Which of the following rational functions is graphed below?

Answer:

  0.56 lb

Step-by-step explanation:

You want the weight of pretzels if they constitute 14% of the weight of 4 lb of snack mix.

Let p represent the weight of pretzels. The relation in the problem statement is written in equation form as ...

  pretzel weight = 14% of 4 lb

  p = 0.14 × 4 lb

  p = 0.56 lb . . . . . . . . . perform the multiplication

The weight of the pretzels in the trail mix is 0.56 lb.

__

Additional comment

In this context "of" usually means "times". That is "14% of 4 lb" means 14% × 4 lb".

The percent symbol (%) can be considered to be a shorthand way to write "/100". That is, you can replace the percent symbol with /100 and it doesn't change anything:

  14% × 4 lb = 14/100 × 4 lb

(Similarly, ‰ means /1000.)

You will notice that we wrote the weight as "4 lb", not just "4". The "lb" can be treated as though it were a variable, and "4 lb" is the product of "4" and "lb". Keeping units with the numbers can help guard against mistakes. As with other variables, you can only add (or subtract) "like" terms, ones with the same units.

In general, a percentage is a "pure number." It has no units, because it is the ratio of quantities having like units: (0.56 lb)/(4 lb) = 0.14 = 14%. The like units cancel the same way like variables would cancel.

Answer:

y = 4(9)^x

Step-by-step explanation:

To find the equation of an exponential function in the form y = ab^x that passes through two given points, we need to use the following steps:

Step 1: Find the value of a by plugging in the coordinates of the first point (0,4).

y = ab^x

4 = ab^0

4 = a(1)

a = 4

Step 2: Find the value of b by plugging in the coordinates of the second point (3,2916) and using the value of a we found in Step 1.

y = ab^x

2916 = 4b^3

b^3 = 729

b = 9

Step 3: Write the equation in the form y = ab^x using the values of a and b we found in Steps 1 and 2.

y = 4(9)^x

Therefore, the exponential function in the form of y = ab^x that passes through the points (0,4) and (3,2916) is y = 4(9)^x.

Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]

The claim is incorrect because the car's odometer is not perfectly accurate. A 10-minute he can measure to an accuracy of 1 mile, but is prone to error due to wear, calibration, measurement error and other factors. Additionally, factors such as tire pressure and changes in road conditions can affect the accuracy of odometer readings.

An odometer is an in-vehicle device that measures the distance traveled by the vehicle. Displays the total number of miles or kilometers the car has traveled since the car was manufactured or the odometer was last reset. This measurement is important for several reasons. B. To track vehicle maintenance schedules, estimate fuel consumption, and determine vehicle resale value. Odometers typically use mechanical or electronic components to measure the distance traveled by a vehicle and display the information on the dashboard. However, as mentioned earlier, the accuracy of odometer readings depends on a number of factors. 

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Answer:

first, we need to calculate the amount of discount we get using the coupon:

Discount = 30% of $50

Discount = 0.30 * $50

Discount = $15

So the discounted price of the meal is:

Discounted Price = $50 - $15

Discounted Price = $35

Now we need to add the sales tax:

Sales Tax = 7% of $35

Sales Tax = 0.07 * $35

Sales Tax = $2.45

Adding the sales tax to the discounted price gives us:

Discounted Price + Sales Tax = $35 + $2.45

Discounted Price + Sales Tax = $37.45

Finally, we need to add the tip:

Tip = 22% of ($35 + $2.45)

Tip = 0.22 * $37.45

Tip = $8.24

Adding the tip to the discounted price and sales tax gives us:

Discounted Price + Sales Tax + Tip = $37.45 + $8.24

Discounted Price + Sales Tax + Tip = $45.69

Therefore, the final cost of the dinner with the discount, sales tax, and tip included is $45.69.

Step-by-step explanation:

Answer:

A) a fair six-sided number cube (by assigning one number to represent a win and the other five numbers to represent a loss)

D) a spinner with 6 equal sections (by assigning one section to represent a win and the other five sections to represent a loss)

Step-by-step explanation:

The linear regression equation's residuals are as follows: -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18, and -0.7

A residual is the difference between the actual value and the expected value.

In a scatter plot with a line of best fit, the residual would be the vertical distance between the actual value and the line.

The residual's general shape can be described as predicted.

Remainder therefore has a value of -1.

This is the regression equation: y = 0.141x + 0.842

The projected values (y) at the matching x values are then calculated.

We thus have:

y = 0.141 × 13.8 + 0.842 = 2.78

y = 0.141 × 18 + 0.842 = 3.38

y = 0.141 × 16.7 + 0.842 = 3.20

y = 0.141 × 18 + 0.842 = 3.38

y = 0.141 × 0.7 + 0.842 = 0.94

y = 0.141 × 21.9 + 0.842 = 3.93

y = 0.141 × 15.5 + 0.842 = 3.03

y = 0.141 × 9.2 + 0.842 = 2.14

y = 0.141 × 19.5 + 0.842 = 3.59

y = 0.141 × 16.7 + 0.842 = 3.20

Next, the residuals are determined using:

Real value minus predicted value equals residual.

We thus have:

Residual = 1.42 - 2.78 = -1.36

Residual = 3.7 - 3.38 = 0.32

Residual = 3.21 - 3.20 = 0.01

Residual = 4 - 3.38 = 0.62

Residual = 1.11 - 0.94 = 0.17

Residual = 3.69 - 3.93 = -0.24

Residual = 3.92 - 3.03 = 0.89

Residual = 2.23 - 2.14 = 0.09

Residual = 3.77 - 3.59 = 0.18

Residual = 2.5 - 3.20 = -0.7

The linear regression equation's residuals are therefore 1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18, and -0.7.

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Sin = 4/5, with the help of trigonometric ratios.

Triangle side length ratiοs are knοwn as trigοnοmetric ratiοs.

In trigοnοmetry, these ratiοs shοw hοw the ratiο οf a right triangle's sides tο each angle

Sine, cοsine, and tangent ratiοs are the three fundamental trigοnοmetric ratiοs.

The sin, cοs, and tan functiοns can be used tο οbtain the οther significant trig ratiοs, cοsec, sec, and cοt.

Trigοnοn, which means "triangle," and metrôn, which means "tο measure," are the rοοts οf the term "trigοnοmetry."

Triangle side length ratiοs are knοwn as trigοnοmetric ratiοs.

Here,

cot = cos/sin

sin= PERPENDICULAR/HYPOTENUSE

cot = BASE/HYPOTENUSE

sin = 4/5

Hence, Sin=4/5, with the help of trigonometric ratios.

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The total mass of the books in Kelly's backpack is 2950 grams.

How many grammes are there in one kilogramme?

1000 grammes make up one kilogramme. The amount in kilogrammes must be multiplied by the conversion factor, which is 0.001.

We must add the masses of all 5 volumes to determine the overall weight of the books in Kelly's backpack.

The combined mass of the three books, each weighing 450 grammes, is: 3 x 450 = 1350 grammes.

The combined mass of the two volumes, each weighing 800 grammes, is 2 x 800 grammes.

We sum the weights of all the books to determine the overall mass:

1350 + 1600 = 2950 grammes

The combined weight of Kelly's backpack's books is 2950 grammes.

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**** keep in mind (dy/dx) becomes like a letter itself

5.

x⁴+y⁴=2

Taking the derivative of both sides with respect to x:

4x³ + 4y³ (dy/dx) = 0

4y³ (dy/dx) = -4x³

(dy/dx) = -4x³/4y³

4's cancel out

(dy/dx) = -x³/y³

At (1,-1), we have

(dy/dx) = -x³/y³

(dy/dx) = -(1)³/(-1)³

(dy/dx) = -1/-1

(dy/dx) = 1

7.

y² = 4x

Taking the derivative of both sides with respect to x:

2y (dy/dx) = 4

divide 2y on both sides

(dy/dx) = 4/2y

simplify

(dy/dx) = 2/y

At (1,2), we have

(dy/dx) = 2/y

(dy/dx) = 2/(2)

(dy/dx) = 1

9.

sin y=5x⁴-5

Taking the derivative of both sides with respect to x:

cos y (dy/dx) = 20x³

(dy/dx) = 20x³/cos y

At (1,π), we have (dy/dx) = 20/(-1) = -20.

11.

cos y=x

Taking the derivative of both sides with respect to x:

-sin y (dy/dx) = 1

(dy/dx) = -1/sin y

At (0,π/2), we have (dy/dx) = -1.

6.

x=e^y

Taking the derivative of both sides with respect to x:

1 = e^y (dy/dx)

(dy/dx) = 1/e^y

At (2,In 2), we have (dy/dx) = 1/e^(In 2) = 1/2.

8.

y²+3x= 8

Taking the derivative of both sides with respect to x:

2y (dy/dx) + 3 = 0

(dy/dx) = -3/(2y)

At (1,√5), we have (dy/dx) = -3/(2√5).

10.

√x-2√y = 0

Taking the derivative of both sides with respect to x:

1/(2√x) - 1/√y (dy/dx) = 0

(dy/dx) = √y/(2√x)

At (4,1), we have (dy/dx) = 1/4.

12.

tan xy=x+y

Taking the derivative of both sides with respect to x:

y sec² (xy) (dy/dx) = 1 + y

(dy/dx) = (1 + y)/[y sec² (xy)]

At (0,0), we have (dy/dx) = 1/0, which is undefined.

5-12. Implicit differentiation Carry out the following steps.

a. Use implicit differentiation to find (dy/dx)

b. Find the slope of the curve at the given point.

5. x⁴+y⁴=2 ; (1,-1)

6. y² = 4x ; (1,2)

7. sin y=5x⁴-5 ; (1,π)

8. cos y=x ; (0, (π/2))

9. x=e^y ; (2, In 2)

10. y²+3x= 8 ; (1, √5)

11. √x-2√y = 0 ; (4,1)

12. tan xy=x+y ; (0,0)

ChatGPT

It would be more cost-effective to purchase the new machine, as the total costs associated with keeping the old machine are significantly higher. The old machine should be replaced with the new one.

Cost is the value of the resources or expenses incurred in the production or acquisition of goods or services. It includes the monetary value of raw materials, labor, machinery, utilities, rent, taxes, and any other expenses necessary for the production or acquisition of goods or services. Cost is an important factor in determining the price of goods and services, and businesses must carefully manage and monitor their costs in order to maintain profitability. In financial accounting, costs are classified into different categories such as direct costs, indirect costs, fixed costs, variable costs, and operating costs, among others.

To calculate the total costs in keeping the old machine and purchasing a new one, we need to calculate the costs associated with each option and compare them.

Option 1: Keep Old Machine

Total costs for keeping the old machine for 10 more years:

Operating expenses: $35,000 x 10 = $350,000

Residual value after 10 years: $13,000

Total costs: $305,000 - $178,000 + $350,000 - $13,000 = $464,000

Option 2: Purchase New Machine

Total costs for purchasing a new machine:

Purchase cost: $233,000

Operating expenses: $10,000 x 10 = $100,000

Salvage value after 10 years: $75,000

Total costs: $233,000 + $100,000 - $75,000 = $258,000

Based on these calculations, it would be more cost-effective to purchase the new machine, as the total costs associated with keeping the old machine are significantly higher.

Therefore, the old machine should be replaced with the new one.

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The area under the curve between two values on the x-axis represents the probability that the random variable falls within that range, with the total area under the curve being equal to 1.

In the graph, the PDF is represented by the smooth curve. The highest point on the curve corresponds to the most likely value of the random variable. In this case, the most likely value appears to be around x = 2.5.

The area under the curve between any two values on the x-axis represents the probability that the random variable falls within that range. For example, the probability that the random variable falls between x = 1 and x = 3 is equal to the area under the curve between those two values.

It's important to note that the probability density function must satisfy the following two conditions:

The total area under the curve must be equal to 1.

The probability of the random variable taking on any specific value is equal to zero, since the function only describes the likelihood of the variable taking on a range of values.

PDFs are often used in statistics to describe continuous distributions, such as the normal distribution, and to make statistical inferences about populations based on samples.

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The area of the new triangle would be 9.9c * m², so the answer is C.

What is triangle ?

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in mathematics, science, engineering, and other fields. Triangles can be classified based on the length of their sides and the size of their angles.

The area of a triangle is given by the formula A = (1/2) * b * h, where A is the area, b is the base, and h is the height.

Let the original base be b and the original height be h, so the original area is A = (1/2) * b * h = 10c * m²

If the base is increased by 10%, the new base is 1.1b, and if the height is decreased by 10%, the new height is 0.9h.

The new area can be calculated as follows:

new area = (1/2) * (1.1b) * (0.9h)

= 0.495bh

= 0.495 * 2A

= 0.99A

= 9.9c * m²

Therefore, the area of the new triangle would be 9.9c * m², so the answer is C.

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Answer:

Cosine theta equals x, sine theta equals y and tangent theta equals y over x,

Step-by-step explanation:

Cos0=sin (90 degrees -0)

Sin0= cos ( 90 degrees -0)

Answer:

sin θ = Perpendicular / Hypotenuse

Step-by-step explanation:

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse. sin(θ + 2nπ) = sin θ for every θ

Answer:

x = -2

Step-by-step explanation:

5(−2x−1) −5x + 2 = 27

-10x - 5 - 5x + 2 = 27

-15x - 3 = 27

-15x = 30

x = -2

So, the answer is x = -2

Answer:

Let's solve for x:

5(-2x-1) - 5x + 2 = 27

Distribute the 5:

-10x - 5 - 5x + 2 = 27

Combine like terms:

-15x - 3 = 27

Add 3 to both sides:

-15x = 30

Divide by -15:

x = -2

Therefore, the solution is x = -2.

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be 6 is the simplified expression.

With constantly shifting variables, calculations that mix joining, deleting, and random division must be made. If they banded together, they could do the following: A software, some information, and a math issue. A statement of truth contains formulas, elements, and arithmetic procedures like additions, subtractions, errors, and groupings. It is possible to assess and analyse both words and phrases.

Here,

Remember that for any real integer a,

=> √a² = a. We can simplify the equation as follows by using this property:

=> √3² x √2² = 6.

Multiplying results in:

3 x 2 = 6

Consequently, √3² x √2² = 6.

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In 5.8 years, $1,000 will amοunt tο $1,700 at 12%.

Simple cοmpοund interest is a quick and easy way tο find οut hοw much mοney has accrued interest. Interest is always charged οn the principal and is calculated at the same rate each periοd.

Every bank we depοsit mοney with pays interest οn that amοunt. Simple interest is οne οf many fοrms οf interest charged by banks. Sο, befοre delving further intο the idea οf simple interest, let's first clarify what a lοan is.

A lοan is an amοunt οf mοney that sοmeοne bοrrοws frοm a bank οr οther financial institutiοn tο cοver expenses. Mοrtgages, autο lοans, student lοans, and persοnal lοans are examples οf lοans.

According to our question-

Principal amοunt = $1,000

Future value = $1,700

Interest rate = 12%

Time = ?

Interest earned = Future value - Principal amοunt

= 1,700-1,000

= $700

Time = Interest earned / ( Principal x interest rate)

= 700/(1,000 x 0.12)

= 700/120

= 5.8 years

Hence, in 5.8 years, $1,000 will amοunt tο $1,700 at 12%.

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Answer:

A = 3, B = 4

Step-by-step explanation:

To find A and B, we need to use the fact that the solution to the system of equations is (2,-4).

Substituting x=2 and y=-4 into the first equation, we get:

A(2) + 2(-4) = -2

Simplifying this equation, we get:

2A - 8 = -2

Adding 8 to both sides, we get:

2A = 6

Dividing both sides by 2, we get:

A = 3

So, we have found that A is equal to 3.

Now, substituting x=2 and y=-4 into the second equation, we get:

5(2) - B(-4) = 26

Simplifying this equation, we get:

10 + 4B = 26

Subtracting 10 from both sides, we get:

4B = 16

Dividing both sides by 4, we get:

B = 4

So, we have found that B is equal to 4.

Therefore, the values of A and B that satisfy the system of equations are A=3 and B=4.

Answer: 3,348 cubic inches

Step-by-step explanation:

1. Since we know that volume= length x width x height, then we can plug our values into this equation.

2. So, we would do volume= 9 x 12 x 21.

3. 9 x 12 = 108, and 108 x 21 =2,268.

4. Now that we have both of the volumes, we have to add them together.

5. 1,080 + 2,268 = 3,348

6. The combined volume is 3,348 cubic inches.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Guide to follow:}[/tex]

[tex]\bullet\large\text{ Difference means to subtract}\\\bullet\large\text{ Product means to multiply}\\\bullet\large\text{ Quotient means to divide}\\\bullet\large\text{ Sum means to add}[/tex]

[tex]\huge\textsf{Now that we have that information out the way,}\\\\\huge\textsf{we can answer your given equation.}[/tex]

[tex]\huge\textsf{Question reads}[/tex]

[tex]\star\large\text{ Find a product of 3 and 2}[/tex]
[tex]\star\large\text{ Since, we are looking for the product of those two numbers (3 \& 2)}\\\large\text{we know that we have to \textsf{\underline{multiply}} them from each other. }[/tex]

[tex]\huge\textsf{What should the equation look like?}[/tex]

[tex]\large\text{3} \times \large\text{2}[/tex]

[tex]\huge\textsf{What is the easiest way to solve for this equation?}[/tex]

[tex]\large\text{3} \times \large\text{2}\\\rightarrow\large\text{3 + 3}\\\rightarrow\large\text{6}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\text{The product of 3 and 2 is: \boxed{\mathsf{6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The value of x is 50°. Triangles are unquestionably similar but not necessarily congruent if two of their angles are equal.

In a planar construction, an angle is a shape made up of two intersecting rays or lines. The vertex and the two rays, which are frequently referred to as an angle's sides, are the same termini for two rays. Two rays that share a terminal are referred to as the angle's sides and vertices in Euclidean geometry, respectively. Two rays can combine to create angles in the plane in which they are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what these are called.

This indicates that although not absolutely equal, the sides of the two triangles are obviously proportional.

The two triangles' respective sides must be equal on at least one side for the sides to be equal.

∠PTQ=∠PSQ

∠PTQ=50°

∠PSQ=50°

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A free semigroup is a collection of all possible finite sequences of symbols generated by a set of symbols, where the multiplication operation is concatenation of such sequences.

A free semigroup is a semigroup that is generated by a set of symbols, where the multiplication operation is defined as concatenation of finite sequences of symbols. In other words, a free semigroup is a collection of all possible finite sequences of symbols, where the multiplication operation is concatenation of such sequences.

The "free" in "free semigroup" comes from the idea that there are no restrictions on how the elements of the semigroup are combined, as long as they are concatenated in a finite sequence. There are no additional relations or rules imposed on the multiplication operation, which makes it "free" in the sense that the operation is determined solely by the set of symbols being used.

For example, consider the set of symbols {a, b}. The free semigroup generated by this set would consist of all possible finite sequences of the symbols a and b, including the empty sequence (). The multiplication operation would be defined as concatenation of sequences, such that (a, b)(b, a, b) = (a, b, b, a, b). Note that there are no additional rules or relations imposed on the multiplication operation.

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The height οf the weather ballοοn frοm the grοund is apprοximately 2156.5 feet.

Trigοnοmetry is branch οf mathematics that deals with  relatiοnships between angles and sides οf triangles. It is used tο sοlve prοblems invοlving right triangles and tο mοdel and analyze periοdic phenοmena, like waves and οscillatiοns.

1)  We can use trigοnοmetry tο sοlve fοr the length οf the ladder. Let's call the length οf the ladder "x".

tan(63) = height/4

height = 4*tan(63)

Next, we can use the Pythagοrean theοrem tο find the length οf the ladder:

x² = height² + 4²

x² = (4*tan(63))² + 4²

x² = 176.4

x = √(176.4)

x ≈ 13.3 feet

Therefοre, the length οf the ladder is apprοximately 13.3 feet.

2)  We can use trigοnοmetry tο sοlve fοr the height οf the weather ballοοn. Let's call the height οf the ballοοn "h".

tan(53) = h/1680

h = 1680*tan(53)

h ≈ 2156.5 feet

Therefοre, the height οf the weather ballοοn frοm the grοund is apprοximately 2156.5 feet.

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Answer:

80 miles per hour

Step-by-step explanation:

The unit rate in this problem is 1 hour.

To find the unit rate, we have to find a factor for 1 hour and 1 [tex]\frac{1}{4\\}[/tex] hours.

A common factor would be  [tex]\frac{1}{4\\}[/tex]  of an hour. Since  [tex]\frac{1}{4\\}[/tex]  is 1 [tex]\frac{1}{4\\}[/tex] divided by 5, we also have to divide 100 miles by 5, which is 20.

So now we have that Blake's car can travel 20 miles in [tex]\frac{1}{4\\}[/tex] of an hour.

We want to know how many miles it can travel in 1 hour. If we multiply [tex]\frac{1}{4\\}[/tex] by 4, we get one hour. Likewise, we multiply 20 miles by 4 to get 80 miles travel in one hour.

Answer:

-6

Step-by-step explanation:

-4(3-1) + 2

=> -4(2) + 2

=> -8 + 2

=> -6

Hence, in answering the stated question, we may say that side every probability time it is tossed five times is 1/16, which corresponds to option D.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

When a fair coin is tossed five times, the probability of obtaining the same side every time is the same as getting all heads or all tails.

Because the chance of receiving heads or tails on one toss is 1/2, the chance of getting heads or tails on five independent tosses is (1/2)5 = 1/32.

The likelihood of receiving all heads or all tails is the sum of the probabilities of receiving all heads and all tails, which is:

P(all heads or all tails) = P(all heads Plus P(all tails) = (1/32 + 1/16)

As a result, the theoretical probability of the coin landing on the same side every time it is tossed five times is 1/16, which corresponds to option D.

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Answer: [tex]x=\frac{19}{5}[/tex]

Step-by-step explanation:

5x + 1 = 20

Move then constant to the right-hand side and change its sign

5x = 20 - 1

Subtract the numbers

5x = 19

Divide both sides of the equation by 5

[tex]x=\frac{19}{5}[/tex]

Periodic function is a function that repeats its values at regular intervals.

What is periodic function?

A linear function is a mathematical function that can be represented by a straight line on a graph. It is a function that has a constant rate of change, meaning that the change in the output (dependent variable) is directly proportional to the change in the input (independent variable). The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the value of the function when the input is zero).

For example, the function f(x) = 2x + 3 is a linear function. Its graph is a straight line with a slope of 2 and a y-intercept of 3. As the input (x) increases by 1, the output (y) increases by 2, which means that the rate of change is constant.

Linear functions are widely used in mathematics, science, and engineering to model and analyze relationships between variables that exhibit a constant rate of change, such as velocity versus time, or cost versus quantity.

A periodic function is a mathematical function that repeats its values at regular intervals or periods. This means that the value of the function repeats after a certain amount of input (independent variable).

For example, the trigonometric functions such as sine, cosine, and tangent are periodic functions. The sine function has a period of 2π radians (or 360 degrees), which means that its value repeats after every 2π radians of input. Similarly, the cosine function also has a period of 2π radians.

Periodic functions are commonly used to model phenomena that repeat regularly over time, such as the motion of a pendulum, the tides in the ocean, or the seasonal variation in temperature. They are also used in engineering, physics, and many other fields to analyze and design systems that exhibit periodic behavior.

There fore we can say that,Periodic function is a function that repeats its values at regular intervals.

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Angle BCD is equal to 65.5°.

What is the formula for the interior angle of a regular polygon?

The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the amount of an interior angle.

It is given that B, A, and D are three consecutive vertices of a regular 8-gon.

The interior angle of a regular 8-gon (Octagon) is 135°.

It is given that C is a vertex of a regular heptagon(7-gon) whose one side is AB.

C, B, and D are at equal distances from A.

So A is the center and C, B, and D are points on the circle.

BD is the cord that is making an angle of 135° at A(center).

At the circumference, the cord makes half the angle.

So angle BCD is equal to 135/2 = 65.5°.

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Answer:

168 = 18 * x + 12* 2x

Step-by-step explanation:

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