Find the co-ordinates of the point of trisection of the line joining the points A(1,8) and B(4,2).


please answer as quickly as possible with correct answer .
Don't answer randomly ​

The equation of the perpendicular bisector of the line AB when A(1 ,0) and B is (-3 ,-4) is; y = -x-3

It follows from the task.comtent that the two lines share the midpoint of.tge line AB.

On this note, it follows that the point shared by the two lines is; (-1, -2)

The slope of the line AB is; 1 from evaluation.

On this note, the equation of the perpendicular bisector with slope -1 is;

-1 = (y - (-2))/(x -(-1))

-1 = y +2/x+1

y = -x-3

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Answer:

Step-by-step explanation:

Can you explain more please?

Answer:

59

Step-by-step explanation:

It's quite simple. A triange has a total of 180 degress. So add 47 and 74 to get 121. Then do 180 minus 121 to get 59

The sum without sigma notation is (-1)^(k+1)sin(kπ).

To evaluate the sum, we substitute the values of k from 1 to 2 into the expression and calculate the sum of the terms.

When k = 1:

(-1)^(1+1)sin(1π) = (-1)^2sin(π) = sin(π) = 0

When k = 2:

(-1)^(2+1)sin(2π) = (-1)^3sin(2π) = -sin(2π) = 0

Since both terms of the sum are zero, the sum is zero.

Therefore, the evaluated sum is σ^2_k=1 (-1)^(k+1)sin(kπ) = 0.

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The two salesperson will both charge the same amount after 5 hours

Setting up the equation for the problem thus:

Salesperson A :

50 + 5h ___(1)

Salesperson B :

15h ____(2)

Equating (1) and (2)

50 + 5h = 15h

collect like terms

50 = 15h - 5h

50 = 10h

divide both sides by 10 to isolate h

h = 5

Hence, they will both charge the same amount after 5 hours .

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The expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

The expression is given as:

5% of 60

Express as fraction and decimal

5% of 60 = 5/100 * 60

5% of 60 = 0.05 * 60

This gives

5% of 60 = 1/20 * 60

Hence, the expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

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Answer:

43 people watch both

Step-by-step explanation:

The solution to the system of equation in ordered pair is (x, y) = (9, 5)

-5x + 3y = 6

x-y=4

Multiply equation (2) by 3

3x - 3y = 12

-5x + 3y = 6

Add both equations to eliminate y

3x + (-5x) = 12 + 6

3x - 5x = 18

-2x = 18

divide both sides by 2

x = 18/2

x = 9

Substitute x= 9 into

x-y=4

9 - y = 4

9 - 4 = y

y = 5

Therefore, (x, y) = (9, 5) is the ordered pair of the equation.

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Answer:

90

Step-by-step explanation:

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

The maximum area of the rectangle is A = xy = 12 * 12 = 144 square units.

Let's assume the two shorter sides of the rectangle are x and y, where x ≤ y, and the longer side is z. According to the given information, we have the following equations:

x + y + z = 36   (Equation 1)
x ≤ y

To maximize the area of the rectangle, we need to find the maximum value of xy.

From Equation 1, we can express z as z = 36 - (x + y).

The area of the rectangle, A, is given by A = xy.

Substituting z in terms of x and y, we have:

A = xy = x(36 - (x + y)) = 36x - x² - xy   (Equation 2)

To find the value of x that maximizes the area, we can differentiate Equation 2 with respect to x and set the derivative equal to zero:

dA/dx = 36 - 2x - y = 0

Since x ≤ y, we can substitute y with x in the equation above:

36 - 2x - x = 0

Simplifying the equation, we get:

36 - 3x = 0
3x = 36
x = 12

Now that we have the value of x, we can substitute it back into Equation 1 to find y:

12 + y + z = 36
y + z = 24

Since the sum of the lengths of the two shorter sides and one longer side is 36, and x = 12, we can deduce that y = 12.

Therefore, the sides of the rectangle are x = 12, y = 12, and z = 12 (since z = 36 - (x + y) = 12). This means we have a square.

In a square, all sides are equal. Therefore, the maximum area of the rectangle is obtained when all sides are equal, i.e., when x = y = z = 12.

The maximum area of the rectangle is A = xy = 12 * 12 = 144 square units.

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Answer:

The common difference between numbers is 7.

3

3+7=10

10+7 = 17

17+7=24

24+7=31

31+7= 38

3, 10, 17, 24, 31, 38

Answer:

a^2+2ab = 21

(a+b)^2= 25

Step-by-step explanation:

(a+b)^2 = a^+2ab+b^2

sub a=3 and b=2 and simplify  

A Gantt chart is indeed a specialized chart type. Basic chart types include bar charts, line charts, and pie charts, which are commonly used for visualizing data. Specialized chart types, such as Gantt charts, serve more specific purposes.

Yes, there are indeed basic chart types as well as specialized chart types. Basic chart types include things like bar graphs, line graphs, and pie charts, while specialized chart types are designed for more specific purposes, such as organizational charts, flowcharts, and Gantt charts.

In particular, a Gantt chart is a specialized chart type that is commonly used in project management to help visualize the tasks, milestones, and dependencies involved in a project. It is designed to show a timeline of when each task or activity needs to be completed, as well as how long it will take and what resources will be needed.

Overall, while basic chart types are great for general data visualization purposes, specialized chart types like Gantt charts can be incredibly useful for specific tasks or industries, and can help users to more effectively communicate and manage complex information.

A Gantt chart is indeed a specialized chart type. Basic chart types include bar charts, line charts, and pie charts, which are commonly used for visualizing data. Specialized chart types, such as Gantt charts, serve more specific purposes. A Gantt chart is designed for project management and helps visualize a project's timeline, tasks, and progress, making it easier to manage and allocate resources.

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The probability of running out of water decreases.

The given problem can be solved by using the concept of the normal distribution. Normal distribution, also called Gaussian distribution, is a probability distribution that occurs naturally in many situations. In this distribution, data values cluster around a central point, and the further away a value is from the center, the less likely it is to occur. The normal distribution has two parameters: the mean (μ) and the standard deviation (σ). The mean is the center of the distribution, and the standard deviation is a measure of how spread out the distribution is. The normal distribution is symmetric about the mean. It is a continuous distribution, meaning that it can take any value between negative infinity and positive infinity. The area under the normal curve represents the probability of a random variable taking a certain value or falling within a certain range of values. The total area under the normal curve is equal to 1.
Given:
The average person drinks 3 Liters of water when hiking the Mission Peak (with a standard deviation of 1 Liter).
You are planning a hiking trip to the Mission Peak for 10 people and will bring 35 Liters of water.
What is the probability that you will run out?
We need to find the probability that the amount of water consumed by 10 people will be greater than 35 Liters. Let X be the random variable representing the amount of water consumed by each person. X is normally distributed with mean μ = 3 Liters and standard deviation σ = 1 Liter.
Then, the total amount of water consumed by 10 people is given by the sum of 10 independent identically distributed (i.i.d.) random variables:
Y = X1 + X2 + ... + X10
where X1, X2, ..., X10 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 35 Liters. Therefore, you will run out of water if:
Y > 35
or equivalently:
(Y - μ10) / σ10 > (35 - μ10) / σ10
where μ10 = 10μ = 30 Liters and σ10 = √(10)σ = √(10) Liters.
Thus, the probability that you will run out of water is:
P(Y > 35) = P[(Y - μ10) / σ10 > (35 - μ10) / σ10]
= P(Z > (35 - μ10) / σ10)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (35 - μ10) / σ10) = P(Z > (35 - 30) / √10)
= P(Z > 1.5811)
= 0.0564 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 10 people is 0.0564.
What if the hiking trip will have 20 people and the amount of water you bring also doubles to 70 Liters. What is the probability you will run out?
In this case, the number of people has doubled, so the total amount of water consumed will also double. Thus, the total amount of water consumed by 20 people is given by:
Y = X1 + X2 + ... + X20
where X1, X2, ..., X20 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 70 Liters. Therefore, you will run out of water if:
Y > 70
or equivalently:
(Y - μ20) / σ20 > (70 - μ20) / σ20
where μ20 = 20μ = 60 Liters and σ20 = √(20)σ = 2.2361 Liters.
Thus, the probability that you will run out of water is:
P(Y > 70) = P[(Y - μ20) / σ20 > (70 - μ20) / σ20]
= P(Z > (70 - μ20) / σ20)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (70 - μ20) / σ20) = P(Z > (70 - 60) / 2.2361)
= P(Z > 4.4721)
= 0 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 20 people is zero.

Will the probability of running out of water increase or decrease? Why?

The probability of running out of water decreases when the number of people increases and the amount of water brought doubles. This is because the total amount of water consumed increases proportionally to the number of people, but the standard deviation of the distribution of the amount of water consumed decreases proportionally to the square root of the number of people. This means that the distribution of the total amount of water consumed becomes narrower and more concentrated around the mean as the number of people increases.

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Answer:

\(sss\)

Step-by-step explanation:

Because

AB = ED ( Side)

BC = EF ( Side )

AC = DF ( Side )

So,

ABC Triangle is congruent to EDF triangle ( SSS)

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The expression of the complex number in rectangular form is:

3√2 - 3√2 i

Complex numbers can be written in several different forms, such as rectangular form, polar form, and exponential form. Of those, the rectangular form is the most basic and most often used form.

The complex number is given as:

6(cos315° + isin315°)

The rectangular form of a complex number is a + bi,

where:

a is the real part

bi is the imaginary part

Euler's formula for this shows the expression:

\(e^{i\theta }\) = cosθ + i sinθ

Applying that to our question gives us:

\(e^{315i }\) = cos 315° + i sin 315°

Evaluating the trigonometric angles gives us:

\(e^{315i }\) = \(\frac{\sqrt{2} }{2} - \frac{\sqrt{2} }{2} i\)

Multiplying through by 6 gives us:

3√2 - 3√2 i

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Answer:

A. The income generated by a 529 plan is tax exempt

Answer:

A The income generated by a 529 plan is tax exempt.

Step-by-step explanation:

I just took the master quiz 5/5

Answer:

\(8\)

Step-by-step explanation:

\(6t - 20 - 32u = 6(6) - 20 - 32( \frac{1}{4} ) = 36 - 20 - 8 = 16 - 8 = 8\)

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Step-by-step explanation:

From the question

Perimeter = 2L + 2W

L = 24 units

W = 11 units

Substitute the values into the above formula

That's

P = 2(24) + 2(11)

P = 48 + 22

P = 70 units

Therefore the perimeter of the rectangle cannot be 60 units since the values when substituted into the above formula will give us 70 units

Hope this helps you

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.

For given question,

When two coins are tossed simultaneously, the sample space is as follows:

S = { HH, HT, TH, TT} where H denotes Head and T denotes tail.

Using the formula of probability,

P = Number of favorable outcomes/total number of outcomes,

we get,

P(HT) = 1/4

and

P(TH) = 1/4

We know that the occurrence of two mutually exclusive events is the sum of their individual probabilities.

So, P(Head on one and Tail on other)

= P(HT) + P(TH)

= 1/4 + 1/4

= 2/4

= 1/2

= 0.5

So, when two coins flipped simultaneously, the probability of flipping 2 coins and getting a head and a tail is 0.5

In this question, we need to find the number of times getting a head and a tail when two coins are flipped simultaneously 24 times

= 0.5 × 24

= 12

Therefore, When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.

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Answer:

s = 6 cm

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

Answer:

6

Step-by-step explanation:

→ Set up 2 simultaneous equations

2x + y = 12

3 + x = y

→ Substitute 2nd equation into 1st

2x + 3 + x = 12

→ Simplify and solve

3x = 9 ⇔ x = 3

→ Substitute back

x = 3, y= 6

Answer:

Step-by-step explanation:

16. 6.9, or 69/10

17. D,  12 feet

18. 6 11/12

Answer:

Step-by-step explanation:

We must use system of equations:

horses = h     chickens = c

horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...

4h + 2c = 120

They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...

h + c = 48

Now we combine the equations and solve:

4h + 2c = 120

h + c = 48

Now we solve...

4h + 2c = 120

h = 48 - c         (subtract c on both sides to single out h)

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

4(48 - c) + 2c = 120

192 - 4c + 2c = 120

-192                  -192

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

-2c = -72           (divide both sides by -2)

c = 36

Now we go back and find the value of h...

h = 48 - c

h = 48 - 36

h = 12

So there are 36 chickens & 12 horses!

Answer:

she will paint one in the inside and the remaining three paints should be outside of the box

Step-by-step explanation:

she will paint one in the inside and the remaining three paints should be outside of the box

Step-by-step explanation:

3(2x + 1) = 6(x + 5)

6x + 3 = 6x + 30

6x - 6x = 30 - 3

0 = 27

0 ≠ 27