The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF. Work out the angle x

The Diagram Shows A Regular Pentagon, ABCDE, A Regular Octagon, ABFGHIJK, And An Isosceles Triangle,

Answers

Answer 1

Answer:

x is 31.5°

Step-by-step explanation:

Here, we have each interior angle of a regular octagon = 135°

Each interior angle of a regular pentagon = 108°

Therefore, 135° + 108° + ∡B = 360°

Hence, ∡B = 360° - (135° + 108°) = 117°

Since, AB = BC = BF ( sides of a regular polygons (octagon and pentagon))

Hence, ΔCBF is an isosceles triangle and ∡x = ∡CFB  from which we have;

∡x + ∡CFB + 117° = 180°

∴  ∡x + ∡CFB = 180° - 117° = 63°

Hence, ∡x = 63° - ∡CFB = 63° - ∡x which gives

2·∡x = 63°

Hence, ∡x = 63°/2 = 31.5°

∡x = 31.5°.


Related Questions

halp me do this pleeeeeasssseee​

Answers

Answer:

Step-by-step explanation:

The question isn't clear...

Determinado automovel, apos sua compra, perde 10% do valor ano a ano nos 3 preimeiros anos. Calcule o valor do automovel ao final desse periodo sabendo que ele foi comprado por R$80.000

Answers

Answer:

The value of the car after 3 years is R$58.320.

O valor do carro ao final desse período é R$58.320.

Step-by-step explanation:

The value of the car after t years is given by the following equation:

[tex]V(t) = V(0)(1-r)^{t}[/tex]

In which V(0) is the initial value and r is the yearly depreciation rate.

In this question, we have that:

[tex]V(0) = 80000, r = 0.1[/tex]

So

[tex]V(t) = V(0)(1-r)^{t}[/tex]

[tex]V(t) = 80000(1-0.1)^{t}[/tex]

[tex]V(t) = 80000(0.9)^{t}[/tex]

Value of the car at the end of 3 years:

[tex]V(3) = 80000(0.9)^{3} = 58320[/tex]

The value of the car after 3 years is R$58.320.

O valor do carro ao final desse período é R$58.320.

The Duquesne Incline in Pittsburgh, Pennsylvania, has an angle of elevation of 30º. The track has a length of about 800 feet. Find the height of the incline.

Answers

The height of the Duquesne Incline in Pittsburgh, Pennsylvania, is approximately 400 feet.

To find the height of the incline, we can use trigonometry, specifically the sine function.

Let's consider the triangle formed by the incline track, where:

The angle of elevation (angle between the incline track and the ground) is 30 degrees.

The length of the incline track (base of the triangle) is about 800 feet.

We want to find the height of the incline (the side of the triangle opposite the 30-degree angle).

Using the sine function, we have:

[tex]sin(angle) = opposite\ side / hypotenuse[/tex]

In this case, the angle is 30 degrees, the opposite side is the height (h) of the incline, and the hypotenuse is the length of the incline track (800 feet).

So, the equation becomes:

[tex]sin(30^o) = h / 800[/tex]

h = 800 * 0.5

h = 400 feet

Therefore, the height of the incline is approximately 400 feet.

Learn more about trigonometry here:

https://brainly.com/question/32391262

#SPJ12

An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet what is the volume of the tank

Answers

Answer:

15707.96

Step-by-step explanation:

Answer:

5000pi ft^3 (exactly) or 15,708 ft^3 (approximately)

Step-by-step explanation:

V = (pi)r^2h

r = radius = diameter/2

r = 20 ft/2 = 10 ft

V = (pi)(10 ft)^2(50 ft)

V = 5000(pi) ft^3

V = 5000(3.14159) ft^3 = 15,708 ft^3

Answer: 5000pi ft^3 (exactly) or 15,708 ft^3 (approximately)

Language arts test is worth 100 points there is a total of 26 question There are spelling words question that I wasn't points each in vocabulary words question worth five points each how much of each type of question are there

Answers

Answer: There are 10 two points and 16 five points questions.

Step-by-step explanation:

This is the detailed question:

A language arts test is worth 100 points. There are a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question is there?

Let y = the number of 2 points questions

Let z = the number of 5 points questions

y + z = 26 ......... i

2y + 5z = 100 ........ ii

Multiply equation i by 2

Multiply equation ii by 1

2y + 2z = 52 ......... iii

2y + 5z = 100 ....... iv

Subtract iv from iii

-3z = -48

z = 48/3

z = 16

Since y + z = 26

y = 26 - 16

y = 10

y = 10 two points questions

z = 16 five points questions

There are 10 two points and 16 five points questions.

Train A has a speed 20 miles per hour greater than that of train B. If train A travels 270 miles in the same times train B travels 210 miles, what are the speeds of the two trains?

Answers

Answer:

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70 miles per hour 

Step-by-step explanation:

Let

speed of train B = a

speed of train A = a + 20

Recall

speed = distance/time

The travel time is same for both train. Therefore, let us make time subject of the formula in the speed equation.

Time = distance/speed

270/a + 20 = 210/a

cross multiply

270a = 210(a + 20)

270a = 210a + 4200

270a - 210a = 4200

60a = 4200

divide both sides by 60

a = 4200/60

a = 70

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70  miles per hour

Solve for x in the following figure.

Answers

Answer:

x=80°

Step-by-step explanation:

supplementary angles equal 180°

∠J=80

80+x+20=180

100+x=180

x=80

I don’t understand this question please help

Answers

Answer:

Between 3² and 4⁴

Between 3 and 4

Step-by-step explanation:

Number 15 is between between 3² and 4⁴

While √15 = 3.8 72 is between 3 and 4.

The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52m ^ 2 . Find the dimensions of the rectangle.

Answers

The dimension of the rectangle is 8m by 6.5m respectively

Area of a rectangle

The formula for calculating the area of a rectangle is expressed as;

A =lw

If the length of a rectangle is 5 m less than twice the width, then;

l = 2w - 5

Substitute

A = w(2w-5)

52 = 2w² - 5w

2w² - 5w = 52

2w² - 5w - 52 = 0

(2w−13)(w+4)=0

Step 2: Set factors equal to 0.

2w−13=0 or w+4=0

w =13/2 or 6.5m

Determine the length

l = 2w - 5

l = 2(6.5) - 5

l = 13 - 5

l =8m

Hence the dimension of the rectangle is 8m by 6.5m respectively

learn more on area of rectangle here: https://brainly.com/question/25292087

#SPJ1

A circle has centre (0, 0) and it passes through the point (5, -3)
Find the radius of the circle, in surd form.

Answers

Answer:

radius = [tex]\sqrt{34}[/tex]

Step-by-step explanation:

The radius r is the distance from the centre to a point on the circle.

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, - 3)

r = [tex]\sqrt{(5-0)^2+(- 3-0)^2}[/tex]

  = [tex]\sqrt{5^2+(-3)^2}[/tex]

  = [tex]\sqrt{25+9}[/tex]

  = [tex]\sqrt{34}[/tex]

Samuel has a bell box that contains
4 door bells, 3 office bells, and 7 big
bells. Without looking, Samuel
Chooses a bell from the box, what is the
relative frequency probability the
when he selects a doorbell?



Answers

Answer:

4 out of 14

Step-by-step explanation:

there is only 4 door bells and 14 bells in total

Find the quotient.

3 divided by 3636

A. 1,212
B. 1,202
C. 122
D. 112
E. 102

help asap!!

Answers

The answer to the question is B

What is
15,379 times 51





Answers

Answer:

784329

Step-by-step explanation:

the answer is : 784329

rectangle with length 11 1/2 in. and width 8 in The area of this rectangle is____________
in2.

Answers

Answer:

Step-by-step explanation:

look, area = length x width

so that means that the area of this rectangle is

= 11 1/2 * 8

= 23/2 * 8

= 23 * 4 (simplified)

= 92 in^2

Answer:

[tex]92in.^{2}[/tex]

Step-by-step explanation:

Area of a rectangle= L×W

If length= 11[tex]\frac{1}{2}[/tex]in. and width= 8in.,

∴ Area = 11[tex]\frac{1}{2}[/tex]in. × 8in.

           = [tex]\frac{23}{2}[/tex] × [tex]\frac{8}{1}[/tex] [tex]in.^{2}[/tex]

           = (23 × 4) [tex]in.^{2}[/tex]

           = 92[tex]in.^{2}[/tex]

Hope this helps!!!

 

5x to the power of 2 =25x to the power of 2​

Answers

Answer:

1:5

Step-by-step explanation:

5x² = 25x²

Divide both sides by 5x²

5x²/5x² = 25x²/5x²

1:5

For circle P , find QN if LM = ON = 7.

A.
3.5
B.
7.5
C.
14
D.
21

Answers

Answer:

A

Step-by-step explanation:

You are just going to have to divide the 7 which gives you 3.5

3. If the legs of an isosceles right triangle are 10 inches long, approximate the length of
the hypotenuse to the nearest whole number​

Answers

Answer:

Using the Pythagorean theorem for isosceles right triangle, the length of  the hypotenuse is sqrt( 2 x 10^2) = ~14.1 in

Hope this helps!

:)

What is the probability of the complement of rolling a number less than 5 by using a six-sided die? StartFraction 1 over 6 EndFraction One-third Two-fifths Two-thirds

Answers

Answer:

1/3 = 0.3333 = 33.33%

Step-by-step explanation:

In the six-sided die we have 6 possible values, from 1 to 6.

To roll a number less than 5, the options are: 1, 2, 3 or 4.

We have 4 options, so the probability is P = 4/6 = 2/3

To find the complement of this probability, we just need to calculate 1 minus the probability, so we have that:

complement = 1 - P = 1 - (2/3) = 1/3 = 0.3333 = 33.33%

(We could also find the probability of rolling 5 or 6, which is the complement of rolling less than 5)

Answer:

1/3

Step-by-step explanation:

I took the test

A cell phone and phone case cost $110 in total. The cell phone costs $100 more than the phone case. How much was the cell phone?

Answers

Answer:

105

Step-by-step explanation:

if both together cost $110

and the cell phone cost 100 more than the phone case, we need to find the cost for the phonecase

and it's 105

hope this helped:D

brainliest is appreciated if u want

Answer:

$105  r e  

Step-by-step explanation:

Maxine and Sammie have the same size lawn. Maxine can mow the lawn in 24 minutes and Sammie can mow the lawn in 36 minutes. At what time will Sammie have twice as much lawn to mow as Maxine?

Maxine and Sammie have to also mow their parking strips that are the same size. Maxine can mow the parking strip in 6 minutes and Sammie can mow the parking strip in 9 minutes. At what time will Sammie have twice as much grass to mow as Maxine?

Answers

Answer: A) 18.2 minutes

B) 4.5 minutes.

Step-by-step explanation:

A) Maxine can mow one lawn in 24 minutes, so the rate of work is:

1/24 of the lawn per minute.

Sammie can mow one lanw in 36 minutes, so the rate of work is:

1/36 of the lawn per minute.

The amount of the lawn that each has left to lawn by the minute x is:

Maxine = 1 -(1/24)*x

Sammie = 1 - (1/36)*x

we want to find the value of x such that:

2*(1 - (1/24)*x) = 1 - *(1/36)*x

which means that the amount that Sammie has left is two times the amount that Maxine has left to mow.

2 - (1/12)*x = 1 - (1/36)*x

2 - 1 = (1/12 - 1/36)*x

1/0.055 = x = 18.2

by the minute 18.2

B) Similar to before, here the rates are:

For Maxine, R = 1/6

For Sammie, R = 1/9

The amount they have left to mow by minute x is:

Maxine = 1 - (1/6)*x

Sammie = 1 - (1/9)*x

We want to solve, similar to before.

2( 1 - (1/6)*x) = 1 - (1/9)*x

2 - (1/3)*x = 1 - (1/9)*x

2 - 1 = (1/3 - 1/9)*x

1 = (2/9)*x

1*9/2 = x = 4.5

So here the solution is 4.5 minutes.

Answer:

`He will never have more grass to maw than Maxine because they do the strips the same size, and their yard is the same size, so they never have more to mow than the other person.

Explanation:

May you pls mark me as brainliest I am new to the program.

What is the axis of symmetry for the function f(x)=7-4x+x2?
X=-3
x = -2
x = 2
x= 3

Answers

Answer:

x = 2

Step-by-step explanation:

C on edg 2020

The axis of symmetry of f(x) = 7-4x + x^2 is x = 2

How to determine the axis of symmetry?

We have:

f(x) = 7-4x + x^2

Differentiate the function

f'(x) = -4 + 2x

Set the function to 0

-4 + 2x = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2

Hence, the axis of symmetry of f(x) = 7-4x + x^2 is x = 2

Read more about axis of symmetry at:

https://brainly.com/question/15709421

#SPJ9

How would you find the area of this?

Answers

the formula for it is bh , multiply 14 by 24 and the answer is 336

Help meeee!!! Whats x

Answers

Answer:

74°

Step-by-step explanation:

The angle on a line = 180°

therefore:.

x + 106° = 180°

x = 180° - 106°

x = 74°

Answer: 74 degrees.

Step-by-step explanation:

Angles on the same side of a line add to 180.

The angle measure of 106 and the angle measure of x lie on the same side of the line WZ, so you can add them both to get 180:

106 + x = 180

x = 74

Write the number for seventy-five million three hundred thousand

Answers

The answer is 75,300,000 hope this helps.

3. The measure of each inscribed
angle is equal to( )times the
measure of the intercepted arc.
a. 1/2
b. 1
c. 2

Answers

Answer: A. 1/2

Step-by-step explanation:

7h=-(2h-18)7h=−(2h−18) Solve for h

Answers

Answer:

h=2

Step-by-step explanation:

7h=−(2h−18)

Distribute the minus sign

7h = -2h +18

Add 2h to each side

7h +2h = -2h+2h +18

9h = 18

Divide each side by 9

9h/9 =18/9

h =2

Answer:

h = 2

I got it right on Kahn Academy

What is the total surface area of the cylinder to the nearest square inch ? Use 3.14 for pi

Answers

Answer:

1,300.62

Step-by-step explanation:

The formula for a cylinder is A= 2 pi r h +2 pi r^2

Which is the best estimate for the liquid volume of a small carton of milk?

Answers

Answer:

Step-by-step explanation:

helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

The answer is C

Step-by-step explanation:

Answer: The answer is C.

hope you do good on quiz! :D

Grace hit 12 balls in the batting cage out of 20 pitches. Tomorrow she is going to go to the same batting cage and get 30 pitches.
Use experimental probability to predict how many of the 30 pitches she will hit.

Answers

Answer:

she is expected to hit 18 out of the 30 pitches

Step-by-step explanation:

In this question, we are required to use experimental probability to make a prediction.

From the hits she has today, we can estimate the number of hits she might be getting tomorrow.

Since she made 12 hits out of 20 today, the probability that she has a hit will be 12/20 = 3/5

Now if she is having 30 pitches tomorrow, the expected number of hits would be the probability of getting a hit multiplied by the total number of pitches.

That would be 3/5 * 30 = 18 pitches

Other Questions
Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in asquare grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of10th avenue and Estreet. who would win and why? A virus is ________ a cell. A)bigger thanb) the same size asC)smaller thand)another word for Find two numbers for which the sum is 101 and the difference is 47 Round to nearest hundreth What factors do 6 and 12 have in common? Which muscle is located on the back of the lower leg?a. Quadricepb. Gluteus Maximusc. Hamstringd. Gastrocnemius An athlete is working out in the weight room. He steadily holds 50 kilograms above his head for 10 seconds. Which statement is true about this situation? many organize a classroom party. there are 20 of cold drinks at the party, 13 of which contain diet Pepsi, what is the probability that randomly selected drink will be a diet Pepsi? answer key Three words that describe peninsula 1.) What three oceans border North America? Which one of the following is NOT a power of the legislative branch What is a set of ordered pairs What is the formula for velocity??? What does controversy mean? Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude? match the type of graph with its description Why do animals have adoptions there's a competition for the same food sources be ecosystems can change see special body parts and behaviors I need for survival d all of the above Choose a synonym for the underlined homonym (a word with two or more meaningsThe dissection of the frog was completely gross.a. totalb. wholec. disgustingd. invitingPlease select the best answer from the choices providedB.D Can someone help me with this? ;^; how many wishes did prince charmant really ask for by the end of the story?