the length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 56 in , find its length and width.

The linear function for the amount of tax owed for a taxable income over $37,450 is given as follows:

y = 0.25x + 4191.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

If your taxable income is between $37,450 and $90,750, then you owe $5156.25 plus 25% of your taxable income over $37,450, hence the function is defined as follows:

y = 5156.25 + 0.25(x - 37450).

y = 5126.5 + 0.25x - 935

y = 0.25x + 4191.5.

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The next number in the list would be -11.

What is Inductive reasoning?

Inductive reasoning is a form of reasoning that derives a general principle from a set of observations. It entails drawing broad conclusions from specific observations. Deductive reasoning differs from inductive reasoning.

Based on the pattern in the list, the next number in the sequence using inductive reasoning would likely be -11.

The pattern appears to be that each number is the previous number minus 3.

Hence, By using inductive reasoning the next number in the list would be -11.

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Answer:

A

Step-by-step explanation:

ABC is similar to DEF because similar triangles are triangles that have the same shape, but their sizes may vary.

On solving the equation, it is seen that about 12 ounces of the 15% solution must be mixed with about 6 ounces of the 6% solution to get 18 ounces of the 12% perfume.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let x = number of liters of the 15% solution

Let 18 − x = number of liters of the 6% solution

Solution Ounces Strength Amount of Perfume

15%         x            15            15x

6%          18 - x      6             6(18 - x)

Mixture   18           12            (18)(12)

So, the equation will be -

(amount of perfume in 15% solution) + (amount of perfume in 6% solution) = (amount of perfume in mixture)

15x + 6(18 − x) = (18)(12)

Solve the equation using distributive property -

15x + 108 - 6x = 216

Combine the like terms -

15x - 6x = 216 - 108

Simplify the equation further -

9x = 108

x = 108/9

x = 12

Now, substituting the value of x in 18 − x = 18 - 12 = 6.

Therefore, the amount in ounces is obtained as 12 ounces and 6 ounces.

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After two hours, Cesar and Camden are both 48 kilometers from their homes as per the coordinates.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

given, Cesar and Camden are brothers and live in the same house. Cesar is 80 kilometers away from home and bikes toward home at a rate of 16 kilometers per hour. Camden is 20 kilometers away from home and keeps walking away from home at a rate of 14 kilometers per hour.

Linear Equation for Cesar:

y = 80- 16x

Linear equation for Camden:

Y = 14x + 20

The coordinates (2, 48) is showing the position of both brothers after 2 hours.

(2, 48) this graph represents that both brothers will be met at 48 kilometers if they are walking the same road.

therefore, As per the given coordinates Cesar and Camden are both 48 kilometers away from home after 2 hours.

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The population being studied in each of the four years is:

The question that was posed to each respondent is:

The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a certain area is depicted by this indicator. The annual variations in population brought on by births, deaths, and net migration are measured as growth rates.

(a) Data and Calculations:

Percentage of employed individuals ages 25-29 with at least a bachelor's degree

in 2016 = 40%.

In the year 2000 = 32%,

in 1985 = 25%,

in 1964 = 16%.+

The percentage has continued to increase steadily.

(b) Numbers are not indicated by categorical data. They have a qualitative character. Instead, categories are used to organize the data. Data about ethnicity, sex, age group, and educational attainment are some examples of categorical data.

U.S. Census Bureau

a. The population being studied in each of the four years is:

O college educated individuals aged 25-29

b. The question that was posed to each respondent is:

O Have your earned a bachelor's degree (or higher)?

c. O categorical

The complete question is,

Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16%.+

(a) What is the population being studied in each of the four years?

O college educated individuals

O college educated individuals aged 25-29

O individuals aged 25-29

O employed individuals aged 25-29

O employed individuals

(b) What question was posed to each respondent?

O Have your earned a bachelor's degree (or higher)?

O Are you enrolled in college?

O Are you between the ages of 25 and 29?

O In what year did you receive your bachelor's degree?

O Are you employed?

(c) Do responses to the question provide categorical or quantitative data?

O categorical

O quantitative

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The smallest number of first-place votes a candidate could win with under the Plurality method is 105.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, an election with 521 votes.

considering an election with 521 votes and 5 candidates up for the election

Dividing the votes amongst 5 candidates

= 521/5 = 104.2  

So, the least number of first-place votes needed by a candidate using the plurality method  would be = 105 votes

104.2+ 104.2 + 104.2 + 104.2 + 104.2 = 521 (Dividing the votes equally)

104+104+104+104+104= 520

Thus, the remaining vote = 521 - 520 = 1

Least first-place vote = 104+1= 105 votes

Therefore, the smallest number of first-place votes a candidate could win with under the Plurality method is 105.

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The orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.

To find this, we can take the derivative of the original equation 3x^2 − y^2 = C with respect to x, which will give us 6x. Then, we can take the negative reciprocal of this derivative, which is -1/6x. This is the slope of the orthogonal trajectories.

We then can use the point-slope form of a line to get y - y1 = -1/6x (x - x1). Since the slope of the orthogonal trajectories is always -1/6x, we can just set the equation y - y1 = -1/6x (x - x1) equal to 0 and solve for x to get x1 = -y1/6.

We can then plug this value back into the point-slope equation to get y - y1 = -1/6(-y1/6) (x - (-y1/6)), which simplifies to y - y1 = y1/6 + x. Now, if we let y1 = -C/3, then we get y - (-C/3) = C/6 + x, which can be rewritten as x^2 + y^2 = C/3.

Therefore, the orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.

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Answer:

y=-3x+4

Step-by-step explanation:

If we use rise over run from one point to the next, you will see that you rise vertically 3 units, then run horizontally 1 unit.

Then Make the rise negative because this is a negative graph. So -3/1

Divide -3 by 1. -3/1=-3. mx=-3

Now we have to find the y-intercept. This is where the graph crosses/intersects the y-axis. As if you look at the y-axis, you will see that the graph intersects the y-axis at (0,4).

So your y-intercept is 4. b=4.

-Hope this helped

The least common denominator to both fraction expressions is; (x - 3)

The least common denominator simply means the least number or expression that is common to both denominators of a given fraction.

Now, the given denominators of the fraction expression are;

(2x - 6) and (7x - 21)

To find the least common denominator here, we will just factoriuze each algebraic expression to getl

(2x - 6)  = 2(x - 3)

(7x - 21) = 7(x - 3)

Thus, we see that the common expression is (x - 3) which we will conclude will be the least common denominator

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The solution to this equation is 7-∛2-x is x=127

Rearrange the radical on the left side of the equation:[tex]\sqrt[3]{2-x}=12-7[/tex]

Calculate the sum or difference:[tex]\sqrt[3]{2-x}=5\\[/tex]

Divide both sides of the equation by the coefficient of the variable:[tex]\sqrt[3]{2-x} =-5[/tex]

Power on both sides:[tex](\sqrt[3]{2-x})^3=(-5)^3[/tex]

Remove the parentheses:[tex](\sqrt[3]{2-x} )^3=(-5)^3[/tex]

Simplify the radical expression: 2-x=(-5)³

Rearrange unknown terms to the left side of the equation: -x=-5³-2

Divide both sides of the equation by the coefficient of the variable:x=5³+2

Calculate the power:x=125+2

Calculate the sum or difference:x=127

When  x=127

LHS= 7-∛2-127=12

RHS=12

LHS=RHS

x=127 is valid

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The total reimbursement for the employee will be $21.75.

It is important to note that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this situation, the employee is reimbursed at a rate of 29 cents per mile and he ravels at a 25 miles 3 days a week.

The total reimbursement will be:

= 0.29 × 25 × 3

= $21.75

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Complete question

An employee is reimbursed at a rate of 29 cents per mile. Travels at a 25 miles 3 days a week. Find the total reimbursement.

Part A

Using the formula for the volume of a cylinder,

[tex]V=\pi r^2 h \approx (3.14)(3^2)(5.5)=\boxed{155.43}[/tex]

Part B

The total volume of 14 candles is [tex](155.43)(14)=2176.02[/tex] cubic inches.

So, the cost is [tex](2176.02)(0.15) \approx \boxed{\$325.50}[/tex]

Part C

Using the formula for the lateral surface area of a cylinder,

[tex]2\pi rh=2\pi(3)(5.5)=\boxed{33\pi}[/tex]

The measure of the missing angle in a triangle is C = 18°.

An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle. Look at the illustration of the 45-degree angle. Angles are expressed in degrees or radians.

A straight angle is one in which the two arms extend in precise opposition to one another. A 180° angle is a straight angle. A protractor can be used to measure angles; a straight angle is an angle that is measured at 90 degrees.

The two arms are perpendicular to one another at a right angle. Each angle measures 45° when the right angle is divided into two equal pieces. An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle.

Given one of the angles A = 45°

And B is 65% of the total angle sum = 65/100 × 180

                                                             = 117°

For angle C, using angle sum property

⇒ A + B + C = 180°

⇒ 45° + 117° + C = 180°

⇒ C = 180° - (45° + 117°)

⇒ C = 180° - 162°

⇒ C = 18°

Thus, The measure of the missing angle in a triangle is C = 18°.

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Complete question:

What is the size, in degrees, of the missing angle of a triangle?

A = 45°

B = 65%

C = x

the two possible values for the third side of the triangle are 22.5 and 24.00.

We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, the third side must be greater than 10.25 and less than 19.75.

From this, we can conclude that the third side of the triangle must be either 22.5 or 24.00.

We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given that two sides of the triangle measure 19.75 and 10.25, the third side must be greater than 10.25 and less than 19.75. Therefore, the only two possible lengths for the third side of the triangle are 22.5 and 24.00. Any length greater than 19.75 or less than 10.25 would not satisfy the triangle inequality and would not be a valid third side for the triangle. Thus, We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

the two possible values for the third side of the triangle are 22.5 and 24.00.

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The volume and the total area of the largest cube of the wood that can be from a log of circular section whose radius is 16.8in is: 7.76 ft³, 23.52 ft².

Diameter of the log

d=2(16.8)

d=33.6in

Edge of cube

a²+a²=d²

2a²=33.6²

a²=564.48

a=23.76 in

Volume of the largest cube

V=a³

V=23.76³

V=13413.41 in³

V=13413.41 in³×(1 ft/12 in)³

V=7.76 ft³

Total area of the largest cube

A=6a²

A=6(23.76²)

A=3,387.23in²

A=3,387.23 in²×(1/ ft12 in)²

A=23.52 ft²

Therefore the Volume of the largest cube is 7.76 ft³ and the total area is 23.52 ft².

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The area that the forest would occupy after 7 years is 2288 km²

An equation is an expression showing the relationship between numbers and variables.

Let y represent area of the forest after x years.

y = abˣ

a is the initial value and b is the multiplication factor.

A certain forest covers an area of 3400 km², hence a = 3400 km². The area decreases by 5.5%, hence b = 100% - 5.5% = 94.5%. Hence:

y = 3400(0.945)ˣ

After 7 years:

y = 3400(0.945)⁷ = 2288 km²

The area of the forest after 7 years is 2288 km²

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Answer: B

Step-by-step explanation:

[tex]3 \frac{5}{8} \div 4=\frac{29}{8} \div 4=\frac{29}{32}[/tex]

simplest polynomial function with zeroes -2 and 3 is expanded form is f(x) = [tex]x^2 - x - 6[/tex].

To write a polynomial function with given zeros, we can use the factorization method. The zeros of a polynomial function are the solutions of the equation f(x) = 0. So, if we know the zeros of a polynomial function, we can use them to write the function in factored form.

For example, if the zeros of the polynomial function are -2 and 3, we can write the function as:

f(x) = (x + 2)(x - 3)

This function can be expanded into:

f(x) = [tex]x^2 - x - 6[/tex]

It's important to notice that the degree of the polynomial function is determined by the highest exponent of the variable in the equation, in this case 2.

It's also important to notice that the zeroes of the function are -2 and 3, as when you substitute them in the equation, the result is zero.

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The complete question is:

What is the simplest polynomial function with zeroes -2 and 3? Write the equation in the expanded form.

a. 17, 15, 8 this can be a right triangle, while b. 7 25 19 is not a right a triangle

There are an endless number of triangles produced when no side is specified.

The three angles produce an unlimited number of distinct triangles if side lengths are not provided.

When the three sides are specified the sides will be such that addition of the two smaller sides will be greater than the third side

For a. 17, 15, 8

the two smaller sides are:15 and 8

15 + 8 > 17

this can be a triangle

For b. 7, 25, 19

the two smaller sides are:7 and 19

7 + 19 > 25

this can be a triangle

For a right triangle the Pythagoras rule should be observe: the squire of the smaller sides will be equal to the square of the longer side. let the longer side be x

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

this is a right triangle

x² = 7² + 19²

x ² = 49 + 361

x² = 410

x = √410

x = 20.25

this is not a right triangle

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The linear equation is [tex]$V=21.45+5.15 t$[/tex].

We are given the dollar value [tex]$\$ 72.95$[/tex] of a product in 2010 and it is changed [tex]$\$ 5.15$[/tex] increase per year.

We are asked to write a linear equation that gives the dollar value V of the product in terms of the year t.

The general linear equation for this case would be,

[tex]$$V=C+5.15 t$$[/tex]

Since the dollar value increases by [tex]$\$ 5.15$[/tex]per year, the slope is[tex]$5.15$[/tex]. And, C is the V-intercept (the value of V when t=0 ).

Let us first determine the value of $C$ by substituting the given dollar value $ 72.95 in 2010 . This gives us:

[tex]V & =C+5.15 t \\[/tex]

[tex]72.95 & =C+5.15(10) \\[/tex]

[tex]72.95 & =C+51.5 \\[/tex]

[tex]72.95-51.5 & =C+51.5-51.5 \\[/tex]

[tex]21.45 & =C[/tex]

[Given that[tex]$\mathrm{t}=10$[/tex] at 2010

[Subtract 51.5 to both sides]

Thus, the value of C=21.45.

Let us substitute the value of C in the Eqn(1):

[tex]$$V=21.45+5.15 t$$[/tex]

Therefore, the linear equation is [tex]$V=21.45+5.15 t$[/tex].

The complete question is,

You are given the dollar value of a product in 2010 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t=10 represent 2010 .)

[tex]$\frac{2010 \text { Value }}{\$ 72.95}$[/tex]

Rate

[tex]$\$ 5.15$[/tex] increase per year

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The ODE's general solution has real solution and complex eigen functions. Typical trajectories are sinusoidal curves.

The general solution of the ODE involves complex eigenfunctions, which are solutions of the form e^(ikx), where k is a real number and i is the imaginary unit. By combining these complex eigenfunctions with real coefficients, a general real solution can be obtained. Typically, these solutions will take the form of sinusoidal curves, with the amplitude and period determined by the coefficients of the eigenfunctions. The coefficients can be determined using initial conditions, allowing for more specific trajectories to be determined. For example, if the initial condition is known, then the coefficients of the eigenfunctions can be determined using Fourier analysis, allowing for the trajectory of the system to be determined.

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Answer:

2x + 3

Step-by-step explanation:

1/2(6x - 10) - x

3x -5 -x

2x -5

We would need the structure of the equation to be 2x plus or minus anything other than 15.

For example:

2x - 5 = 2x + 3  if we subtract 2x from both sides we are left with

-5 = 3  This is a false statement and their will be no solution.

The number in the 17th position in the list is 7425

We start by eliminating some of the options. The smallest possibility for the larger number is if the larger number were twice the smaller number. [tex]$2457\times2=4914$[/tex], since [tex]$2457$[/tex] the least value in the group. In order for the largest possibility to be less than or equal to 7542, the largest number in the set, when multiplied by 2, it must be twice as large as the largest number in the set.This happens to be [tex]$2754\times2=5508$[/tex]. As a result, the number would need to be even and between 4914 and 5508. 5472 and 5274 are the only even numbers in the set and in this range. Both of these numbers are not twice a number in the set, according to a cursory check. The number cannot be four times or higher than any other number in the set because [tex]$2457\times4=9828$[/tex], well past the range of the set. Therefore, the number must be triple another number in the set. The least possibility is [tex]$2457\times3=7371$[/tex]and the greatest is [tex]$2475\times3=7425$[/tex], since any higher number in the set multiplied by 3 would be out of the range of the set. Reviewing, we find that the upper bound does in fact work, so the multiple is [tex]$2475\times3=7425[/tex].

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Answer:

5 oranges and 10 apples were sold  

Step-by-step explanation:

Let x be the number of oranges sold and y be the number of apples sold

Since 15 fruits were sold in all we get the following equation

x + y = 15 ....................[1]

Each orange costs $1 so if x oranges were sold that would fetch x dollars in sales = x dollars in sales

Each apple costs $2 so if y apples were sold, that would result in 2y dollars in sales

Total sales in $ = x + 2y and we know this is $25 so we get the second equation as

x + 2y = 25 ..................[2]

Look at the two equations. The coefficient of the x term is the same. We can eliminate the x term by subtracting equation [1] from equation [2] as follows:

x + 2y = 25
                    -
x  +   y = 15
-----------------
        y = 10

(2y - y = y and 25-15 = 10)

Now that we know y = 10, we can use equation [1] to find x

x + 10 = 15

which makes x = 5

ANSWER

5 oranges and 10 apples were sold  

The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.

When two quantities are inversely related, that is, when an increase in one quantity causes a decrease in the other and vice versa, they are said to be in inverse proportion. The product of the given two quantities is equal to a constant value in inverse proportion.

Given that the two ratios are 96:38 and 38:96. The value of the two ratios will not be the same because both the ratios are inverse of each other or are reciprocals of each other.

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Answer:

The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.

Step-by-step explanation:

I took the quiz.

The graph in the upper left corner best shows the population size of a K-selected species over time in a stable environment.

This graph shows the population of the species increasing at a slow rate until it reaches the carrying capacity of the species (the dashed line). After reaching the carrying capacity, the population of the species remains relatively stable, fluctuating slightly around the carrying capacity. This is evidence of a K-selected species, which tend to have a higher carrying capacity and longer life spans, and the population size remains relatively stable over time in a stable environment. Mathematically, this can be expressed as y = K = C, where y is the population size, K is the carrying capacity, and C is the constant value of the carrying capacity.

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X = 88.1. The total of all interest, dividends, or other income that an investment provides divided by the age of the investment or the period over which the investor has held it is the average yield on an investment.

What is average yield?

The average yield on an investment or a portfolio is calculated by dividing the total interest, dividends, or other income received by an investment by the investment's age or the period over which the investor has held it. In particular, it alludes to yield, or the total revenue from an investment divided by the number of years kept.

There are numerous yield kinds, and the calculating process varies depending on the specific yield type and the type of security. Because of these variations, comparisons of yields between other financial product categories should be used with caution.

In the case of stocks, yield is determined by dividing the price rise plus dividends by the original purchase price. Both cost yield and current yield can be used to examine bond yield.

Given data :

Let x be the number of trees in the orchard and N the yield per tree.

No of trees = 70

yield = 10

formula for N in terms of the unknown x :

(10+(70-x)0.55)

10 + 38.5 - 0.55x

-0.55x = 48.5

x = 48.5/ 0.55 = 88.1

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a. (3, 4, 5) will create a triangle.

b. (10, 20, 30) will not create a triangle

c. (15.5, 45, 20.5) will not create a triangle.

What is a triangle?

A triangle is a polygon with three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their sides (such as equilateral, isosceles, or scalene) or by their angles (such as acute, right, or obtuse).

The set of lengths (3,4,5) will create a triangle. This is because it follows the "triangle inequality theorem" which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The set of lengths (10, 20, 30) will not create a triangle. This is because 10 + 20 is less than 30, so it does not satisfy the triangle inequality theorem.

The set of lengths (15.5, 45, 20.5) will not create a triangle. This is because 15.5 + 20.5 is less than 45, so it does not satisfy the triangle inequality theorem.

Hence,

a. (3, 4, 5) will create a triangle.

b. (10, 20, 30) will not create a triangle

c. (15.5, 45, 20.5) will not create a triangle.

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The measure of angle C is 149°.

In mathematics, an angle is a figure made up of two rays that share a terminal and are referred to as the sides of the angle and the vertices of the angle, respectively.

Angles, which are frequently expressed in terms of degrees or radians, are used to quantify the size of turns.

The law of cosines, the law of sines, and the Pythagorean theorem are only a few examples of mathematical equations that use angles, which are a key component of geometry.

When understanding shapes, angles are equally crucial.

The angles within a triangle, a quadrilateral, and a polygon can provide information on the number of sides a shape has in addition to whether or not it is regular.

Angles are also used to calculate the arcs and circles of an object.

From the given figure,

It is a pentagon, sum of sides of a pentagon is 540°

It is clear that,

90 + 90 + 90 + 6x + 1 + (8x - 11) = 540°

⇒ 260 + 14x = 540°

⇒ 14x = 540 - 260

⇒ 14x = 280

⇒ x = 20

∠ C = 8 × 20 - 11 = 160 - 11 = 149°

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