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uranmaximum [27]
3 years ago
12

A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the giv

en line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Mathematics
2 answers:
Zigmanuir [339]3 years ago
7 0
1) slope = (y₂-y₁)/(x₂-x₁)

Let A and B be A(4,-6) and B(0,2) ; 

m = [2-(-6)]/[0-4) = (2+6)/(-4) → m = -2 

2) Midpoint = value of x of the midpoint = (x₁+x₂)/2
value of y of the midpoint = (y₁+y₂)/2

x(midpoint) =  (4+0)/2  → x= 2
y(midpoint) =  (-6+2)/2 → y= - 2, so Midpoint M(2,-2)

3) Slope of the perpendicular bisector  to AB:
The slope of AB = m = -2
Any perpendicular to AB will have a slope m' so that m*m' = -1 (or in other term, the slope of one is inverse reciprocal of the second, then if m =-2, then m' = +1/2 ; Proof [ (-2)(1/2) = -1]

4) Note that the perpendicular bisector of AB passes through the midpoint of AB or M(2,-2). Moreover we know that the slope of the bisector is m'= 1/2
The equation of the linear function is :

y = m'x + b or y = (1/2)x + b. To calculate b, replace x and y by their respective values [in M(-2,2)]

2= (1/2).(-2) + b → 2 = -1 + b → and b= 3, hence the equation is:

y = (1/2)x + 3

QveST [7]3 years ago
5 0

Answer:

-2

(2,-2)

1/2

y=(1/2)x-3

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Which expression has the same value as 4÷25 in fraction form
otez555 [7]

Answer:

4/25

Step-by-step explanation:

It is a fraction with 4 in the numerator and 25 in the denominator.

4

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25

6 0
2 years ago
A bag contains 20 marbles: 12 red, 4 blue, 3 yellow, and 1 green. Arielle takes out 2 marbles. What is the probability that they
Marysya12 [62]

Total number of marbles in the bag =20

Number of blue marbles =4

Now we just want two blue marbles out of four.

Probability of taking out first marble which is blue =4/20

Now after we took out one blue marble , number of blue marbles left are 3.

Probability of taking out second marble which is blue =3/20

Total probability = 4/20 *3/20 = 12/400

So probability of taking out two blue marbles is 0.03 or 12/400.


3 0
2 years ago
Write an equation in slope-intercept
Sliva [168]
Y= 1x + 2

Use the formula y=mx+b when trying to do things like this.
Y intercept form is when your line intersects through the y axis, and this is also your b. M is your slope.
7 0
3 years ago
A cheetah ran 230 feet in 1.932 seconds. What is the cheetah's speed in miles per hour?
Bumek [7]

Answer:

The answer to your question is speed = 81.5 mi/h

Step-by-step explanation:

Data

distance = 230 ft

time = 1.932 s

speed = ? mi/h

Process

1.- Convert the distance to mi

                1 mile ----------------- 5280 ft

                 x        ----------------- 230 ft

                 x = (230 x 1) / 5280

                 x = 0.044 mi

2.- Convert time to hours

                 1 h    ------------------ 3600 s

                  x      ------------------ 1.932 s

                        x = (1.932 x 1) / 3600

                        x = 0.00054 h

3.- Calculate the speed

speed = distance / time

-Substitution

speed = 0.044/ 0.00054

-Result

speed = 81.5 mi/h

         

4 0
3 years ago
Solve the equation 3(x +4.5) = 36
vovangra [49]

Answer:

x=7.5

Step-by-step explanation:

8 0
3 years ago
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