Answer:
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How to Solve a Hexagon
Updated October 23, 2018
By Chris Deziel
A polygon is any closed two-dimensional figure with 3 or more straight (not curved) sides, and a 12-sided polygon is known as a dodecagon. A regular dodecagon is one with equal sides and angles, and it's possible to derive a formula for calculating its area. An irregular dodecagon has sides of different lengths and different angles. A six-pointed star is an example. There's no easy way to calculate the area of an irregular 12-sided figure unless you happen to have it plotted on a graph and can read the coordinates of each of the vertices. If not, the best strategy is to divide the figure into regular shapes for which you can calculate the area.
Calculating the Area of a Regular 12-Sided Polygon
To calculate the area of a regular dodecagon, you have to find its center, and the best way to do that is to scribe a circle around it that just touches each of its vertices. The center of the circle is the center of the dodecagon, and the distance from the center of the figure to each of its vertices is simply the radius of the circle (r). Each of the 12 sides of the figure is the same length, so denote this by s.
You need one more measurement, and that's the length of a perpendicular line drawn from the midpoint of each side to the center of the 12-sided shape. This line is known as the apothem. Denote its length by m. It divides each section formed by the radius lines into two right-angled triangles. You don't know m, but you can find it using the Pythagorean theorem.
The 12 radius lines divide the circle you scribed around the dodecagon into 12 equal sections, so at the center of the figure, the angle each line makes with the one next to it is 30 degrees. Each of the 12 sections formed by the radius lines is made up of a pair of right-angled triangles with hypotenuse r and one angle of 15 degrees. The side adjacent to the angle is m, so you can find it using r and the sine of the angle.
Step-by-step explanation:
The area of the polygon is 344.18 square inches.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
A regular 12-gon has a side length of 8 inches.
Apothem of the polygon,
a = {8/2(tan180/8)}
a = 8/2tan22.5
a = 7.17 inches.
The area of the polygon,
= 12 x 8 x 7.17 / 2
= 344.18 square inches.
Therefore, the area is 344.18 square inches.
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What is the reason for each step in the solution of the inequality?
700 + 16 < -5(4 – 5x)
Match the reason with the correct step in the inequality.
Terri spent $4.75 on candy,
$1 on soda, and $8.20 on a
ticket. If Terri paid with a
$20 bill, how much money
did she have left
Answer:
Step-by-step explanation:
$4.75+1+$8.20= $13.95
$20.00 - $13.95 = $6.05
Answer:
$6.05
Step-by-step explanation:
candy - $4.75
soda - $1
ticket - $8.20
4.75 + 1 + 8.20
$13.95
bill - $20
20 - 13.95
$6.05
Marc wants to know if the mean age of the prison population in his city is less than 26 years. He obtains a random sample of 25 prisoners, and finds a mean age of 24.4 years and a standard deviation of 9.2 years. Ata significance level of 0.05, what is his conclusion?
Answer:
gsgsbsbsbs
Step-by-step explanation:
yewhsgshdhhssjbs
Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each and the milkshakes cost $5 each. If Mrs. Browning spent a total of $21, how many of each type of treat did she buy?
Please help me please !!!
Answer:
3 milkshakes and 3 sundaes
Step-by-step explanation:
3 * 5 = $15 + 3 * 2 = $21
PLEASE HELP!
Find the real or imaginary solutions of the following equation by factoring.
y^3 + 27 = 0
Answer:
-31.5(1 + i√3)1.5(1 - i√3)Step-by-step explanation:
y³ + 27 = 0(y + 3)(y² - 3y + 9) = 01. y + 3 = 0 ⇒
y = -32. y² - 3y + 9 = 0
y = (3 ±√(3² -4*9))/2y = (3 ± √-27)/2y = (3 ± i√27)/2y = 3/2(1 ± i√3)y = 1.5(1 ± i√3)Answer:
Do u still need the answer?
Step-by-step explanation:
Find the it out 12 divided by 3/5. 12 divided by 2/25. 8divided by 1/7. 12divided by 1/5
Answer:
Step-by-step explanation:
1. 20
2. 150
3. 56
4. 60
hope this helps. i am in algebra two so you can trust my answers. happy holidays and stay safe
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. The retail price of a particular smartphone and the number of units sold at that price
Answer:
no correlation
Step-by-step explanation:
The price of the smartphone is fixed beforehand, therefore price does not depend upon the number of units sold.
Hence, there is no correlation between the two given variables.
Hence, no correlation would be the answer.
Find the perimeter of image below. 42 square units, 52 square units, 56 square units, 44 square units
Answer:
194 square units
Step-by-step explanation:
perimeter is the measurement of the distance surrounding a shape. There fore, the perimeter of the shape is: 42+53+56+44=194 square units
For an acute angle θ, the equation sin(θ)=cos(6) is true. What is the value of θ? Show or explain your answer
Answer:
(θ) = 84°
Step-by-step explanation:
Given:
sin(θ)=cos(6)
Find:
value of θ
Computation:
sin(θ)=cos(6)
We know that
cos(90-a) = sin(a)
So,
sin(θ)=cos(90-84)
sin(θ)=sin(84)
So,
(θ) = 84°
The value of (θ) = 84°
Given that,
The equation is sin(θ)=cos(6)Based on the above information, the calculation is as follows:
sin(θ)=cos(6)
We know that
cos(90-a) = sin(a)
So,
sin(θ)=cos(90-84)
sin(θ)=sin(84)
So,
(θ) = 84°
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PLEAS PLEAS PLEAS HELP ME!!!!!!!!!!!!!!!
The Garcias are on their way to the beach. They are traveling at
a rate of 30 miles per hour. Use the ordered pairs to graph the
distance traveled over time.
Answer:
draw a line for the plotted points and put an arrow at the end, see my answer
Step-by-step explanation:
please click the heart button to give thanks for my work! :)
6. An ice cream costs 15 more than a cold drink. If the cost of
buying 5 ice creams is 125, find the price of a cold drink.
Answer:
The price of a cold drink is 10 dollars.
Step-by-step explanation:
We can use proportion.
[tex] \frac{5 \: ice \: creams}{125 \: dollars} = \frac{1 \: ice \: cream}{x} \\ \\ \frac{5x}{5} = \frac{125}{5} \\ \\ x = 25[/tex]
So we found out that one ice-cream costs $25.00.
The statement said, "An ice cream costs 15 more than a cold drink"
In other words, A cold drink costs 15 dollars less than an ice cream.
So we would subtract.
[tex]25 - 15 = 10[/tex]
So a cold drink costs $10.00.
Martina used 3/4 of a bottle of conditioner in 7/12 of a year. How much conditioner would she use in a full year
Step-by-step explanation:
7 months = 3/4
1 month = 3/4 ÷ 7
= 3/28
12 months / 1 year = 3/28 x 12
= 9/7
not sure if its correct
Answer: 1 2/7
trust me it just worked for me on IXL
I need help please I have to finish this
Answer:
We want to get y and x such that it satisfices all geometric relations:
3y=87
y=87/3 = 29 degree
Hence y= 29 degree
Two parallel lines tell us that 87=3x such that x=29
Step-by-step explanation:
Please help answer the first 5 boxes for brainslt
> for brainslt
Step-by-step explanation:
5 points is too small for this..
1. Change the following into 12 hour clock time
a) 1720 hours. b)0235 hours
Answer:
A) 5:20 pm
B) 2:35 am
Step-by-step explanation:
The hours in am are from 00:00 - 12:00, the numbers after 12 for example 17, you subtract 12 and the remaining is the hours and what is left of the number for example 20 is the minutes.
I am horrible at explaining but I hope this helps... :)
Answer:
a) 5:20
b) 2:35
Step-by-step explanation:
a) Subtract 12 from the 17 at the beginning of 1720, leaving you with 5. This is the hour component of standard time, and will be placed on the left side of the colon (5:__). Then, put the last two digits onto the other side of the colon in standard time like so: 5:20.
b) For this one, because the first two digits don't exceed twelve, you simply have to divide the first two digits from the last two digits and put a colon between them: 02:35, or 2:35.
The happy apple farm has 560 apple trees. Each apple tree has 169 apples. How many apples are on all the trees together?
Answer:94,
Step-by-step explanation:
16y5+4y5-12y3+15y3?
What is the simplified form?
Answer:
[tex]20y^5+3y^3[/tex]
Step-by-step explanation:
[tex]16y^5 + 4y^5 -12y^3 + 15y^3[/tex]
All we can do here is combine like terms (add those that have the same the same exponent)
[tex]20y^5+3y^3[/tex]
Good luck!
Answer:
[tex]20y^{5} +3y^{3}[/tex]
Step-by-step explanation:
[tex]16y^{5} +4y^{5} =20y^{5}[/tex] and [tex]-12y^{3} +15y^{3} =3y^{3}[/tex]
So [tex]20y^{5} +3y^{3}[/tex]
Is it SSS or SAS. Please helpp
Amplitude: 6 Period: 44
Phase shift:
Step-by-step explanation:
provide more details, please
There are 60 seconds in a minute use a tape diagram to find the total number of seconds in 5 minutes and 45 seconds
60 x 5 + 45 = 345 Seconds
PLEASE HELP!!!!!!
Solve the following system of equations using elimination.
5x+y=24
-5x-4y=-56
Answer:
x = 8/3 and y = 32/3
Step-by-step explanation:
Add the two equations, getting -3y = -32, thus y = 32/3
Sub for y in first equation, getting 5x + 32/3 = 24
5x = 40/3
x = 8/3
simplify the expression
4.2v - 5 -6.5v =
Answer:
-5 - 2.3v
Step-by-step explanation:
You want to combine like terms and since two of the numbers have variables, then you can add them both together
4.2v - 6.5 v = -2.3 v
So... -5 - 2.3v or
-2.3v - 5
either or there both same
Hope this helped!
Which expression is represented by the set of algebra tiles below?
O x+6
O x-6
O 6-X
O 6x- 1
Answer:
The answer is B
Step-by-step explanation:
Lol I just had this same question on edge 2021 (◕‿◕✿)
Answer:
It Is B, x-6.
Step-by-step explanation:
I Just Did The Unit Test Review (ﾉ◕ヮ◕)ﾉ*.✧
PLEASE HELPPPPPPPPP! 44 POINTS
Answer:
#6-
1. 9x30=(9x10)+(9x10)+(9x10)
2. 9x30=9(10+10+10)
3. 9x30=270
#7-
1. 7x50=7x(10+10+10+10+10)
2. 7x50=7x(25+25)
3. 7x50=350
#8-
1. 2x90=(2x45)+(2x45)
2. 2x90=90+90
3. 2x90=180
Step-by-step explanation:
Hope this helps!
In an animal shelter, the ratio of dogs to cats is 5 to 3. There are 25 dogs. Write and solve a proportion to find the number of cats.
Ο 18
Ο 21
Ο Ο Ο Ο
Ο 15
Ο 16
Answer:
15 cats
proportion 3x : 5x
in this case x= 5
Step-by-step explanation:
divide 25 by 5
=5
now you know the factor is 5
multiple 3 by 5
=15
What is the magnitude of the vector shown?
5
13
radical 5
radical 13
Answer:
D on edge
Step-by-step explanation:
radical 13
I need the answer ASAP! Please help me!
Answer:
Please check the explanation.
Step-by-step explanation:
Determining the length of BC
From the diagram, it is clear that
The point B is located at (-8, 10) and point C is located at (8, 10)Since points A and C are located on a horizontal straight line. Thus, the length of BC can be determined by counting the x-axis units from reaching x = -8 to x = 8. i.e. 8-(-8) = 8+8 = 16
Thus, the length of BC = 16 units
Determining the length of CD
Given
C (8, 10) D (2, -2)The distance between C(8, 10) and D(2, -2)
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}[/tex]
[tex]=\sqrt{6^2+12^2}[/tex]
[tex]=\sqrt{36+144}[/tex]
[tex]=\sqrt{180}[/tex]
[tex]=\sqrt{36\times 5}[/tex]
[tex]=6\sqrt{5}[/tex]
Thus, the length of CD [tex]=6\sqrt{5}[/tex] units
Determining the length of ED
Given
E (-8, -4) D (2, -2)The distance between E(-8, -4) and D(2, -2)
[tex]ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}[/tex]
[tex]=\sqrt{10^2+2^2}[/tex]
[tex]=\sqrt{100+4}[/tex]
[tex]=\sqrt{104}[/tex]
[tex]=\sqrt{26\times \:4}[/tex]
[tex]=2\sqrt{26}[/tex]
Thus, the length of ED [tex]=2\sqrt{26}[/tex] units
Determining the length of EB
From the diagram, it is clear that
The point E is located at (-8, -4) and the point B is located at (-8, 10)Since points E and B are located on a vertical straight line. Thus, the length of EB can be determined by counting the y-axis units from reaching y = -4 to y = 10. i.e. 10-(-4) = 10+4 = 14
Thus, the length of EB = 14 units
Of 15 possible books, you plan to take 7 with you on vacation. How many different collections of 7 books can you take?
The number of collections of 7 books can you take is 1685.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Total books= 15
n = 15 (the number of possible books) and r = 7 (the number of books to be taken).
Now,
To find the number of different collections of 7 books, we can use the formula for combinations. Combinations are ways of selecting items from a collection, such that the order of selection does not matter.
The formula for combinations is:
nCr = n! / (r! (n - r)!)
where n is the number of items in the collection, r is the number of items to be selected, and ! is the factorial operator.
We can plug these values into the formula:
15C7 = 15! / (7! (15 - 7)!)
= 15! / (7! 8!)
= (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8!) / (7! 8!)
= (15 x 14 x 13 x 12 x 11 x 10 x 9) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
= (6435 x 1320) / (5040)
= 8491770 / 5040
= 1685.25
Since we cannot have a fraction of a collection, we round down to get the final answer:
15C7 = 1685
Therefor, by algebra the answer will be 1685.
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The temperature is 15º and is expected to fall 2º each hour during the night. write the linear equation
Answer:
y = 15 - 2x
Step-by-step explanation:
The starting temp is 15, and we expect it to fall 2 degrees each night. We substitute x and y, y = total temp at the end of the examined time period, x = number of hours.
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Answer:
15 - 2(x)
x = hours
Step-by-step explanation:
Pleaseeee help me I need help reallly bad
