Point-slope form
Complete the point-slope equation of the line through (8, —8) and (9.8).
Use exact numbers.
y-8=

Answers

Answer 1

Answer:

The equation in point-slope form is:

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

The equation of the line in slope-intercept form is:

[tex]y=16x-136[/tex]

Step-by-step explanation:

Given the points

(8, -8)

(9, 8)

Finding the slope between (8, -8) and (9, 8)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(8,\:-8\right),\:\left(x_2,\:y_2\right)=\left(9,\:8\right)[/tex]

[tex]m=\frac{8-\left(-8\right)}{9-8}[/tex]

[tex]m=16[/tex]

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

Here:

m is the slope  and (x₁, y₁) is the point

substituting the values m = 16 and the point (8, -8)  in the point-slope form

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

Thus, the equation in point-slope form is:

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

now completing the point-slope form equation of the line

[tex]y+8=16\left(x-8\right)[/tex]

subtract 8 from both sides

[tex]y+8-8=16\left(x-8\right)-8[/tex]

[tex]y=16x-136[/tex]

Thus, the equation of the line in slope-intercept form is:

[tex]y=16x-136[/tex]


Related Questions

the inequality 7-2/3 x

Answers

−  14x/ 3  i think this would be the answer

​  

 

Which expression has a value different from the others?
A. -108 + 105
B. 9.9 + (12.9)
C. -7 2/9 - ( -4 2/9)
D. 637 - 641

Answers

Answer:

I think B

Step-by-step explanation:

A. -108+105

-3

B. 9.9+(12.9)

22.8

C. -7 2/9 -(-4 2/9)

-3

D. 637 - 641

-4

Is the last one written wrong because if that one is 637-640 or 638-641 than it would equal -3. Then the answer would be B.

As the height of a dropped ball decreases, what happens to its potential energy?
a. it increases
b. it remains the same
c.it decreases
d. it runs out

Answers

Answer:

it's potential energy decreases

Each ___ in a cell has its own specific function.

Answers

Answer:

organelle

Explanation: Mitochondria and the cell wall are both examples of organelles since they have their own specific functions (Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

Each "organelle " in a cell has its own specific function.

What is organelles ?

Mitochondria and the cell wall are both examples of organelles since they have their own specific functions. Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

A Cellular respiration is a component of a metabolic process which splits the glucose sugar molecule to produce energy in the form of ATP.

Since we know that Krebs' cycle, oxidative phosphorylation, and glycolysis are all components of cellular respiration.

The cellular respiration activities take place in the mitochondria of the cell, where the oxygen-rich environment which causes the sugar-like glucose to break down into an energy molecule.

A cell organelle having a membrane is a 'mitochondria'. It is a location for cellular respiration and metabolic activities which produce energy.

Learn more about mitochondria by using this link:

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1. 1.5 ÷ 1.2

2. 3.42 ÷ 0.6

3. 11.77 ÷ 1.1

4. 18.16 ÷ 0.4

5. 140.21 ÷ 1.4

Answers

Answer:

1. 25

2. 5.7

3. 10.7

4. 204

5. 100.5

Step-by-step explanation:

calculator

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 4, negative 2, B double prime at 4, negative 1, C double prime at 1, negative 1, D double prime at 1, negative 2. Reflected over the x‒axis and reflected over the y-axis Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise

Answers

Answer:

Reflection over the y-axis and rotation of 180°

Step-by-step explanation:

We have,

Rectangle ABCD with co-ordinates A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

It is transformed to a new rectangle A'B'C'D' with co-ordinates A'(-4,-2), B'(-4,-1), C'(-1,-1) and D'(-1,-2).

The graph of both the triangles is shown below.

we see that,

The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

                     Reflected about y-axis                     Rotation of 180°

A= (-4,2)                     (4,2)                                              A'= (-4,-2)

B= (-4,1)                      (4,1)                                                B'= (-4,-1)

C= (-1,1)                       (1,1)                                                 C'= (-1,-1)

D= (-1,2)                      (1,2)                                                 D'= (-1,-2)

Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.

Answer:

b- reflect over y- axis and rotate 180 degrees

Step-by-step explanation:

Reflected about y-axis                     Rotation of 180°

A= (-4,2)                     (4,2)                                              A'= (-4,-2)

B= (-4,1)                      (4,1)                                                B'= (-4,-1)

C= (-1,1)                       (1,1)                                                 C'= (-1,-1)

D= (-1,2)                      (1,2)                                                 D'= (-1,-2)

8(7q+6p+11) please help me

Answers

Answer:

56p + 48q + 88

Step-by-step explanation:

When you see parentheses in math, it usually means that you are distributing (multiplying).

So here you would multiply everything inside the parentheses by 8.

7q x 8 = 56q

6p x 8 = 48p

8 x 11 = 88

56q + 48p + 88

There are no like terms here so the answer cannot be simplified any further.

What is the value of the expression 8³?
A. 24
B. 83
C. 512
D. 6,561 ​

Answers

The answer is c. 512

Answer:

its c and thats on purrrr

Step-by-step explanation:

If 7x-3x+17-x+1=108, what is the value of 4x+x?

Answers

Answer:

150

Step-by-step explanation:

1. combine like terms

7x-3x-1x=3x

17+1=18

2. subtract

108-18=90

3. divide

90/3=30

which means x=30

4. plug it in

4X30+30=150

Find the value of x.
6x+6
9x-9
32
24
x = [?]

Answers

Answer:

x=3

Step-by-step explanation:

[tex]\frac{6x+6}{32} =\frac{9x-9}{24}[/tex]

Cross mutiply and x is equal to 3

choose all the polygons

Answers

Answer:

A, B, E, F

Step-by-step explanation:

A polygon is ANY shape formed with only straight lines.

What is 10/8 written as a decimal?

Answers

Answer:

10/8= 1.25

Step-by-step explanation:

10 divided by 2=5 8 divided by 2= 4=5/4

5÷4=1.25

The fraction 10/8 as the decimal equivalent is A = 1.25

What are decimal numbers?

The decimal numbers can only be expressed as fractions since they contain a fractional component. The accepted method for representing both integer and non-integer numbers is the decimal numeral system. There are 10 single-digit numbers in the decimal system:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. After the number 9, comes 10, then comes 11, then 12, and so on. Each time the digit to the right exceeds 9, the number on the left is increased by 1.

Given data ,

Let the decimal number be represented as A

Now , the value of A is

Let the fraction be represented as n

The value of n = 10 / 8

On simplifying , we get

The value of n in the decimal equivalence is given by dividing the number 10 by 8

So , A = 10 ÷ 8

A = 1.25

Therefore , the value of A is 1.25

Hence , the decimal number is 1.25

To learn more about decimal numbers click :

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Student #1:

6(x - 0.5) > 3
6x - 3 > 3
6x > 0
x > 0


Solved the inequality incorrectly but graphed their solution correctly.
Solved the inequality correctly and graphed their solution correctly.
Solved the inequality correctly but graphed their solution incorrectly.
Solved the inequality incorrectly and graphed their solution incorrectly.

Answers

Answer:

D, both incorrect

Step-by-step explanation:

Answer:

Student #1:

6(x - 0.5) > 3

6x - 3 > 3

6x > 0

x > 0

2) Solved the inequality correctly and graphed their solution correctly.

What is the value of x in the equation 4 and StartFraction 3 Over 10 EndFraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)?

Answers

Answer:

5

Step-by-step explanation:

Edge i think dont quote me on this plz

According to the 2014 national population projections published by the U.S. Census Bureau, the U.S. population is projected to be 334.4 million in 2020 with an estimated growth rate of 0.79% per year. Assuming the growth rate remains constant, find the projected population in 2050.

Answers

Answer:

423,437,744

Step-by-step explanation:

Given that :

Projected population in 2020 = 334.4 million

Estimated growth rate (r) = 0.79%

Projected population in 2050 ;

Using the exponential growth function :

Estimated value = initial value(1 + growth rate)^time

Initial value = i

Time = 2020 - 2014 = 6 years

334.4 = i(1 + 0.0079)^6

334.4 = i(1.0079)^6

334.4 = i2.43087455521E−13

i = 3.189786E8

Initial population = 318. 978 million

Estimated Population in 2050:

2050 - 2014 = 36

Projected population = 3.189786E8(1.0079)^36

Projected population = 3.189786E8*1.3274801

= 423437743.82586

= 423437744 million

Write a cubic function whose graph is shown

Answers

Answer:

what grade

Step-by-step explanation:

Help please!! There are two pictures. This is timed. I’ll give brainliest also!

Answers

Answer:

X=-5 y=31

X=-1 , y=7

X=0 , y=1

X=1 y=-5

Step-by-step explanation:

Answer:

x = -5, y = 31

x = -1 , y = 7

x = 0, y = 1

x = 1, y = -5

Step-by-step explanation:

y = -6x + 1

1. y = -6 ( -5 ) + 1

y = 31

2. y = -6 ( -1 ) + 1

y = 7

3. y = -6 ( 0 ) + 1

y = 1

4. y = -6 ( 1 ) + 1

y = -5

Please help..

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11ft^3

Which equation gives the volume of the sphere?

^(Answers above on picture)^

Answers

9514 1404 393

Answer:

  (d)  2/3(11)

Step-by-step explanation:

The height of the cylinder is h=2r, so the volume of the cylinder in terms of radius is ...

  V = πr^2·h = πr^2·(2r) = 2πr^3

The volume of the sphere is given by the formula ...

  V = (4/3)πr^3

So, the ratio of the sphere volume to the cylinder volume is ...

  sphere volume / cylinder volume = ((4/3)πr^3)/(2πr^3) = (4/3)/2 = 2/3

That is, the sphere volume is ...

  sphere volume = (2/3) × (cylinder volume)

  V = (2/3)(11)

Find the distance between each pair of points. Round your answer to the nearest tenth, if
necessary.
5) (1, 2), (-5,4)

Answers

Answer:

2(10^.5)

Step-by-step explanation:

d = ((x2 - x1)^2 + (y2 - y1)^2)^0.5

A watermelon seed is 0.4cm long. How far would a line of 126 stretch?

Answers

Answer:

0.504m

Step-by-step explanation:

First, we would multiply 0.4cm by 126 watermelon seeds to find the length of the line in cm.

0.4*126

= 50.4cm

Therefore, the line of watermelon seeds stretches 50.4cm.

Now, because the question wants us to type the answer in meters, we must convert 50.4cm into meters. We do this by dividing 50.4 by 100 since 100cm makes up 1 meter.

50.4/100

= 0.504m

Therefore, the line of watermelon seeds stretches 0.504m.

I hope this helps!

What are 5 fractions equivalent to 7/8?

Answers

Answer:

14/16

24/32

48/64

96/128

192/256

Step-by-step explanation:

Take 7 multiply it by 2, then take 8 and multiply it by 2

When you get your answer (14/16) multiply that by two

Keep going until you have 5 numbers

Answer:

14/16

21/24

28/32

35/40

42/48

Step-by-step explanation:

1. 7/8

7x2=14

8x2=16

14/16

2. 7/8

7x3=21

8x3=24

21/24

3. 7/8

7x4=28

8x4=32

28/32

4. 7/8

7x5=35

8x5=40

35/40

5. 7/8

7x6=42

8x6=48

42/48

What is the value of A in the equation shown?​

Answers

Answer:

is this algebra 1

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

you isolate the variable by dividing each side

What is the value of 9x - 4y if x = 3 and y = 2?

Answers

Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

27-8

I need answer as quick

Answers

Answer:

C

Step-by-step explanation:

(x+7)(x+1)(x+4)=

x^3+12x^2+39x+28 or C

Answer:

C

Step-by-step explanation:

Given

(x + 7)(x + 1)(x + 4) ← expand the second/ third factors using FOIL

= (x + 7)(x² + 5x + 4)

= x(x² + 5x + 4) + 7(x² + 5x + 4) ← distribute both parenthesis

= x³ + 5x² + 4x + 7x² + 35x + 28 ← collect like terms

= x³ + 12x² + 39x + 28 → C

Find the distance from San Antonio to El Paso.


633 mi


344 mi


558 mi


261 mi

Answers

Answer:

558

Step-by-step explanation: I just took the quiz!

Distance from San Antonio to El Paso in Miles is 558 miles

Find:

Distance from San Antonio to El Paso in Miles

Computation:

We know that

Distance from San Antonio to El Paso is 888 km

So,

1 km = 0.621371 miles

Distance from San Antonio to El Paso = 888 × 0.621371

Distance from San Antonio to El Paso in Miles = 558 miles

Learn more:

https://brainly.com/question/19679508?referrer=searchResults

Evaluate the
determinant.

Answers

Answer:

I think it's 21

Step-by-step explanation:

(2x−6)+4(x−3)
Find the sum.

Answers

Answer:

6x - 18 or 6*(x - 3)

Step-by-step explanation:

Pull out like factors: 6x - 18  =   6 • (x - 3)

Hope this helps! Please mark as brainlest.

Thanks!

What are the domain and range of the function x^2-2x^2-4?

Answers

[tex] {x}^{2} - 2 {x}^{2} - 4 \\ - {x}^{2} - 4[/tex]

The Quadratic Function has the domain as the set of all real numbers.

For the range, start from minimum value to maximum value.

But because the parabola is downward as a < 0. Thus, there are no minimum value but the maximum value instead.

Therefore the range is y <= -4

What is the common ratio between successive terms in the sequence?
2.-4.8.-16, 32, -64,...
0-2
-6
6
2

Answers

Answer: -2

Step-by-step explanation:

You multiply the number before in the sequence by -2 to get the number that follows.

2*-2 = -4

-4*-2 = 8

And so on...

Which is true about the product of 3/8 and 7/2?

Answers

Answer:

Nothing ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎

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