac{23}{x+3}

Steps:

\mathrm{Divide}\:\frac{2x^3+4x^2-5}{x+3}:\quad \frac{2x^3+4x^2-5}{x+3}=2x^2+\frac{-2x^2-5}{x+3}

\mathrm{Divide}\:\frac{-2x^2-5}{x+3}:\quad \frac{-2x^2-5}{x+3}=-2x+\frac{6x-5}{x+3}

\mathrm{Divide}\:\frac{6x-5}{x+3}:\quad \frac{6x-5}{x+3}=6+\frac{-23}{x+3}

\mathrm{Simplify}, =2x^2-2x+6-\frac{23}{x+3}

\mathrm{The\:Correct\:Answer\:is\:2x^2-2x+6-\frac{23}{x+3}}

2. Solution, \frac{4x^3-2x^2-3}{2x^2-1}:\quad 2x-1+\frac{2x-4}{2x^2-1}

Steps:

\mathrm{Divide}\:\frac{4x^3-2x^2-3}{2x^2-1}:\quad \frac{4x^3-2x^2-3}{2x^2-1}=2x+\frac{-2x^2+2x-3}{2x^2-1}

\mathrm{Divide}\:\frac{-2x^2+2x-3}{2x^2-1}:\quad \frac{-2x^2+2x-3}{2x^2-1}=-1+\frac{2x-4}{2x^2-1}

\mathrm{The\:Correct\:Answer\:is\:2x-1+\frac{2x-4}{2x^2-1}}

\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

4 0
3 years ago
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