A rectangular octagon is shown in the ceiling of a cathedral. The radius is 10.5 feet and the perimeter is 64 feet. The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet. What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot. feet Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot. square feet

Answers

Answer 1

Answer:

9.7 , 310.4

Step-by-step explanation:

length of each side = 64/8=8

using theorem Pythagoras

A²=10.5² – (8/2)²

A=9.7 ft

area of triangle

1/2×8×9.7=38.8

area of octagon

38.8×8=310.4

Answer 2

The Length of the octagon  is 9.7 and the area of octagon is 310.4.

Length and  area of octagon

Length of octagon

Length of each side = 64/8

Length of each side =8

Pythagoras theorems

A²=√10.5² – (8/2)²

A²=√110.25 – 16

A²=√94.25

A=9.7 ft

Area of octagon

Area of triangle=1/2×8×9.7

Area of triangle=38.8

Area of octagon=38.8×8

Area of octagon=310.4

Therefore the Length of the octagon  is 9.7 and the area of octagon is 310.4.

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Related Questions

Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one sentence summary comparing the blue line to the black line. Hint: Find the y-intercept. Then count up and over (y/x) to the next point on the line to determine the slope.

Answers

Answer:

y=1/2x+2(2 is the y-intercept)

The blue line and black line have the same y-intercept, but the black line has a slope 1/6 greater than the blue line.

Hope it helps <3

Answer:

[tex]\boxed{y=\frac{1}{2} x+2}[/tex]

Step-by-step explanation:

Let's take any of the coordinates of blue line to find the slope

The coordinates are (4,4) and (0,2)

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{2-4}{0-4}[/tex]

Slope = [tex]\frac{-2}{-4}[/tex]

Slope = m = 1/2

Y-intercept = b = 2 (Because here x= 0)

So, the slope intercept equation becomes:

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{1}{2} x+2[/tex]

What is the next term of the arithmetic sequence?
6,2, -2, -6,

Answers

Answer:

-10

Step-by-step explanation:

-4 between each number

State whether the data described below are discrete or continuous, and explain why The durations of movies in minutes A Choose the correct answer below OA. The data are continuous because the data can take on any value in an interval. St O B. The data are continuous because the data can only take on specific values OC. The data are discrete because the data can take on any value in an interval. O D. The data are discrete because the data can only take on specific values. G D

Answers

Answer:

D. The data are discrete because the data can only take on specific values.

Step-by-step explanation:

Continuous variables are variables that can take on any value in an interval. Examples of continuous variables are length, time, etc.

Discrete variables on the other hand are variables that can only take on specific values.

The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.

The correct option is D.

PLZZZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEE what is the factorization of the polynomial graphed below? assume it has no constant factor. write each factor as a polynomial in descending order.

Answers

Answer:

(x-5)(x-8)(x+2)=0

Step-by-step explanation:

first look at the x intercept to find the factor

x:-2,5,8

x=-2 then x+2=0

x=5 then x-5=0

x=8 then x-8=0

(x-5)(x-8)(x+2)=0

check for y in the polynomial when x=0

x^3-11x^2+14x+80

x=0 y=80 ( correct according to the graph

2/3a= -15 - a Please Explain

Answers

Hi there! :)

Answer:

a = -9

Step-by-step explanation:

Starting with:

2/3a = -15 - a

Solve for 'a' by isolating the variable:

2/3a = -15 - a

On the right-hand side of the equal sign, make 'a' have a common denominator of 3 to make the simplifying easier:

2/3a = -15 - 3/3a

Add 3a/3 to both sides:

5/3a = -15

Divide both sides by 5/3, or multiply by its reciprocal (3/5)

5/3a(3/5) = -15(3/5)

a = -9

Which points are coplanar?

Answers

J and K are on plane BFG and J and I are on plane BAD

Answer: ABFE or ABJCDI

Step-by-step explanation: Any points that are in the same plane or face of a 3D figure

What is the Greatest common divisor of 378 and 420?

Answers

Answer:

42

Step-by-step explanation:

When calculating the greatest common divisor, you must look for the smallest divisors that can divide the no. s given simultaneously.

So in this case the smallest divisor will be 2.

378 =189. 420 =210

2. 2

The next divisor that 189 and 210 can both be divided with is 3

189 =63. 210 =70

3. 3

The third smallest divisor that can 63 and 70 can be divided with is 7

63 =9. 70 =10

7. 7

9 and 10 have no common divisors that can divide them fully without leaving a remainder

So to get the greatest common divisor, multiply all the divisors you have used

In this case we've used 2,3,7

2x3x7= 42

in the given figure angle 1 is equal to angle 2 then the measurements of angle 3 and angle 4 are​

Answers

Answer:

(3) =  119

(4) =  119

Step-by-step explanation:

Given isosceles triangle with vertex angle 58.

Need exterior angles of base angles 1 & 2.

Solution:

Vertex angle = 58.

Base angle = x

Sum of triangles = 180 =>

x + x + 58 = 180

Solve for x

x = (180-58)/2 = 122/2 = 61

Exterior angles are supplementary to interior (base) angles, so

(3) = 180-(1) = 180 - 61 = 119

(4) = 180-(2) = 180 - 61 = 119

* note: supplementary means sum of two angles = 180.

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

The sum of the interior angle of the triangle is 180degrees.

According to the diagram shown:

m<1 + m<2 + 58 = 180

Since <1 = <2, hencce:

m<1 + m<1 + 58 = 180

2m<1 = 180 - 58

2m<1 = 122

m<1 = 122/2

m<1 = 61 degrees

Since <1 = <2, thereofore m<3 = m<4

Get the measure of m<3

m<1 + m<3 = 180 (supplementary angles)

61 + m<3 = 180

m<3 = 180 - 61

m<3 = 119 degrees

Recall that m<3 = m<4, hence m<4 = 119degrees

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

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The diagram shows three angles at point. Work out the value of x

Answers

169+123=291
360-291=69
X=69

Answer:

x = 69°

Step-by-step explanation:

[tex]168 + 123 + x = 360 \\2 91 + x = 360 \\ x = 360 - 291 \\ x = 69 \: \: degrees[/tex]

Find the equation of the line passing
through the points (3, 3) and (4, 5).
y = [? ]x + [

Answers

The equation in standard form is Y=2x-3

If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude of 6,
what is the relationship between the intensities of the two earthquakes?

Answers

Answer:

sister and brother

If the diagonal path is 750 feet long and the width of the park is 450 feet, what is the length, in the feet, of the park?

Answers

Answer:

The length is 600 ft

Step-by-step explanation:

We can use the Pythagorean theorem since we know the diagonal which is the hypotenuse and the width

a^2 + b^2 = c^2

450 ^2 + b^2 = 750^2

b^2 = 750^2 - 450^2

b^2 =562500-202500

b^2 =360000

Taking the square root of each side

sqrt(b^2) = sqrt(360000)

b =600

One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?

Answers

Answer:

29

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

Answer: 29

Step-by-step explanation:

Helppp!!!! please!!!

Answers

Answer:

I. (x - 6)² + (y + 7)² = 121

Step-by-step explanation:

Given a circle with coordinates of the center as (6, -7), and with a diameter of 22, equation of the circle is given below using the standard equation formula of a circle:

Formula => (x - a)² + (y - b)² = r²

Where,

a = 6

b = -7

r = radius of circle = ½ of diameter = ½ of 22 = 11

Thus, plug in the above values into the standard equation formula:

(x - 6)² + (y - (-7))² = 11²

(x - 6)² + (y + 7)² = 121

Our answer, which is the equation of the circle is I. (x - 6)² + (y + 7)² = 121

What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. Negative 1 and one-fourth + one-half A number line going from negative 3 to 0 in increments of one-fourth. Negative 1 and three-fourths Negative 1 and one-half Negative three-fourths Negative one-half

Answers

Answer:

C. Negative three-fourths

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Answer:

-3/4

Step-by-step explanation:

-1 1/4 +1/2

-5/4    +    2/4

-3/4

What conclusion can you make from the information below?
Three people (Jack, Karen, and Louis) drive three different types of cars
(Ford, Chevrolet, Honda).
• Jack does not drive a Chevrolet.
• Karen does not drive a Chevrolet,
A. Louis drives a Chevrolet
B. Jack drives a Honda
C. Karen does not drive a Ford.
D. Louis does not drive a Chedly let.
M

Answers

Answer:

A.louis drive a chevolet

Step-by-step explanation:

from the question three different people drive different cars . since two out of the three people has been excluded from driving a particular car i.e the third person is the one driving Chevrolet

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

Answer:

D.

Step-by-step explanation:

As long as the function's largest power is two, it is a quadratic function.

a. (3x - 2)(4x + 7)

= 12x^2 - 8x + 21x - 14

The largest power is 2. This is a quadratic function.

b. 7x^2 + 8x

The largest power is 2. Quadratic function.

c. (2x - 1)^2

= 4x^2 - 4x + 1

Largest power is 2. Quadratic function.

d. 8x^4- 3x^3 + 5x^2

Largest power is 4. Non-quadratic function.

Hope this helps!

Joe takes out a 30-year fixed rate amortized loan for 220,000, and makes equal size payments at the end of each month. The rate is quoted as being an annual nominal interest rate of 5.25% compounded monthly and Joe also has to pay closing fees equal to 5% of the value of the loan. Based on this information, find the actual interest rate realized by Joe (i.E. Taking into account the loan given to Joe and the 5% that he pays for the closing fees). Give the value as an annual nominal rate compounded monthly, and round your percent answer to two decimal places.

Answers

Answer:

Annual Interest Rate, r  = 5.69%

Step-by-step explanation:

Amount of loan taken = 220,000

Closing fee is 5% of the loan value

Closing fee = 5% of 222,000 = 0.05 * 220000 = 11000

Therefore, Principal, P = Loan amount + closing fee

P = 220000 + 11000

P = 231, 000

Annual rate, r= 5.25% = 0.0525

Monthly rate, i = 0.0525/12 = 0.004375

Time, n = 30 years = 30*12 = 360 months

The monthly payment will be calculated by:

[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\PMT = \frac{231000 * 0.004375}{1 - (1 + 0.004375)^{-360}} \\\\PMT = 1275.59[/tex]

Assuming payments are made based on 220,000, let us calculate the monthly interest rate.

[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\1275.59 = \frac{220000 * i}{1 - (1 + i)^{-360}} \\\\i = 0.00474229[/tex]

Annual rate, r = 12 * 0.0047429

r = 0.0569 = 5.69%

Find the gradient of the line y - x = 2

Q.3

Answers

Answer:

The gradient is 1

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the gradient

c is the y intercept

first write the equation in the formula above

That's

y = x + 2

the coefficient of x is 1

so the gradient is 1

Hope this helps you

Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.

Answers

Answer:

The cup holds 26.2 in3 more ice cream than the cone.

Step-by-step explanation:

1. Let's find the volume of ice cream that the cone holds, this way:

Volume = π * r² * h/3

Replacing with the real values, we have:

Volume = 3.14 * 2.5² * 5/3

Volume =32.7 inches³

2. Let's find the volume of ice cream that the cup holds, this way:

Volume = π * r² * h

Diameter = 5 inches ⇒ Radius = 2.5 inches

Replacing with the real values, we have:

Volume = 3.14 * 2.5² * 3

Volume =58.9 inches³

3. Let's find the difference, this way:

Volume of the cup - volume of the cone = 58.9 - 32.7 = 26.2 inches³

The cup holds 26.2 in³  more ice cream than the cone.

A chef planning for a large banquet thinks that 2 out of every 5 dinner guesis will order his soup appetizer he excepts 800 guests at the banquet

Answers

Answer:

320 people

Step-by-step explanation:

[tex]\frac{2 people}{5 people}[/tex]=[tex]\frac{x}{800 people}[/tex]

solve for x by using cross multiplication

     -multiply 2 by 800 to get 1,600

     -divide 1,600 by 5 people to get 320

your answer is 320 people

What is the slope of the function, represented by the table of values below?

Answers

Answer:

b.) -4

Step-by-step explanation:

rise/run so its 8/2

The slope of a function will be -4. Then the correct option is B.

What is the slope?

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall, and the difference between the abscissa is called run.

Slope = (y₂ - y₁) / (x₂ - x₁)

Take two point from table.

(-2, 13) and (3, -7)

(x₁, y₁) = (-2, 13)

(x₂, y₂) = (3, -7)

Then the slope of a function will be

Slope = (–7 – 13) / (3 + 2)

Slope = –20 / 5

Slope = –4

Then the correct option is B.

More about the slope link is given below.

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Write "3 divided by n to the fifth" as an expression.
A. 3/n^5
B. (5/n)3
C. 5/n^3
D. (3/n)5

Answers

Answer:

The answer is option A.

[tex] \frac{3}{ {n}^{5} } [/tex]

Hope this helps you

The expression for " 3 divided by n to the fifth" is given by

[tex]\frac{3}{n^{5} }[/tex].

What is expression?

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

According to the given question.

We have a statement

" 3 divided by n to the fifth"

Since, n to the fifth can be written as [tex]n^{5}[/tex].

Therefore,

the expression for " 3 divided by n to the fifth" is given by

[tex]\frac{3}{n^{5} }[/tex].

Thus, option A is the correct.

Find out more information about expression here:

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Hey everyone, can you please help me with this question? THANKS!

Answers

Answer:

6 granite, 3 marble, 14 sandstone, 1 slate

ratio of sandstone to marble

how many sandstone does she have .....14

how many marble does she have......3

so the ratio would be 14:3

Answer:

C. 14:3

Step-by-step explanation:

Dana has 14 pieces of sandstone.

Dana has 3 pieces of marble.

The ratio of pieces of sandstone to pieces of marble is 14:3.

The ratio cannot be simplified further.

Factorize: 9(2a – b)^2 – 4(2a – b)

Answers

Answer:

(2 a - b) (18 a - 9 b - 4)

Step-by-step explanation:

Factor the following:

9 (2 a - b)^2 - 4 (2 a - b)

Factor 2 a - b out of 9 (2 a - b)^2 - 4 (2 a - b):

(2 a - b) (9 (2 a - b) - 4)

9 (2 a - b) = 18 a - 9 b:

Answer: (2 a - b) (18 a - 9 b - 4)

Hi everyone please help me with two questions,THX...this is for 6th grade

Answers

Answer:

A. 12 for every 7

Step-by-step explanation:

There are 12 peas in her bowl.

There are 7 peas in her hair.

The ratio of peas in her bowl to peas in her hair is 12 for every 7.

root( x-1 ) = 2 - root (x+3)

Answers

Answer: x = 4

Explanation: root x-1 = 2- root x+3
First let’s take out the root by square both side by 2 we get:
x-1= 4-x+3
x-1 = -x+7
x+x = 7+1
2x= 8
x= 8/2=4

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]\sqrt{x-1} =2-\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(\sqrt{x-1}\right)^2=\left(2-\sqrt{x+3}\right)^2[/tex]

[tex]x-1=x+7-4\sqrt{x+3}[/tex]

Subtract x on both sides.

[tex]x-1-x=x+7-4\sqrt{x+3}-x[/tex]

[tex]-1=-4\sqrt{x+3}+7[/tex]

Subtract 7 on both sides.

[tex]-1-7=-4\sqrt{x+3}+7-7[/tex]

[tex]-8=-4\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(-8\right)^2=\left(-4\sqrt{x+3}\right)^2[/tex]

[tex]64=16x+48[/tex]

Subtract 48 on both sides.

[tex]64-48=16x+48-48[/tex]

[tex]16=16x[/tex]

Divide both sides by 16.

[tex]\frac{16}{16} =\frac{16x}{16}[/tex]

[tex]1=x[/tex]

Switch sides.

[tex]x=1[/tex]

Calculate the equation of the line through the points (1, 1), (4,3), (10, 7) and (40, 27).​

Answers

Answer:

y = 2/3x + 1/3

Answer:

y = 2/3x + 1/3

Step-by-step explanation:

y=(x+1)(x-3) plot the x-intercept of the function

Answers

Answer:

The two x-intercepts are (-1, 0) and (3, 0).

Step-by-step explanation:

Set each factor = to 0 and solve for x:

x + 1 = 0 => x = -1.  One x-intercept is thus (-1, 0).

x - 3 = 0 => x = 3.  The other x-intercept is (3, 0).

Which graph represents the scenario? PLEASE HELP VERY EASY

Answers

Answer:

The answer is option B.

The second graph.

Hope this helps you

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