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yan [13]
3 years ago
7

Write an equation of the perpendicular bisector of the segment with endpoints G 9,8       and H 3,2      .

Mathematics
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer:

y = -x + 11

Step-by-step explanation:

The equation of a straight line is is given by:

y = mx + b; where m is the slope and b is the y intercept

The equation of the line joining G(9, 8) and H(3, 2) is given as:

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-8=\frac{2-8}{3-9}(x-9)\\\\y-8=x-9\\\\y=x-1

The perpendicular bisector of the line joining G(9, 8) and H(3, 2) is perpendicular to the line joining G(9, 8) and H(3, 2) and passes through the midpoint of line joining G(9, 8) and H(3, 2).

Let (x, y) be the midpoint of the line joining G(9, 8) and H(3, 2). Hence:

x = (9 + 3)/2 = 6

y = (8 + 2)/2 = 5

The midpoint = (6, 5)

Two lines are perpendicular if the product of their slopes is -1.

The line joining G(9, 8) and H(3, 2) has a slope of 1, hence, the slope of the perpendicular bisector would be -1.

This means that the perpendicular bisector has a slope of -1 and passes through (6, 5). Using:

y-y_1=m(x-x_1)\\\\y-5=-1(x-6)\\\\y-5=-x+6\\\\y=-x+11

The equation of the perpendicular bisector is y = -x + 11

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The length of the sides of a square measure 2x-5. The length of a rectangle measures 2x, and the width measures x + 2. For what
vladimir1956 [14]

Answer:

x = 12

Step-by-step explanation:

Perimeter of a square:

The perimeter of a square of side x is given by:

P_s = 4x

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

P_r = 2(l + w)

The length of the sides of a square measure 2x-5.

This means that the perimeter of the square is:

P_s = 4(2x - 5) = 8x - 20

The length of a rectangle measures 2x, and the width measures x + 2.

This means that the perimeter of the rectangle is:

P_r = 2(2x + x + 2) = 2(3x + 2) = 6x + 4

For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

This is x for which:

P_s = P_r

So

8x - 20 = 6x + 4

8x - 6x = 20 + 4

2x = 24

x = \frac{24}{2}

x = 12

3 0
2 years ago
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
Varvara68 [4.7K]
Given that volume is:
V=s³
where:
s=side length
The volume of a cube whose side length, s=3/4 yards will be given by:
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8 0
3 years ago
Read 2 more answers
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviat
Harlamova29_29 [7]

Answer:

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Step-by-step explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.    

Let us find the sample score that corresponds to z-score of bottom 4%.  

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

z=\frac{x-\mu}{\sigma}

-1.75=\frac{x-5.71}{0.08}

-1.75*0.08=x-5.71

-0.14=x-5.71

-0.14+5.71=x-5.71+5.71

5.57=x

Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.

Now let us find sample score corresponding to z-score of 1.75 as upper limit.

1.75=\frac{x-5.71}{0.08}

1.75*0.08=x-5.71

0.14=x-5.71

0.14+5.71=x-5.71+5.71

5.85=x  

Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.

7 0
3 years ago
A carousel has 56 horses 3/8 of them are white how many horses are not white
olga_2 [115]

5/8 of them are not white, so 5/8 times 56, you get 35.


4 0
3 years ago
To the person who makes a graph and doesn't copy from another question
allochka39001 [22]

Answer:

H=9;8)

B=(5;4) (ball)

R=(7;0) (hit point)

B'=symetric of B axis perpendicular of x in R

B'=(7+(7-5);4)=(9;4)

Equation BR: y-4=(0-4)/(7-5)(x-5)==>y=-2x+14

Equation RB': y-4=(4-0)/(9-7)(x-9)==>y=2x-14

Is H a point of RB'? y=2x-14 : 8=? 2*9-14==>8=?4 No!

 

you will not make your putt

Step-by-step explanation:

7 0
3 years ago
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