an irregular convex hexagon has 5 exterior angle measures, what is the measure of the interior angle

Answers

Answer 1

The required measure of the interior angle of the given irregular convex hexagon is equal to 135 degrees.

The sum of the exterior angles of any polygon, including a hexagon, is always 360 degrees.

Each exterior angle of a convex polygon is supplementary to its corresponding interior angle.

Sum of each exterior angle and its corresponding interior angle is always 180 degrees.

Let x be the measure of the sixth exterior angle of the hexagon, then the sum of all six exterior angles is,

⇒ 360 = 5a + x

where a is the measure of each of the other five exterior angles.

Rearrange this equation to solve for x,

⇒ x = 360 - 5a

Since each exterior angle is supplementary to its corresponding interior angle,

x + a = 180

Substituting x = 360 - 5a into this equation, we get,

⇒ 360 - 5a + a = 180

Simplifying this equation, we get,

⇒4a = 180

⇒ a = 45

Each of the other five exterior angles has a measure of 45 degrees.

The sum of each interior angle and its corresponding exterior angle is 180 degrees,

so the measure of each interior angle of the hexagon is,

180 - 45 = 135 degrees.

Therefore, the measure of the interior angle of the irregular convex hexagon is 135 degrees.

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Related Questions

A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.

Answers

Answer:

64 Bottles

Step-by-step explanation:

that is the procedure above

A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds

What is the difference of 620 and 89.7?

Answers

Answer: 530.3

Step-by-step explanation:

Difference means to subtract

620-89.7=530.3

Answer:

530.3

Step-by-step explanation:

You want to subtract 620-89.7. If you want to use the standard algorithm you have 620.0-89.7. You "borrow" from the 2 in the tens place, then "borrow" from the ones place. To subtract 10-3 tenths. Then you subtract the ones place which is 9-9=0 ones. Now you subtract 62-8=53 tens. So you have 530.3 as the difference.

1) Name 2 decimals whose sum is less than 1.

Answers

The decimals whose sum is less than 1 are 0.4 and 0.5.

How to illustrate the expression?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

As an illustration, the expression x + y has the terms x and y with an addition operator between them. In this case, the decimals whose sum is less than 1 are 0.4 and 0.5 as the sum is 0.9.

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Which is greater, 2 5/6 hours or 2.8 hours?

Answers

Answer:

2.8 hours

Step-by-step explanation:2.8 hours is greater because 2.8 hours is 3 hours and 20 minutes.

2 5/6 is not a full 3 hours, its just 2 hours and 50 minutes

Find f(g(3)) for the functions f(x) =3x+8 and g(x) =-x^3

Answers

We are given:

f(x) = 3x + 8

g(x) = -x³

__________________________________________________________

The Concept:

We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.

Finding f(g(3)):

Finding g(3):

g(x) = -x³

g(3) = -(3)³

g(3) = -27

Finding f(g(3)):

f(x) = 3x + 8

f(g(3)) = 3(g(3)) + 8

f(g(3)) = 3(-27) + 8

f(g(3)) = -81 + 8

f(g(3)) = -73

Hence, f(g(3)) = -73

A school band has `70` students.



`50\%` of them are sixth graders, `30\%` are seventh graders, and the rest are eighth graders.



How many band members are 6th graders and how many are 7th grader

Answers

6th - 35 members
7th - 21 members
A school band has `70` students.`50\%` of them are sixth graders, `30\%` are seventh graders, and the

Answer:

Step-by-step explanation: Half of 70 is 35 so there are 35 Sixth-grader and then you do 70 multiplied by 30% and get 21

Which equation descibes the pattern shown in the table?

Which equation descibes the pattern shown in the table?

Answers

The answer is D. If you put all of the values into the equation the only one that works for all of them is D

What is the whole story about? An uncomfortable bed and Tell tale heart

Answers

answer →a murder most heinous and a narrator who fights his insanity

explanation: I read the book in cass

HELP!!!!!!!!!!!!!!!!!!!!!!!!

HELP!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(n) represent the total cost of shoe rentals for n games, hence:

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

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Find the zeros and give the multiplicity of

F(x)= x^2(x^2+18x+81)

Answers

Answer:

Step-by-step explanation:

To find the zeros of F(x), we need to solve the equation F(x) = 0.

F(x) = x^2(x^2+18x+81)

The expression F(x) can be factored as:

F(x) = x^2(x+9)^2

So, the zeros of F(x) are x = 0 and x = -9, with a multiplicity of 2 for both.

The factor x^2 contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = 0 but does not cross it. The factor (x+9)^2 also contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = -9 but does not cross it.

To summarize, the zeros and their multiplicities for F(x) are:

x = 0 (multiplicity 2)

x = -9 (multiplicity 2)

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, one after the other, find the probability that all of them are acceptable. Consider these as independent.

Answers

Answer:

\(Probability = 34.3\%\)

Step-by-step explanation:

Given

Represent acceptable with A and defective with D

\(A = 70\%\)

\(B = 30\%\)

Required

Determine the probability that three selected are acceptable

This can be represented as:

\(Probability = AAA\)

Substitute values for A

\(Probability = 70\% * 70\% * 70\%\)

\(Probability = 34.3\%\)

The outside diameter of an electrical conduit is 6.3 centimeters. The thickness of the conduit is 0.4 centimeter. Find the inside diameter of the conduit. Carry the answer to one decimal place.​

Answers

Answer:

  5.5 cm

Step-by-step explanation:

You want the inside diameter of a conduit with an outside diameter of 6.3 cm and a wall thickness of 0.4 cm.

Walls

There is a wall at each end of the inner diameter, so it will differ from the outside diameter by twice the wall thickness:

  6.3 cm - 2×0.4 cm = 5.5 cm

The inside diameter is 5.5 cm.

The outside diameter of an electrical conduit is 6.3 centimeters. The thickness of the conduit is 0.4

A pair of equations is shown below:
y=7x- 8
y= 5x-2
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)
Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points

Answers

Answer:

x=3, y=13. (3, 13).

Step-by-step explanation:

7x-8=5x-2

7x-5x-8=-2

2x-8=-2

2x=-2+8

2x=6

x=6/2=3

y=5(3)-2=15-2=13

Answer:

given y=7x-8 i

y=5x-2 ii

Step-by-step explanation:

equating equation i and ii which is i=ii

7x-8=5x-2

7x-5x= -2+8

2x=6

x=6÷2

x=3

now

putting the value of xbin equation i

y=7x-8

y=7×3-8

y=21-8

y=13

hence the value of x and y is 3 and 13 respectively

Find the value of L that Will Maximize the profit Q=L²e^0.01L​

Answers

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

Finding the value of L that will maximize the profit

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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A survey of 800 randomly selected adults in a certain country found that 82% believed that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
a. Verify the Central Limit Theorem conditions.
b. Find a 95% confidence interval for the proportion of adults in the country who believe that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
c. Would a 90% confidence interval based on this sample be wider or narrower than the 95%
interval? Give a reason for your answer.

Answers

a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

How to Verify the Central Limit Theorem conditions.

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins

Answers

A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins.

112 feet

Evaluate -x+23y if x=9 and y=2

Answers

Answer:

The answer is 37

whats 2 2/9 times 2 1/5

Answers

Answer:

1/45

Step-by-step explanation:

Answer:

8/45

Step-by-step explanation:

2 *  2/9 * 2 * 1/5

2 * 2.9 * 2/5

2 * 2*2/9*5

=8/45

Please help me understand this handwriting can some pls re write and label I DONT UNDERSTAND CURSIVE :(

Please help me understand this handwriting can some pls re write and label I DONT UNDERSTAND CURSIVE

Answers

Answer:

7:01

29%

Doyan of low

Shiman 1-R-1

Flous 1-1 Gambe 1-4-20

12 dual purpose

Martins 1-2-3 Flores 1-2, 1-3, 14

Gamba 2-1-5

Custand 1-4, 2-1

Conditions " humanitarian groups Salahiel 1-1-1, 1-1-2, 1-2-3 1-R-5, 2-L-2, 2-L-3, 2-14, 2-1-5, 2-RI

Flores 1-30

Munting 1-2-4

Gumbon 1-1-3 CDP 1-1-3

Status oppose ending 742 Montoya 1-1, 1-2, 1-3

federal courts challenge

Gamboa 1-R-2 Custom 1-7

CDP 1-L-36, 1-2-4

de Vogue 1-2-1, 2-1-5, 2-L-6

7 expulsions at boders

root causes textul Amer.

Cop 1-L-34, 1-1-2, 1-R-4

Border Report 1-2

CDP 1-R-2, 1-R-3 Montoya 1-8

Custarda 2-2

=

CLOSE

Hopes this helps :)

(8)
Tricia used 2 bags of sugar to bake some cupcakes.
She used of another bag of sugar to make some macaroons.
How many bags of sugar did she use altogether?
bags of sugar​

Answers

Answer:

She used 3.

Step-by-step explanation:

You have 2 bags.

You have another bag.

You use all of them.

How many did you use altogether?

3.

Tricia used 2.5 bags of sugar altogether.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. It can be as simple as a single number or variable, or it can be more complex, involving multiple terms and operations.

Tricia used 2 bags of sugar to make cupcakes and used 1/2 of another bag of sugar to make macaroons.

Therefore, the total amount of sugar she used is:

2 + 1/2 = 2.5 bags of sugar.

So, The number of bags Tricia used was 2.5 bags of sugar altogether.

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Help meee I don’t understand

Help meee I dont understand

Answers

The bottom half are where your answers are
Help meee I dont understand

The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
O The function is increasing for all real values of x
where
x < 0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1 O The function is decreasing for all real values of x
where
x < 1.5.

Answers

The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.

Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).

The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.

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Polygon A is similar to Polygon B.
Find the perimeter of Polygon B.
24
A
PA = 128
15
B
PB = [?]

Polygon A is similar to Polygon B.Find the perimeter of Polygon B.24APA = 12815BPB = [?]

Answers

Answer:

\(P_{B}\) = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is

\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )

8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )

\(P_{B}\) = 80

Refer to the given terms . A pattern defines the relationship between the first two terms . Determine the relationship and identify the missing term of the second pair , such that both the pairs are analogous . AZP : ZAR :: TXK :

Refer to the given terms . A pattern defines the relationship between the first two terms . Determine

Answers

The missing term in the second pair is YUL.

To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.

If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.

So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:

T + 1 = U

X + 1 = Y

K + 1 = L

Therefore, the missing term in the second pair is YUL.

The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.

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What is the range of the function shown on the graph

What is the range of the function shown on the graph

Answers

Answer:

-2<=y<=-7

Step-by-step explanation:

(h+3)2 find the square. Simplify your answer.

Answers

(h+3)² simplified is:(h+3)² = h² + 6h + 9

What is binomial?

Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.

The expression (h+3)² is a binomial squared. When we square a binomial, we use the formula:

(a+b)² = a² + 2ab + b²

where a and b are any numbers or variables. In this case, our binomial is (h+3), so we can use the formula with a=h and b=3:

(h+3)² = h² + 2h3 + 3²

The first term, h², comes from squaring the h in the binomial. The second term, 2h3, comes from multiplying the two terms in the binomial together and then doubling the result. Finally, the third term, 3^2, comes from squaring the 3 in the binomial.

Simplifying the expression, we can combine like terms. We have h² as the first term, 23h as the second term, and 3^2 as the third term. 23h is equal to 6h, so we can rewrite it as:

(h+3)² = h² + 6h + 9

And that is the simplified form of the expression (h+3)².

Therefore,  (h+3)² simplified is:(h+3)² = h² + 6h + 9

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in a bag if marbles 1/2 are blue 1/6 are green 1/12 are yellow you pick a marble with out looking what color marble are you most likely going to choose

Answers

Answer: Blue

Step-by-step explanation:

Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.

I hope it helps!

PLS HELO THANK YOUUUUU

PLS HELO THANK YOUUUUU

Answers

Answer:

divide 500 by 125.

You get 4x = 568

Answer is 142

Happy Learning

Answer:

142

Step-by-step explanation:

For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $537,000 worth of assets after t years, that depreciate at 17% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 9 years?

a
Vo = $537,000, b = 0.17, and the value after 9 years is $0.45

b
Vo = $537,000, b = 0.83, and the value after 9 years is $100,386.92

c
Vo = $537,000, b = 1.17, and the value after 9 years is $98,291.76

d
Vo = $537,000, b = 0.83, and the value after 9 years is $91,290.00

Answers

Answer:

I think it is D

Step-by-step explanation:

The sum of three consecutive even integers is
312. Find the Integers.

Answers

Answer:

104, 105, 106

Step-by-step explanation:

Consider three consecutive integers.  If the first is x then the second is 1 more than x (or x+1) and the third is x+2

The sum of these three integers is x + x+1 + x+2 and is known to be 312, so

x + x+1 + x+2 = 312, gather like terms

3x + 3 = 312, subtract 3 from both sides

3x = 309, divide both sides by 3

x = 104, so the integers are

104, 105, 106

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