1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm.

2)What is the area of each triangle?

3)What is the area of the octagon?

4) Use your work from above to derive a generic formula for any octagon with side length that is n units.

1)An Octagon Can Be Divided Into 8 Congruent Triangles With Base Angles That Are 67.5. This Octagon Has

Answers

Answer 1

Answer:

(a) [tex]Area = 14.7824cm^2[/tex]

(b) [tex]Area = 118.2592cm^2[/tex]

(c) [tex]Area = 4nh[/tex]

Step-by-step explanation:

Given

[tex]\theta = 67.5[/tex]

[tex]b= 8cm[/tex] --- base

[tex]n = 8[/tex] --- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle

[tex]\sin(67.5) = \frac{h}{8/2}[/tex]

[tex]\sin(67.5) = \frac{h}{4}[/tex]

Solve for h

[tex]h =4*\sin(67.5)[/tex]

[tex]h =4*0.9239[/tex]

[tex]h =3.6956[/tex]

The area of each triangle is:

[tex]Area = \frac{1}{2} *b * h[/tex]

[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]

[tex]Area = 14.7824cm^2[/tex]

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

[tex]Area = 8 * 14.7824cm^2[/tex]

[tex]Area = 118.2592cm^2[/tex]

Solving (c): Area of octagon of side length n

In (a), we have:

[tex]Area = \frac{1}{2} *b * h[/tex]

Replace b with n

[tex]Area = \frac{1}{2} *n * h[/tex]

Multiply by 8 (the sides) to get the area of the octagon

[tex]Area = 8 * \frac{1}{2} *n * h[/tex]

[tex]Area = 4nh[/tex]


Related Questions

PLS HELP IF U WOULDNT MIND

Answers

Answer:

64 cm³

Step-by-step explanation:

The figure can be decomposed to two rectangular prism, one smaller person on top and one bigger prism beneath.

Volume = volume of smaller rectangular prism + volume of bigger rectangular prism

✔️Volume of smaller rectangular prism = L*W*H

L = 2 cm

W = 2 cm

H = 8 - 4 = 4 cm

V = 2*2*4

V = 16 cm³

✔️Volume of bigger rectangular prism = L*W*H

L = 6 cm

W = 2 cm

H = 4 cm

V = 6*2*4

V = 48 cm³

✔️Volume of the figure = 16 + 48 = 64 cm³

PLEASE HURRY

Tameron rolls a 6-sided die 3 times.
What is the probability that he rolls a 5 on every roll?

A. 1/216
B. 3/216
C. 1/64
D. 3/64

Answers

Answers:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

What is the effect on the graph of f(x) = 1 when it is transformed to
g(x) = 1 – 162
O A. The graph of f(x) is shifted 16 units up.
O B. The graph of f(x) is shifted 16 units to the left.
O C. The graph of f(x) is shifted 16 units down.
O D. The graph of f(x) is shifted 16 units to the right.

Answers

Answer: C) Shifted 16 units down

The minus 16 at the end is directly the reason why. Think of y = 1/x, and subtracting 16 from both sides to get y-16 = (1/x) - 16. The y-16 will shift every point down 16 units. For instance, the point (1, 1) moves to (1, -15).

What type of triangle is this triangle?

acute isosceles

obtuse isosceles

acute scalene

right isosceles

Answers

Answer:

Obtuse isosceles

Step-by-step explanation:

Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.

Answer:

obtuse isosceles

Step-by-step explanation:

im kinda bad but since the top angle is obtuse its an obtuse isosceles

Can someone help me step by step with this probelm please thanks a lot

Answers

1. A 3 letter word with a value of 14 could be MOB, 6+6+2=14

2. A word that has the same value as boat.
Well, BOAT (2,6,2,8) adds up to 18. A word with the same value could be CARS (2,27,7)

3. A 4 letter word I can think of is HELP (4,3,5,7) and the value is 19

-The other part where it says “my word has a value of 20- guess the word” it could be KITE (5,4,8,3)

There are thirteen shirts in your closet,
eight blue and five green. You randomly
select one to wear on Monday and then a
different one on Tuesday. You wear a blue
shirt on Monday and a green shirt on
Tuesday.

Answers

11 shirts

Step-by-step explanation:

You start off with 13, wear one monday, 12, then another tuesday 11

13-2=11

Let f(x)=√3x and g(x)=x-6 What's the smallest number that is in the domain of fog?

Answers

9514 1404 393

Answer:

  6

Step-by-step explanation:

Maybe you have ...

  f(x) = √(3x)

  g(x) = x-6

Then ...

  f(g(x)) = √(3(x -6))

The square root function is only defined for non-negative arguments, so we require ...

  3(x -6) ≥ 0

  x -6 ≥ 0 . . . . . divide by 3

  x ≥ 6 . . . . . . . . add 6

The smallest number in the domain of f(g(x)) is x = 6.

45,39,33,27,21,15, ?

Answers

Answer:

9

(i hope this helped!)

Answer:

The answer is 9.

Step-by-step explanation:

45-6=39-6=33-6=27-6=21-6=15-6=9.

Drag each label to the correct location on the image.
Here is a multiplication sentence:
1 x (4 x 4) = 16
Drag the numbers and the parentheses to create an equivalent multiplication sentence that illustrates the associative property of
multiplication

Answers

Answer:

4 x (1 x 4) = 16

Step-by-step explanation:

1 x 4 = 4

4 x 4 = 16

The St. Croix junior hockey
team won 3 out of every 4
games it played.
The team played 56 games.
How many games did it lose?

Answers

Answer:

14

Step-by-step explanation:

56 divided by 4 is 14

Peter had $4.80 to spend at the store. He spent 1/3 of the money on a model car, 1 /4 of the
money on glue, 1/8 of the money on paint. He spent the rest on a hot dog and soda. How
much money did Peter spend on the ...
model car?_________.
glue?_____________.
paint?___________ .
hot dog and soda?________.​

Answers

Answer:

model car?___$1.60______.

glue?_____$1.20________.

paint?_____$0.60______ .

hot dog and soda?___$1.40_____.​

Step-by-step explanation:

model car: $4.80/3 = $1.60

glue: $4.80/4 = $1.20

paint: $4.80/8 = $0.60

hot dog & soda: $4.80 - $1.60 - $1.20 - $0.60 = $1.40

if Lisa is 12 years old now how old was she at the age at 1/4 of her current age​

Answers

Answer:

3

Step-by-step explanation:

12/4=3

PLEASE HELP! ILL GIVE BRAINLIEST!! PLEASEE

Answers

The answer is A which is 30. :D

Answer:

30

Step-by-step explanation:

2x + x - 10 = 80

3x - 10 = 80

3x (- 10 + 10)= 80 + 10

3x = 90

3x/3 = 90/3

x = 30

8+
3
z

=12 its z over 3 btw how do i show my work

Answers

8+z/3=12

8+4=12

12/3=4

z=12

can someone please help me on this

Answers

V= 64cm3

Regards,
Cee:)

help i need the value of X

Answers

Answer:

x = 20

Step-by-step explanation:

The square signifies the angle is 90 degrees.

All triangle interior angles add up to 180 so:

2x + 10 + 40 + 90 = 180

2x + 140 = 180

2x = 180 - 140

2x = 40

x = 20

Answer:

20

Step-by-step explanation:

2x + 10 + 40 + 90 = 180

2x + 140 = 180

180 - 140 = 40

40 / 2

20

x = 20

I need help fast plz
You don’t need to show work

Answers

Step-by-step explanation:

uy6rhjf08yssyoludysyosyiwyeiwyowyiyiwywoyiw

Mr. Poplin asked his students to write the following expression: "Two to the fifth power plus seven squared" Which answer choice shows this expression? A 52 - 27 B (2-5) + (7.2) © 25-74 D 2572​

Answers

Answer:

B

Step-by-step explanation:

they rest The two by five and separate the square

Help pleaseeeee thanks

Answers

Answer:

We know that 3 l 3 = 3.3, so the values of the stem and leaf plot would be;

4 l 8, 9

5 l 1, 6, 8, 8, 9

6 l 8, 9, 9, 9, 9

7 l 0, 2, 2, 2, 5, 5

8 l 0, 9

Hope this helps!

W
Simplify the expression to
V3
6/3
divided by
2/3

Answers

i don’t know the answer but i also need this very bad

solve the equation

f(n)=10⋅2n for n = 5

Answers

Answer:

f(5) = 100

Step-by-step explanation:

f(n) = 10•2n for n = 5

for n = 5 means we will plug in 5 for every instance of n.

f(5) = 10•2(5)

Multiply.

f(5) = 10•10

Multiply.

f(5) = 100

Hope this helps!

4. Tyquan had his car towed by Lakeview's Towing Service. It cost him $3.00 per mile to have it towed
plus a flat fee of $70.00. The function for his cost is represented by the function C(m) = 3m + 70. What
does C(22) represent in this situation?
a. Tyquan had hisbear towed for 136 mile and it cost $22.00
b. Tyquan had his car towed for 22 miles and it cost him $136.00
c. Tyquan had his car towed for 3 miles at $70.00
d. Tyquan had his car towed 22 miles for $70.00

Answers

Answer:

B is the answer trust me I already took the math.

Step-by-step explanation:

Given below are the rating and performance scores of 15 laptop computers. Performance Score 115 191 153 194 236 184 184 216 185 183 189 202 192 141 187 Overall Rating 74 78 79 80 84 76 77 92 83 78 77 78 78 73 77 How will you classify the linear relationship between the performance scores and the rating

Answers

Answer:

moderate positive relationship

Step-by-step explanation:

From the data:

The linear relationship between score and rating can be obtained by calculating the Pearson correlation Coefficient between the two variables. This can be obtained more easily by using technology, a linear correlation Coefficient calculator. The result of the correlation Coefficient for the data above is about 0.66. This value is positive which shows that the association between the variables is positive, increase in one leads to increase in the other and vice versa. Also the value shows that the relationship is fairly strong.

The following sample was collected during registration at a large middle school. At the 0.05 level of significance, can it be concluded that level of math is dependent on grade level?
Honors Math Regular Math General Math
6th Grade 34 45 15
7th Grade 37 49 13
8th Grade 29 45 17
Hypotheses:
sub(H,0): Level of math is independent of/dependent on grade level.
sub(H,1): Level of math is independent of/dependent on grade level.
Enter the expected matrix - round to 4 decimal places.
Honors Math Regular Math General Math
6th Grade
7th Grade
8th Grade
After running an independence test, can it be concluded that level of math is dependent on grade level?
Yes/No

Answers

Answer:

use Ma.thway it helps

Step-by-step explanation:

Asap,,,,,,,,,,,,,,,,,,,,,

Answers

Answer:

3n^2 -24n+36

Step-by-step explanation:

If f(x) =
3x-2
———
6
which of the following is the inverse of f(x)?
O A. f-'(x) =
x= 2x
O B. F'(x) = 6x-2
O c. f'(x) = 6**2
OD. F'(x) = 2x32

Answers

Answer:

i thin correct answer is b

The nth term of sequence is n2 + 20
Work out the first three times of sequence

How many times in the sequence are less than 50

Answers

Answer:

First three terms:

22,24,26

There are 15 terms in the sequence that are 50 or less, yet only 14 if its just less than 50.

Answers:

The first three terms are 21, 24, 29

5 terms of the sequence less than 50.

======================================================

Explanation:

Plug in n = 1 to find that n^2+20 = 1^2+20 = 1+20 = 21. The first term is 21.

Repeat for n = 2 and you should get 2^2+20 = 24 as the second term.

The third term is 29 through similar steps, but this time you use n = 3 of course.

The first three terms are 21, 24, 29

It's effectively the first three perfect squares 1, 4, 9 but we have a tens digit of 2 stuck to the left of each value.

--------------------

We want to find when n^2+20 is less than 50. We could keep plugging values of n into that expression and record if the result is less than 50 or not, then tally those occurrences. You should record 5 such occurrences.

Or we could do a bit of algebra like so

n^2+20 < 50

n^2 < 50-20

n^2 < 30

sqrt(n^2) < sqrt(30)

n < sqrt(30)

On a calculator, sqrt(30) is roughly 5.4772 which means n < 5.4772. If n is a a natural number, then the largest it can get is n = 5 to ensure n^2+20 is less than 50.

We can see that,

n^2+20 = 5^2+20 = 45 when n = 5n^2+20 = 6^2+20 = 56 when n = 6

This helps show that n = 5 is the largest n to make n^2+20 < 50 a true statement. This means that there are 5 terms of the sequence less than 50.

Will give brainliest

Answers

Answer:

I think the car's acceleration is 20 mph forward

Answer:

20m/s^2

Step-by-step explanation:

Acceleration is (Change in velocity÷change in time)

(20-0)÷ (1-0)

20

Grandma Marlene and Grandpa Gary are putting holiday lights on the gutters of their house. Grandma Marlene leans a 16-foot ladder up against the house, which makes the base of the ladder 9 feet from the house. How far up the house is the ladder?

Answers

Answer: 48

Step-by-step explanation: if i did the math correct 1/3 times the base (9) times 16 is 48. the formula is 1/3 x Bh

Find the value of x in the isosceles triangle shown below.

Answers

Answer:

The anwser to this would be x=6 so C hope this helps :)

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