Please fill in the blank

Answer:

(1) The slope of the line segment AB is 1.[tex]\bar 3[/tex]

(2) The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is (5, 7)

(4) The slope of a line perpendicular to the line AB is-0.75

Step-by-step explanation:

The coordinates of the line segment AB are;

A(2, 3) and B(8, 11)

(1) The slope of a line segment is given by the following equation;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where;

(x₁, y₁) and (x₂, y₂) are two points on the line segment

Therefore;

The slope, m, of the line segment AB is given as follows;

A(2, 3) = (x₁, y₁) and B(8, 11) = (x₂, y₂)

[tex]Slope, \, m_{AB} =\dfrac{11-3}{8-2} = \dfrac{8}{6} = 1 \frac{1}{3} = 1.\bar3[/tex]

The slope of the line segment AB = 1.[tex]\bar 3[/tex]

(2) The length, l, of the line segment AB is given by the following equation;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Therefore, we have;

[tex]l_{AB} = \sqrt{\left (11-3 \right )^{2}+\left (8-2 \right )^{2}} = \sqrt{64 +36} = 10[/tex]

The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is given as follows;

[tex]Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )[/tex]

Therefore;

[tex]Midpoint, M_{AB} = \left (\dfrac{2 + 8}{2} , \ \dfrac{3 + 11}{2} \right ) = (5, \ 7)[/tex]

The coordinates of the midpoint of AB is (5, 7)

(4) The relationship between the slope, m₁, of a line AB perpendicular to another line DE with slope m₂, is given as follows;

[tex]m_1 = -\dfrac{1}{m_2}[/tex]

Therefore, the slope, m₁, of the line perpendicular to the line AB, that has a slope m₂ = 4/3 = 1.[tex]\bar 3[/tex] is given as follows;

[tex]m_1 = -\left (\dfrac{1}{\frac{4}{3} } \right ) = -\dfrac{3}{4} = -0.75[/tex]

The slope, m₁, of the line perpendicular to the line AB is m₁ = -0.75.

Answer:

The answer to da question is 3

9514 1404 393

Answer:

Step-by-step explanation:

Let b represent the speed of runner B. then the ratio of speeds is ...

  b/(b+5) = 8/18

  18b = 8(b +5) . . . . cross multiply

  10b = 40 . . . . . . . . subtract 8b

  b = 4 . . . . . . . . . . . divide by 10

Runner B's speed is 4 mph; runner A's speed is 5 mph more.

Runner A is running at 9 mph; Runner B is running at 4 mph.

Answer:

56 music files

Step-by-step explanation:

From the above question:

Let the number of music files

Arely has = x

Valerie has = y

Arely has 4 fewer than twice as many music files as Valerie.

x = 2y - 4

They have a combined number of 86 music files.

x + y = 86

We substitute 2y - 4 for x in the above equation

2y - 4 + y = 86

3y - 4 = 86

3y = 86 + 4

3y = 90

Divide both sides by 3

3y/3 = 90/3

y = 30

Hence, Valerie has 30 music files.

The number of music files that Arely has is calculated as:

x = 2y - 4

x = 2(30) - 4

x = 60 - 4

x = 56

Arely has 56 music files

Answer:

X=135

Step-by-step explanation:

180-69-66=45

And the angle of a line is also 180 and 180-45=135

Me too, your not alone

Answer:

i feel that lol

Step-by-step explanation:

Answer:

slope = -720

y-intercept: 8,000

Step-by-step explanation:

The slope in this case is a negative slope, since the word "decreased" is being used. The rate of 720 gallons per hour can be seen as -720 / 1, which gives you the -720 slope.

The y-intercept in an equation represents the initial value. Since 2,000 gallons has already been pumped out, the initial value is 8,000.

The constant rate at which the water decreases results in a straight line

function between the volume of water in the tank and time of pumping.

The slope is -720 (gal/hour)

The y-intercept is 8,000 (gallons)

Reasons:

The volume of the swimming pool = 10000 gallon

Volume of water already pumped out = 2,000 gallons

Rate at which the water is being pumped out = 720 gallons per hour

Required:

The slope and y-intercept of the function

Solution:

Volume of water in the tank = (10,000 - 20,000) gallons = 8,000 gallons

Volume of water decreasing from the tank after t hours = 720·t

Therefore;

Volume of water in the tank after t hours, is V(t) = 8000 - 720·t

Comparing the above function with the equation of a straight line, in slope

and intercept form, y = m·x + c, we have;

V(t) = -720·t + 8000

Learn more here:

https://brainly.com/question/13881458

Answer:

5^3 - 8/n

Step-by-step explanation:

It helps to think backwards on these sometimes; try starting with the last value and going from there.

HTH :)

The answer is 6.6 feet above the ground

Step-by-step explanation: :)

Answer:

make me the branliest  the answer is C

Step-by-step explanation:

Pool X has 1200 gallons of water in it. It is being drained at a rate of 15 gallons per minute. If lowercase x is the number of minutes, then it has 1200-15x gallons left in the pool.

Consider after 1 minute we have x = 1, so,

1200-15x = 1200-15*1 = 1200-15 = 11185

Then after 2 minutes we have x = 2, which means,

1200-15x = 1200-15*2 = 1200-30 = 11170

is the amount left over in gallons.

----------------

In contrast, Pool Y is empty and we add 25 gallons per minute. So we start with 0 and add on 25x getting 0+25x = 25x as the expression representing the amount of gallons of water in Pool Y

-----------------

So we found these two expressions

1200-15x

25x

to represent the amount of water (in gallons) for Pool X and Pool Y respectively.

We want to know when Pool Y will have more water. So we get to this final answer

1200 - 15x < 25x

It is in the form A < B, where A  is the amount of water in Pool X and B is the amount of water in Pool Y.

Answer:

the answer is (5,-1)

Step-by-step explanation:

if you click on the image it will show you the image full screen

Answer:

It’s c

Step-by-step explanation:

Answer:

$19

Step-by-step explanation:

First you need to make a equation out of given information and this will be easiest to solve as an equation.

3.5      $66.50

1               x

-----------------------

3.5:1=66.50:x

3.5x=66.50/:3.5

x=19

On the right side you put one information(in this case number of yards) and on the left other information(cost) and you make proportion from up to down and solve for x.

Answer:

The last one I did the math

Answer:

D

Step-by-step explanation:

bc it is just put it

Answer:

The total number of votes was 7968.

Step-by-step explanation:

From the information given, you know that the ratio of yes votes to no votes was 7 to 5 and you can use a rule of three to find the number of no votes if there were 4648 yes votes:

    7 yes    →   5 no

4648 yes  →      x

x=(4648*5)/7=3320

Now, you have to add up the amount of yes votes and no votes:

4648+3320=7968

According to this, the answer is that the total number of votes was 7968.

Answer:

It is 4x + 4y.

Step-by-step explanation:

All you have to do is add all of the y's toghther and then add all of the x's toghther.

Answer:

4x+4y

Step-by-step explanation:

Combine the four "x" so x+x+x+x likewise the four "y" y+y+y+y.

Step-by-step explanation:

the answer is 10x +100 = 250

Answer:

isosceles

Step-by-step explanation:

Answer:

Everything except second and third one

Answer:

v equals 3

Step-by-step explanation:

2 times 3 is 6 and 6 plus 3 is 9 I hope this helps

Answer:

v = 3

Step-by-step explanation:

Given

2v + 3 = 9 ( subtract 3 from both sides )

2v = 6 ( divide both sides by 2 )

v = 3

Answer:

Not all labels will be used. ... They charge a certain rate for the rental of a sailboat and an additional ... according to the length of time for which the tourists rent the boat.

Answer:

126 feets

Step-by-step explanation:

Given that :

Equation of line repressing nature trail :

y = 13x - 4

Distance of gazebo from nature trail :

Each unit in coordinate plane = 10 feets

Hence,

y = 13(10) - 4

y = 130 - 4

y = 126 feets

Answer:-3 and -7 equals 10

Step-by-step explanation: two negatives equal a positive and vice versa. Combining those 2 gives you the highest answer

Answer:

c = 4

Step-by-step explanation:

p(x) is divisible by (x - 3).

So, p(3) = 0

-(3)³ + c(3)² - 4 *3 + 3 = 0

-27 + 9c - 12 + 3 = 0

         9c - 36     = 0

                9c     = 36

                     c = 36/9

c = 4

Answer:

7/8 miles

Step-by-step explanation:

1/4 can be rewritten as 2/8 to have the same denominator between the two numbers. 2 2/8 - 1 3/8. 2 2/8 - 3/8 = 1 7/8. 1 7/8 - 1 = 7/8

Answer:

4

Step-by-step explanation:

Answer:45 ?

Step-by-step explanation:

Answer:

3m/s

Step-by-step explanation: