What is |–6.5|?........................................................

If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint.

If a system has 1 sοlutiοn, it means that the lines being graphed intersect at a single pοint.

If a system has infinitely sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther.

A linear equatiοn in 2 variables is an algebraic expressiοn that represents a straight line οn a 2D cοοrdinate plane.

It can be written in the fοrm οf y = mx + b, where m is the slοpe οf the line, b is the y-intercept, and x and y are the twο variables.

PART A:

If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint. This implies that there are nο values οf the variables that can satisfy bοth equatiοns simultaneοusly.

PART B:

If a system has one sοlutiοn, it means that the lines being graphed intersect at a single pοint. This implies that there is οnly οne unique sοlutiοn that satisfies bοth equatiοns simultaneοusly.

PART C:

If a system has infinitely many sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther. This implies that there are an infinite number οf values οf the variables that can satisfy bοth equatiοns simultaneοusly since every pοint οn the shared line is a valid sοlutiοn tο the system.

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The length of AC is 12.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given is a line.

A, B, C, D, E and F are equally spaced on the line.

Given that, EF = 2x

This means that distance between each of the point is 2x.

AB = 2x, BC = 2x, CD = 2x, and DE = 2x

Given BE = 10x - 12

BE = BC + CD + DE

     = 2x + 2x + 2x

     = 6x

So, 10x - 12 = 6x

10x - 6x = 12

4x = 12

x = 3

Now, we have to find AC.

AC = AB + BC

     = 2x + 2x

     = 4x

     = 4 × 3

     = 12

Hence AC is 12.

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Answer:4,383,900

Step-by-step explanation:

4,383,900

Answer:

good morning!

Step-by-step explanation:

the answer to your question is 4(7x^2+5)

hope you have a great day!

The correct statements regarding the translation are given as follows:

A translation changes only the position of the figure, keeping angle measures and orientation correct, hence the second and the third options are correct.

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Neither of the given points is a solution to the system of linear inequalities.

What does solution to the system of linear inequalities mean ?

A system of linear inequalities is a set of two or more linear inequalities with the same variables. This system consists of two linear inequalities, each involving the variables x and y, and each inequality uses one of the inequality symbols.

The solution to a system of linear inequalities is the set of values for the variables that satisfy all the inequalities in the system simultaneously. This solution can be represented graphically as the region of the coordinate plane that satisfies all the inequalities in the system.

Check the given points whether they are solutions to the system of linear inequalities or not :

Substitute the x and y values of each point into both inequalities and check if they are true.

(a) (-4,1) :

y ≤ -3x - 2

1 ≤ -3(-4) - 2

1 ≤ 10

This is false, so (-4,1) is a not solution to the first inequality.

y > x - 2

1 > -4 - 2

1 > -6

This is true, so (-4,1) is a solution to the second inequality.

Since (-4,1) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.

(b) (2,2):

y ≤ -3x - 2

2 ≤ -3(2) - 2

2 ≤ -8

This is false, so (2,2) is not a solution to the first inequality.

y > x - 2

2 > 2 - 2

2 > 0

This is true, so (2,2) is a solution to the second inequality.

Since (2,2) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.

Therefore, neither of the given points is a solution to the system of linear inequalities.

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The slant height [tex]l = 29 \: mm[/tex].

A cone is a three-dimensional geometric shape with a smooth transition from a flat, usually circular base to the apex or vertex, which forms an axis to the base's center.

As per the given data:

Height = 21 mm

Volume = 8792 mm

Radius = 20 mm

For slant height of the one ([tex]l[/tex]):

[tex]l = \sqrt{r^2 + h^2}[/tex] {using Pythagoras theorem}

[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]

[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]

[tex]l = \sqrt{400 + 441}[/tex]

[tex]l = 29 \: mm[/tex]

Hence, the slant height [tex]l = 29 \: mm[/tex].

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Answer: -3,9

Step-by-step explanation: plug in -3 for x which gives u 9

The product of 69 and 5.6 x 10⁵ expressed in scientific notation is 3.864 x 10⁷.

Scientific notation, also known as standard form, is a way of writing very large or very small numbers in a concise and convenient way. It expresses a number as the product of a decimal number between 1 and 10 (known as the coefficient) and a power of 10.

The general form of a number written in scientific notation is:

a × 10^n

where a is the coefficient, and n is an integer exponent that indicates the number of places the decimal point must be moved to obtain the original number.

To multiply numbers in scientific notation, we multiply their coefficients and add their exponents.

69 x 5.6 x 10⁵ = (6.9 x 10¹) x (5.6 x 10⁵)

= (6.9 x 5.6) x 10¹⁺⁵

= 38.64 x 10⁶

= 3.864 x 10⁷ (in scientific notation)

Therefore, the product of 69 and 5.6 x 10⁵ expressed in scientific notation is 3.864 x 10⁷.

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The complete question is :

Answer:

Exponential notion makes a big number easier to write and read.

Step-by-step explanation:

Based on the dot plot, it appears that the data is spread relatively evenly across the teams, with no one team dominating the others by a wide margin.

Data is the raw information that can be collected and analyzed to provide insights. It is the foundation of decision-making and can be used to identify trends, patterns, and relationships. Data can come from many different sources, including surveys, databases, and software applications. Data can be qualitative or quantitative, static or dynamic, structured or unstructured, and can be used to inform decisions, inform policy, and inform research. Data can also be used to make predictions, monitor performance, and improve efficiency.
This suggests that the competition between the teams is relatively balanced, and that no team is significantly outperforming the others in terms of number of wins. This could indicate that the teams are of about equal skill level, or that the schedule for each team is balanced enough that no team has an advantage over the others.

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The two solutions to the linear equation is given by the ordered pairs (0, 6) and (-4, 5).

In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point that lie on it;

y = 0.25x + 6.00

Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (-4, 5) and (0, 6).

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By answering the above question, we may state that Debra would thus function need to travel 150 miles for the price of the two plans to be the same.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The starting charge and the cost per mile would be added together for the first plan's total cost:

Costs for plan 1 total 47.96 plus 0.19x.

The first charge and the cost per mile would be added together for the second plan's total cost:

Plan 2's overall cost is 53.96 plus 0.15x.

Set the two total cost expressions equal to one another and solve for x to get how many miles Debra would need to go for the two plans to be the same in price:

47.96 + 0.19x = 53.96 + 0.15x

0.04x = 6

x = 150

Debra would thus need to travel 150 miles for the price of the two plans to be the same.

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One change that Pedro can make to his plan to ensure that he meets his daily running goal is to increase the estimated number of steps per mile.

If Pedro overestimates the number of steps in a mile, he will end up taking more steps than he initially planned for, which can help him reach his daily goal.

For example, if Pedro increases his estimate from 2,000 steps per mile to 2,500 steps per mile, he will need to run approximately 4 miles per day to reach his goal of 10,000 steps. This will make it more likely for him to reach his daily goal within the 4 hours of running over the 5 days.

Alternatively, Pedro can increase his running speed to cover more distance in a shorter period of time. For instance, if he increases his running speed from 6 miles per hour to 8 miles per hour, he will need to run for only about 2.5 hours per day to reach his goal of 10,000 steps.

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The constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

What is the exponential functions?

An exponential function is a mathematical function of the form:

[tex]f(x) = a^x[/tex]

The given formula for the number of visitors to the county parks system is:

[tex]A = 20.6(1.03)^t[/tex]

where t is the number of years after 2010 and A is the number of visitors in thousands.

To find the constant percent rate of change per unit interval, we can take the derivative of A with respect to t:

[tex]dA/dt = 20.6(1.03)^t * ln(1.03)[/tex]

The constant percent rate of change per unit interval is given by the expression:

r = (dA/dt) / A

Substituting the values of dA/dt and A, we get:

[tex]r = [20.6(1.03)^t * ln(1.03)] / [20.6(1.03)^t]\\r = ln(1.03)\\r = 0.0305[/tex]

Hence, the constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

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These two situations are examples of poor conflict resolution because they do not offer a space for dialogue between the individuals involved, but rather there is only judgment by law without any mediation.

Conflict resolution is a term that refers to the ability of individuals to resolve conflicts or differences with others in a peaceful manner agreed upon by all parties involved. In this case, these two examples are not examples of good conflict resolution because there is no space for dialogue between students and teachers, but rather there is only aggression and prosecution before the entities in charge of justice in each country.

Due to the above, we believe that some strategies to end the culture of violence in schools is to spread messages of dialogue and conflict resolution in a peaceful manner. Also, offer workshops for parents so that from home conflict resolution is reinforced through dialogue.

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The domain and the range of h(n) consist of all possible sets of whole numbers.

Other answers are listed below

How to determine the domain and the range of h(n)

From the question, we know that:

h(n) is the number of houses

n and h(n) can only take whole numbers as its values

So, we have

Thus, the domain and range consist of all possible sets of whole numbers.

How to determine h(5) and h(11)

From the figure, we can see that

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

How to represent the explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Here, we have

s(n) is the number of segments

From the figure, we can see that

The number of segments is twice the the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Recall that:

The number of segments is twice the the figure number

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

The number of segments is twice the the figure number

Mathematically, this can be expressed as

s(n) = 2n

How to complete the table for f(5) and f(7)

From the table, we can see that

The division of a term by 2 gives the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

How to determine the domain of f(n)

The possible values of n are real numbers

Thus, the domain consist of all possible sets of real numbers.

The observation of the function

Above, we have

The division of a term by 2 gives the next term

This represents the observation

How to determine the value of g(4)

From the question, we have

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

How to complete the statements

The function is a doubling function

So, we have

g(n) = g(n - 1) * 2, g(n) = g(n - 2) * 4 and  g(n) = g(n - 3) * 8

How to determine the value of g(24)/g(21)

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

When the equations are divided, we have

g(24)/g(21) = 2(9)^23/2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value is 729

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Answer:

Let's use A to represent the number of adult tickets sold and C to represent the number of children's tickets sold.

We know that A + C = 166, since the total number of tickets sold is 166.

We also know that the revenue earned from adult tickets is $5A and the revenue earned from children's tickets is $3C. Since the total revenue earned is $718, we can write:

5A + 3C = 718

Now we have two equations with two variables:

A + C = 166

5A + 3C = 718

We can solve for A in the first equation to get:

A = 166 - C

Then we can substitute this expression for A into the second equation:

5(166 - C) + 3C = 718

Simplifying and solving for C, we get:

830 - 2C = 718

2C = 112

C = 56

So 56 children's tickets were sold. We can substitute this value back into the first equation to solve for A:

A + 56 = 166

A = 110

Therefore, 110 adult tickets were sold.

Answer:

Step-by-step explanation:

Let's use the following variables:

a = number of adult tickets sold

c = number of children tickets sold

We know that:

a + c = 166 (total number of tickets sold)

5a + 3c = 718 (total revenue)

We can solve this system of equations by substitution or elimination. Here, we'll use elimination:

Multiply the first equation by 3: 3a + 3c = 498

Subtract the second equation from the first: 2a = 220

Solve for a: a = 110

So 110 adult tickets were sold. We can find the number of children's tickets by substituting a = 110 into either of the original equations:

c = 166 - a = 166 - 110 = 56

Therefore, 110 adult tickets and 56 children's tickets were sold.

The solution for the function at the different values of x are,

f(-10) = 20001

f(2) = 49

f(3) = 214

In mathematics, functions are often represented by equations or formulas, and take one or more input values to produce an output value. They can be used to model a wide variety of phenomena, from physical systems to economic behavior to social dynamics.

The given function is f(x) = 2x⁴ + x² - 10x + 1. The output of the function at the different values of x will be calculated as,

At x = -10,

f(x) = 2x⁴ + x² - 10x + 1

f(-10) = 2(-10)⁴ + (-10)² - 10(-10) + 1

f(-10) = 20001

At x = 2,

f(x) = 2x⁴ + x² - 10x + 1

f(2) = 2(2)⁴ + (2)² + 10(2)  + 1

f(2) = 49

At x = 3,

f(x) = 2x⁴ + x² - 10x + 1

f(3) = 2(3)⁴ + (3)² + 10(2) + 1

f(3) = 214

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Answer:

Step-by-step explanation:

To find the value that separates the lower 40% of the bills from the rest, we need to find the z-score corresponding to the 40th percentile of the standard normal distribution, and then use this z-score to find the corresponding value in the distribution of electricity bills.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 40th percentile is approximately -0.25.

To find the corresponding value in the distribution of electricity bills, we can use the formula:

z = (x - mu) / sigma

where z is the z-score, x is the corresponding value in the distribution, mu is the mean, and sigma is the standard deviation.

Rearranging this formula to solve for x, we get:

x = mu + z * sigma

Substituting the given values, we get:

x = 106.27 + (-0.25) * 17.15

x = 101.63

Therefore, the value that separates the lower 40% of the electricity bills from the rest is approximately $101.63.

Therefore, the area of the base of the aquarium is 5760 square centimeters.

Area is a measure of the amount of space inside a two-dimensional (2D) shape or figure. It is usually measured in square units, such as square meters (m²) or square centimeters (cm²). The area of a shape is calculated by multiplying the length of one side or dimension of the shape by the length of another side or dimension. The resulting value represents the total number of square units that are contained within the shape. Area is an important concept in mathematics and is used in various fields, such as geometry, physics, and engineering. It helps in measuring and comparing the sizes of shapes and figures, and in determining how much material is needed to cover or fill a certain area.

Here,

The area of the base can be calculated using the dimensions of the aquarium.

Let's assume that the aquarium has a rectangular base with length L, width W, and height H. Then, the area of the base of the aquarium can be calculated as:

Area of base = Length x Width = L x W

If Monica measured the length and width of the base, we can use those measurements to calculate the area of the base. If not, we'll need to make additional assumptions or measurements.

Assuming we have the length and width of the base, we can calculate the area as follows:

Area of base = Length x Width

Area of base = 96 cm x 60 cm

Area of base = 5760 cm²

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Average cost per square foot to build a fast-food restaurant is $238 .

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.

Given,

Area of the restaurant = 4000 sqft

Total average cost to build the restaurant

= $952000

Average cost of per sqft

= 952000/4000

= $238

Hence, $238 is the average cost per square foot to build a fast-food restaurant.

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By using Venn diagram the following probabilities are 0.75,0.25,0.9 and 0.625.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Number of clients= 200

Number of television= 150

Magazines=80

Both magazine and television=50

Now,

To complete the diagram, we can fill in the following values:

The size of T is 150.

The size of M is 80.

The size of TM (the overlap between T and M) is 50.

The size of C (the total number of clients who use either T or M) is 150 + 80 - 50 = 180.

The size of U (the number of clients who use neither T nor M) is 200 - 180 = 20.

Now we can use the Venn diagram to answer the following probabilities:

i. P(T) is the probability that a randomly selected client uses television. This is the size of T divided by the total number of clients, which is 150/200 = 0.75.

ii. P(T ∩ M) is the probability that a randomly selected client uses both television and magazines. This is the size of TM divided by the total number of clients, which is 50/200 = 0.25.

iii. P(T ∪ M) is the probability that a randomly selected client uses either television or magazines (or both). This is the size of C divided by the total number of clients, which is 180/200 = 0.9.

iv. P(T|M) is the probability that a randomly selected client uses television given that they use magazines. This is the size of TM divided by the size of M, which is 50/80 = 0.625.

Therefore, by probability the answer will be 0.75,0.25,0.9 and 0.625.

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The equation of the new graph is:

f(x) = e^(x-6)

The graphs of the two functions f(x) = e^x and f(x) = e^(x-6) are shown below

From the question, we are to determine the equation of the new graph.

If the graph of the function f(x) = e^x is shifted 6 units to the right, the equation of the new graph can be found by replacing x with (x - 6) in the original equation.

This is because a horizontal shift of a function f(x) to the right by c units can be achieved by replacing x with (x - c) in the equation of the function. So, for the given function, a shift to the right by 6 units would be achieved by replacing x with (x - 6) in the original equation f(x) = e^x.

Therefore, the equation of the new graph is:

f(x) = e^(x-6)

This can also be written as:

f(x) = e^x / e^6

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There won't be enough aphids to completely harm the maize plants because 10,000 is less than 2,000 50 (the maximum number of aphids that can be on all the plants without killing them).

To determine if there are enough aphids to kill the corn plants, we need to know the total number of aphids on each plant after 3 weeks. Let's assume that on average, each plant has 200 aphids after 3 weeks.

Then, the total number of aphids in the field would be:

50 plants × 200 aphids/plant = 10,000 aphids

Since 10,000 is less than 2,000 × 50 (the maximum number of aphids that can be on all the plants without killing them), there will not be enough aphids to completely destroy the corn plants.

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Answer:

9.50 : 25

19 : 50

28.50 : 75

Step-b-step explanation:

Answer:

answer is 5

Step-by-step explanation:

2x=5×2

so 2x=10

10-5=5

so 2x-5=5

Answer:

5

Step-by-step explanation:

2x - 5 first, substitute

2(5) - 5 then, multiply

10 - 5 = 5

Answer:404087

Step-by-step explanation:

use the calculator frfr

Answer:

404087

Step-by-step explanation:

the perimeter of the shape  is [tex]8 + 2\sqrt(2) units.[/tex]

AB = [tex]\sqrt ((4-2)^2 + (0-0)^2)[/tex] = [tex]\sqrt (4)[/tex] = 2

BC = [tex]\sqrt ((4-4)^2 + (3-0)^2) = 3[/tex]

CD =[tex]\sqrt ((3-4)^2 + (4-3)^2) = \sqrt (2)[/tex]

DE = [tex]\sqrt ((2-3)^2 + (3-4)^2) = \sqrt(2)[/tex]

EA =[tex]\sqrt ((2-2)^2 + (3-0)^2) = 3[/tex]

AB + BC + CD + DE + EA = [tex]2 + 3 + \sqrt(2) +\sqrt sqrt(2) + 3 = 8 + 2\sqrt(2)[/tex]

As a result, the shape has a perimeter of [tex]8 + 2 \sqrt(2)[/tex] units.

The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. Units are used to measure perimeter (m, cm, in, feet, etc.)

From the question;

The lengths of all the sides must be added up in order to determine the shape's perimeter.

Let's begin by giving the shape's vertices the following labels:

A = (2, 0)

B = (4, 0)

C = (4, 3)

D = (3, 4)

E = (2, 3)

The lengths of each side can be determined using the distance formula:

AB = [tex]\sqrt ((4-2)^2 + (0-0)^2)[/tex] = [tex]\sqrt (4)[/tex] = 2

BC = [tex]\sqrt ((4-4)^2 + (3-0)^2) = 3[/tex]

CD =[tex]\sqrt ((3-4)^2 + (4-3)^2) = \sqrt (2)[/tex]

DE = [tex]\sqrt ((2-3)^2 + (3-4)^2) = \sqrt(2)[/tex]

EA =[tex]\sqrt ((2-2)^2 + (3-0)^2) = 3[/tex]

AB + BC + CD + DE + EA = [tex]2 + 3 + \sqrt(2) +\sqrt sqrt(2) + 3 = 8 + 2\sqrt(2)[/tex]

As a result, the shape has a perimeter of [tex]8 + 2 \sqrt(2)[/tex] units.

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Answer:the perimeter of the shape  is

AB =  =  = 2

BC =

CD =

DE =

EA =

AB + BC + CD + DE + EA =

As a result, the shape has a perimeter of  units.

what is the perimeter?

The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. Units are used to measure perimeter (m, cm, in, feet, etc.)

From the question;

The lengths of all the sides must be added up in order to determine the shape's perimeter.

Let's begin by giving the shape's vertices the following labels:

A = (2, 0)

B = (4, 0)

C = (4, 3)

D = (3, 4)

E = (2, 3)

The lengths of each side can be determined using the distance formula:

AB =  =  = 2

BC =

CD =

DE =

EA =

AB + BC + CD + DE + EA =

As a result, the shape has a perimeter of  units.

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Step-by-step explanation:

The input rule to find the output is 19.67 multiplied by the input value.

One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.

Given:

An input value is 3, and the corresponding output value is 59.

The unit rate is 59 divided by 3.

We get,

59/3 = 19.67

The input rule to find the output is 19.67 multiplied by the input value.

Now, the required table is,

Input            Output

2                   39.33

4                  78.67

7                   137.67

Therefore, the required table is given above.

To learn more about the division;

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