A town's population is 43,650. About 125 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 45,675. It has no one moving in and an average of 150 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question. Which equation mode +​

                                               Question 1)

Given the points

Finding the slope between (3, 5) and (3, -6)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [-6 - 5] / [3 - 3]

               = -11 / 0

               = undefined or ∞

Thus, the slope of the line = m = undefined.

Note: The undefined slope means the line is vertical.

                                            Question 2)

Given the points

Finding the slope between (-6, 2) and (8, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 2] / [8 - (-6)]

               = 0 / 14

               = 0

Thus, the slope of the line = m = 0.

Note: The zero slope means the line is horizontal.

Answer:

You can't find the area or perimeter with the information given. If this is a calculus level problem then it is possible.

Answer:

12 : 58.8   which simplies to 1 : 4.9

Step-by-step explanation:

Answer:

5/64 of a cup.

Step-by-step explanation:

Is there two columns of data and two data points? Like this:

Strawberries          Water

384                         30

320                         25

If so, then there are two ways to do it.

1) You can set up a ratio like this

384/30 = 1/x

Where x is the number of cups of water for 1 strawberry.

So,

x = 30/384 of a cup

x = 5/64 of a cup.

2) Look at the increase from one to the other.

64 strawberries requires 5 cups of water

Divide by 5 by 64 to get the water for one strawberry

5/64 of a cup.

Answer:

x = 6.22 cm

Step-by-step explanation:

The lines on the sides of the triangle means they are the same length

Since it is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

Substituting what we know

a^2 + a^2 = x^2

a=4.4

(4.4)^2 + (4.4) ^2= x^2

19.36 + 19.36 = x^2

38.72 = x^2

Taking the square root of each side

6.222539674 = x

Rounding to 3 significant figures

x = 6.22 cm

Answer:

Please check the explanation.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

k = y/x

here k is the constant of variation.

From the table,

substitute x = -3, y = -4 in the equation

k = y/x

k = -4/-3

k = 4/3

substituting x = -2, y = -1

k = y/x

k = -1/-2 = 1/2

substituting x = -1, y = 2

k = y/x

k = 2/-1 = -2

substituting x = 0, y = 5

k = y/x

k = 5/0 = ∞

substituting x = 1, y = 8

k = y/x

k = 8/1

k = 8

substituting x = 2, y = 11

k = y/x

k = 11/2

substituting x = 3, y = 14

k = y/x

k = 14/3

It is clearly visible that there is no constant of variation because the ratio y = k/x is variating for different ordered pairs.

Thus, It is clear that none of the answers in the answer choices represent the constant of variation in this relation.

Answer:

A

Step-by-step explanation:

180⁰= a+b+81⁰

a=180⁰-117⁰=63⁰

b=180⁰-63⁰-81⁰=36⁰

Answer:

I think

y=1/3x-10/3

Step-by-step explanation:

Perpendicular Lines mean they have the negative reciprocal slope. This line has slope m = -1/3 so the perpendicular line has slope m = + 1/3

Our point is (3, 5)

Now use point slope form to find the equation: (y - y1) = m(x - x1)

(y - 5) = m(x - 3)

(y - 5) = 1/3(x - 3)

y -5=1/3x-10/3

Answer:

it's 7

Step-by-step explanation:

this needs to be 20 characters long

Answer:

switch the -14 to positive and the add 35+14 and then divide the number you get by 7

Step-by-step explanation:

y=7

Answer:

I believe it is BCG

Step-by-step explanation:

Answer:

12 for 6.97 is better

Step-by-step explanation:

for 12 pack

$6.97/12 markers = .58 per marker

for 4 pack

$2.77/4 markers = .69 per marker

thus 12 pack is better, a lower cost per marker

Answer:

12 for $6.97

Step-by-step explanation:

If u get 12 pack for $6.97 its .58 for each marker

If u get 4 pack for $2.77 its .69

And I would prefer to get a 12 pack cuz its cheaper and more markers.

I hope this helped:)

Answer:

m = -3

b = 9

y = -3x + 9

Step-by-step explanation:

Let us solve the question

∵ The line passes through points (4, -3) and (3, 0)

∵ The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex]

∵ (x1, y1) and (x2, y2) are 2 points on the line

∴ x1 = 4 and y1 = -3

∴ x2 = 3 and y2 = 0

→ Substitute them in the rule of the slope to find it

∵ m = [tex]\frac{0--3}{3-4}[/tex] = [tex]\frac{0+3}{-1}[/tex] = -3

∴ m = -3

∵ The form of the equation of the line is y = m x + b

→ Substitute the value of m in the form of the equation.

∴ y = -3x + b

→ To find b substitute x and y by the coordinates of the point (3, 0) or (4, -3)

∵ x = 3 and y = 0

∴ 0 = -3(3) + b

∴ 0 = -9 + b

→ Add 9 to both sides

∴ 9 = b

∴ b = 9

→ Substitute the value of b in the equation

∵ y = -3x + 9

∴ The equation of the line is y = 3x + 9

Answer:

12,000

Step-by-step explanation:

There are 1,000 meters in a kilometer. So, if you have 12 kilometers, that's 12,000 meters.

Answer:

12000

Step-by-step explanation:

One kilometer = 100 meters 12 times 1000 = 1200

Answer:

A or B

Step-by-step explanation:

[tex]3.5+m<4.6[/tex]

that's what it means

so if we solve it

[tex]3.5+m-3.5<4.6-3.5\\\\m+0<1.1\\\\m<1.1[/tex]

and now we check

[tex]3.5+(1)<4.6(\:something\:less\:than\:1.1)\\\\4.5<4.6[/tex]

which satisfy

now choose an option

it's either A or B

m<1.1 is the answer if you have to highlight the thing that m is less than then B is your answer

if you have to highlight an option that works then it's A

Answer:

32 cubes

Step-by-step explanation:

I would first determine the volume in inches of the rectangular prism.

V = 1/3 x 2/3 x 2/3 = 4/27 cubic inches.

Then I would calculate the volume of the cube with 1/6 inch sides

V = 1/6 x 1/6 x 1/6 = 1/216 cubic inches.

Then I would divide the V of the large prism by the V of the small cube

(4/27) / (1/216) = (4/27) * (216/1) = 32 cubes

Answer:

She draw 40 flowers

Step-by-step explanation:

Given

[tex]Length = \frac{1}{5}m[/tex]

[tex]Flower = \frac{1}{200}m[/tex]

Required

Determine the number of flowers

To do this, we simply divide the length of the border by the length of the flower.

[tex]Number = \frac{1}{5}/ \frac{1}{200}[/tex]

Convert to multiplication

[tex]Number = \frac{1}{5}* \frac{200}{1}[/tex]

[tex]Number = \frac{200}{5}[/tex]

[tex]Number = 40[/tex]

Hence, she draw 40 flowers

Answer: 12x+8y=80

8x-2y=60

Step-by-step explanation:

The equations that could be part of the process of solving this system are 12x+8y=80 and 8x-2y=60.

The original equation was 3x+2y= 20 and 4x-y=30. Multiplying all through by 4 gives 12x+8y=80 and 8x-2y=60.

Answer:

( - ∞, ∞)

Step-by-step explanation:

Any value of t makes the interval notation ^^^

I think it's

1.61x

plsbrainliest if it helped!

Answer:

[tex]x = -1[/tex]

[tex]y = 3[/tex]

Step-by-step explanation:

Given

The attached table

Required

Fill in the blanks

First, we need to calculate the slope

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

Where:

[tex](x_1,y_1) = (1/2,1)[/tex]

[tex](x_2,y_2) = (3,-9)[/tex]

So, we have:

[tex]m = \frac{-9-1}{3-1/2}[/tex]

[tex]m = \frac{-10}{3-0.5}[/tex]

[tex]m = \frac{-10}{2.5}[/tex]

[tex]m = -4[/tex]

Next, we calculate the equation:

[tex]y - y_2 = m(x - x_2)[/tex]

This gives:

[tex]y - (-9) = -4(x - 3)[/tex]

[tex]y +9 = -4(x - 3)[/tex]

[tex]y +9 = -4x +12[/tex]

Make y the subject:

[tex]y = -4x +12-9[/tex]

[tex]y = -4x +3[/tex]

So,

When y = 7:

We have:

[tex]y = -4x +3[/tex]

[tex]7 = -4x +3[/tex]

Collect Like Terms

[tex]4x = 3 - 7[/tex]

[tex]4x = -4[/tex]

Divide through by 4

[tex]x = -1[/tex]

When x = 0, we have:

[tex]y = -4x +3[/tex]

[tex]y = -4 * 0 + 3[/tex]

[tex]y = 0 + 3[/tex]

[tex]y = 3[/tex]

Answer:

it increases

Step-by-step explanation:

hope this helps <3

Answer:

The answer is it increases

Step-by-step explanation:

Answer:

6 1/2

Step-by-step explanation:

Answer:

6.5 quarts.

Step-by-step explanation:

This is rather simple math because 2 pints equal 1 quart. You divide 13 by 2, which is an uneven number so you are guaranteed a half, and you get 6.5

Answer:

x = 66.5

x + 1 = 67.5

x + 2 = 68.5

x + 3 = 69.5

x + 4 = 70.5

x + 5 = 71.5

x + 6 = 72. 5

x + 7 = 73.5

x + 8 = 74.5

x + 9 = 84.5

Step-by-step explanation:

Given that :

Age of 10 friends are consecutive integers :

Let the ages be :

x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9

The sum of their ages = 710

Hence,

x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7 + x+8 + x+9 = 710

10x + 45 = 710

10x = 710 - 45

10x = 665

x = 665 / 10

x = 66.5

x + 1 = 67.5

x + 2 = 68.5

x + 3 = 69.5

x + 4 = 70.5

x + 5 = 71.5

x + 6 = 72. 5

x + 7 = 73.5

x + 8 = 74.5

x + 9 = 84.5

Answer:

a+b = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

3(a + b)^2 = 81

(a + b)^2 = 27

a + b = sq rt 27

a + b = [tex]\sqrt{9}[/tex]· [tex]\sqrt{3}[/tex]

a + b = 3[tex]\sqrt{3}[/tex]

Answer:

answer is also 60.

Step-by-step explanation:

Since angle 2 is also 60 degrees, angle 6 will also be 60 degrees.

Answer:

angle 5 =60° (corresponding angles)

angle 5 = angle 6 =60° (vertically opposite angles)