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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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4 drivers/ 30 square miles is they want to offer service to country of 75 square miles, how many must they have
dmitriy555 [2]
By proportion:-

4 / 30 = x / 75  where x is number needed for  the '75' country

30x = 300

x = 10


They need 10 drivers.
3 0
3 years ago
One of Shakespeare's sonnets has a verb in 11 of its 18 lines, an adjective in 13 lines, and both in 8 lines. How many lines hav
horrorfan [7]

Answer:

Step-by-step explanation:

The total number of lines, n(U) = 18

Let the number of lins with verb be n(V) = 11

Let the number of lines with adjectives be n(A) = 13

n(V n A) = 8

Find the number of lines that have a verb but no adjective, that is, n(V n A')

Mathematically, according to sets theory,

n(V) = n(V n A) + n(V n A')

So,

n(V n A') = n(V) - n(V n A) = 11 - 8 = 3.

Hence, only 3 lines have a verb but no adjectives.

4 0
3 years ago
Multi-step)<br> -3(y + 7) + 8 = -28<br> Unit<br> Mrs.<br> Each<br> How<br> Answer
SSSSS [86.1K]
-3y -21 +8 = -28
-3y -13 = -28
-3y = -15
y= 5
4 0
3 years ago
In a class there are two girls for every three boys. The ratio 2 : 3 compares the
alekssr [168]

Answer:

a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class

B. 12 boys

4 0
2 years ago
What is the set fee, or initial value, of this function
Ber [7]
Answer:
The set fee would be $15

Explanation:
The set fee is the starting value. This means that it is the value of the y at x = 0 (y-intercept).

To get the set fee, we would first need to get the equation of the line.

Equation of the linear line has the following general formula:
y = mx + c
where m is the slope and c is the y-intercept

1- getting the slope:
we are given two points which are:
(20,25) and (50,40)
the slope = \frac{y2-y1}{x2-x1}=  \frac{40-25}{50-20} = 0.5

The equation now is:
y = 0.5x + c

2- getting the value of the y-intercept:
To get the value of the c, we will use any of the given points, substitute in the equation and solve for c.
I will choose the point (20,25)
y = 0.5x + c
25 = 0.5(20) + c
25 = 10 + c
c = 15

The equation of the line representing the scenario is:
y = 0.5x + 15

Now, we know that the value of the c is the y-intercept which is the initial value of the function at x=0.
In our situation, this represents the set fee.

Hope this helps :)
6 0
3 years ago
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