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den301095 [7]
2 years ago
7

Write an equation of the perpendicular bisector of the segment joining a(-2,3) and b(4,-5).

Mathematics
2 answers:
Bas_tet [7]2 years ago
8 0

Answer:

C) 3x - 4y = 7

Step-by-step explanation:

The midpoint of AB is

M( (-2 + 4)/2, (-5 + 3)/2 ) = M(1, -1)

Line AB has slope:

(3 - (-5))/(-2 - 4) = 8/(-6) = -4/3

Slopes of perpendicular lines are negative reciprocals.

A perpendicular to line AB has slope 3/4.

The perpendicular to line AB that passes through the midpoint of segment AB is the line we want.

y - y_1 = m(x - x_1)

y - (-1) = \dfrac{3}{4}(x - 1)

y + 1 = \dfrac{3}{4}(x - 1)

4y + 4 = 3(x - 1)

4y + 4 = 3x - 3

3x - 4y = 7

kirza4 [7]2 years ago
6 0

Answer:

C

Step-by-step explanation:

Segment joining a and b

m = 8/(-6) =-4/3

For that of the perpendicular bisector...

m = 3/4

Midpoint of Segment joining a and b

([-2+4]/2 , [3-5]/2)

=(1, -1)

y=mx+c

-1=(3/4)(1)+c

c= -7/4

y=3x/4 - 7/4

4y=3x - 7

3x-4y = 7

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Answer:

3.46

Step-by-step explanation:

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3 years ago
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ivanzaharov [21]

Answer:

C. 5 units

Step-by-step explanation:

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4 0
2 years ago
If (x + 1)(x-3) = 5, then which of the following statements is true?
bixtya [17]

Answer:

x=−2 or x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x2−2x−3=5

Step 2: Subtract 5 from both sides.

x2−2x−3−5=5−5

x2−2x−8=0

Step 3: Factor left side of equation.

(x+2)(x−4)=0

Step 4: Set factors equal to 0.

x+2=0 or x−4=0

x=−2 or x=4

5 0
3 years ago
Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walki
Sonbull [250]

Answer:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis: \mu \geq 15

Alternative hypothesis: \mu

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

Step-by-step explanation:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis: \mu \geq 15

Alternative hypothesis: \mu

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

And the data given from the sample is:

\bar X = 13.2 represent the sample mean

\sigma represent the population deviation

n = 40 represent the sample size

And the statistic would be given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

8 0
3 years ago
The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
mr_godi [17]

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

<u><em>Formula</em></u>: ‘<u><em>area of a rectangle</em></u>’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

<u><em>Solving the quadratic equation</em></u> w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2

  or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

<u><em>Conclusion</em></u>:

Width = 2

Length = 2 + 3 = 5

6 0
1 year ago
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