What is the midpoint of the line segment With end points 0,4 and -4,-6?

Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.

We will find that working together, they need to work for 8 hours.

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Let's start by defining the variables that we will use:

Now let's see the given information:

"Aran and Beatrice can build an ant hill in 10 hours"

This can be written as:

(A + B)*10 h = 1 ant hill

"Aran and Charlie can build the ant hill in 12 hours"

This can be written as:

(A + C)*12 h = 1 ant hill

"Beatrice and Charlie can build the ant hill in 15 hours"

This can be written as:

(B + C)*15 h = 1 ant hill.

Then we have 3 equations:

[tex](A + B)*10 h = 1[/tex]

[tex](A + C)*12 h = 1[/tex]

[tex](B + C)*15 h = 1[/tex]

Where for commodity, I removed the "ant hill" unit.

Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.

I will isolate A in the first equation:

[tex]A = \frac{1}{10h} - B[/tex]

Now we can replace it in the second equation to get:

[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]

Now we can isolate C in the last equation to get:

[tex]C = \frac{1}{15h} - B[/tex]

Replacing that in the above equation we get:

[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]

This means that Beatrice alone would construct the hill in 24 hours.

Now that we know the value of B, we can use:

[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]

This means that Charlie needs 40 hours to finish the hill alone.

Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:

[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]

Now if the 3 ants work together, the total rate at which they work is:

[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]

This means that they need to work for the inverse of that rate

[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]

Working together, they need to work for 8 hours to complete an ant hill

If you want to learn more, you can read:

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Answer:

The answer is C, 40.32

Step-by-step explanation:

If you put 6.25 in your calculator times 40.32% you get 2.52. Then you add the 2.52 to 6.25 to get 8.77.

Answer:

50 deciliters

Step-by-step explanation:

Given that,

Jennifer buys a 2-liter bottle of apple juice and a 3-liter bottle of orange juice at the market.

Total = 2 L bottle of apple juice + 3 L bottle of orange juice

= 5 L

We need to find how many deciliters of juice does Jennifer buy in all.

Since, 1 L = 10 Deciliter

5 L = 50 Deciliter

So, she will buy 50 deciliters of juice.

Answer + explanation

x^3 -8x^2 -4x +32

answer= (x - 8)(x + 2)(x - 2)

Answer:

Below...

Step-by-step explanation:

Scientific Notation:

2.004 × 10-5

Scientific Notation:

1.203 × 10-2

Answer:

Step-by-step explanation:

Answer:

$ 30. okkkkkkkpkkpkkkpkdodjei

Answer:

[tex] - 5 \times - 1 = 5[/tex]

[tex]5 + 4 = 9[/tex]

Step-by-step explanation:

Therefore

[tex]a = - 5 \times - 1 = 5[/tex]

[tex]b = 4[/tex]

So 5+4=9

Answer:

69

Step-by-step explanation:

:)

Answer:

(x, y) = (1, -9)

Step-by-step explanation:

y = -9x

-8x-6y = 46

By substituting the value of y (first equation) into the second equation, we get,

-8x - 6*(-9x) = 46

-8x + 54x = 46

46x = 46

x = 1.

So, y = -9

Answer:

speed = distance/time

Step-by-step explanation:

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Answer:

What the english?

Step-by-step explanation:

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Answer:

1/7

Step-by-step explanation:

$1, 7 students

simply put 1 over 7 and you've got your fraction.

each student will get 1/7 of a dollar

The  equation has a vertex at (0, 5) and focus of (three-halves, 5) is,

- 6 x + y²- 10 y + 25 = 0

−6x+y² −10y+25=0

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line.

Given

The equation of a parabola is x = [tex]\frac{1}{4 \left(f - h\right)} \left(y - k\right)^{2} + h[/tex], where (h,k) is the vertex and (f,k) is the focus.

Thus, h = 0 k = 5, f = 3/2

The standard form is x = [tex]\frac{y^{2}}{6} - \frac{5 y}{3} + \frac{25}{6}x[/tex]

The general form is - 6 x + y² - 10 y + 25 = 0

The vertex form is x = [tex]\frac{\left(y - 5\right)^{2}}{6}[/tex]

The directrix is x = d

To find d, use the fact that the distance from the focus to the vertex is the same as the distance from the vertex to the directrix: [tex]0 - \frac{3}{2} = d - 0[/tex]

Thus, the directrix is x = - 3/2

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = 5

The focal length is the distance between the focus and the vertex: 3/2

The length of the latus rectum is four times the distance between the vertex and the focus: 6.

The eccentricity of a parabola is always 1.

To know more about parabola refer to :

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Answer:

Step-by-step explanation:

It's a

Answer:

Let c = the number of cookies

cookies/scoops of flour: 12/2 = c/3

Cross multiply.

2c = 36

c = 18 cookies

Step-by-step explanation:

Answer:

32 cookies.

Step-by-step explanation:

Find how much cookies Bill can bake with just 1 scoop of flour:

2 scoops of flour = 16 cookies

1 scoop of flour = 16 ÷ 2 = 8 cookies

Now, find 4 scoops of flour.

4 scoops of flour = 8 x 4 = 32 cookies

Answer:

16

Step-by-step explanation:

let the number be x , then

[tex]\frac{3}{4}[/tex] x = 15 ( multiply both sides by 4 to clear the fraction )

3x = 60 ( divide both sides by 3 )

x = 20 , then

[tex]\frac{4}{5}[/tex] × 20 = 4 × 4 = 16

Answer:

16

Step-by-step explanation:

let the number be x , then

\frac{3}{4} x = 15 ( multiply both sides by 4 to clear the fraction )

3x = 60 ( divide both sides by 3 )

x = 20 , then

\frac{4}{5} × 20 = 4 × 4 = 16

Answer:

Remember that the two non-adjacent interior angles, which are opposite the exterior angle are sometimes referred to as remote interior angles. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees

Answer:

m=-2/5

Step-by-step explanation:

Slope is rise over run. In this graph the slope is negative because rise (change in the Y value) is decreasing.