Draw the following regular polygons inscribed in a circle:
square
pentagon
hexagon
octagon
decagon
For each polygon, include the following information in the paragraph box below:
What was the central angle you used to locate the vertices? Show your calculation.
What is the measure of each interior angle of the polygon? Show your calculation.
Answer the questions below.
What is the relationship between the central angle and the interior angle?
As the number of sides increases, how do the angles change?
Answers
Answer:
Step-by-step explanation:
Firstly we draw the circle marking its center point.
Then we choose an arbitrary point anywhere on the circumference of the circle.
Then we draw a line connecting the point and the center of the circle.
Now, we mark the next vertex of polygon on the circumference of the circle by measuring an angle with respect to the first line drawn from the center of the circle.
The measurement of the angle is based upon no. of vertices (=no. of side) of the polygon. We divide the full round angle 360° with the no. of vertices and obtain the angle between the each consecutive vertices from the center of the circle since the polygons are regular.
Polygons with the no. of vertices is as follows:
square -- 4
pentagon -- 5
hexagon -- 6
octagon -- 8
decagon -- 10
For decagon the central angle between each consecutive vertex:
[tex]\angle_{10}=\frac{360}{10}[/tex]
[tex]\angle_{10}=36^o[/tex]
For octagon the central angle between each consecutive vertex:
[tex]\angle_{8}=\frac{360}{8}[/tex]
[tex]\angle_{8}=45^o[/tex]
For hexagon the central angle between each consecutive vertex:
[tex]\angle_{6}=\frac{360}{6}[/tex]
[tex]\angle_{6}=60^o[/tex]
For pentagon the central angle between each consecutive vertex:
[tex]\angle_{5}=\frac{360}{5}[/tex]
[tex]\angle_{5}=72^o[/tex]
For square the central angle between each consecutive vertex:
[tex]\angle_{4}=\frac{360}{4}[/tex]
[tex]\angle_{4}=90^o[/tex]
The internal angle of a regular polygon is calculated as:
[tex]\angle=180-\frac{360}{n}[/tex] where, n = number of sides (=vertices)
for example, in case of hexagon interior angle is:
[tex]\angle=180-\frac{360}{6}[/tex]
[tex]\angle=180-60[/tex]
[tex]\angle=60^o[/tex]
As the no. of sides increase the interior angles widen up and their values increase, which the central angle between the consecutive vertices decrease.
Answer:
The other person is definitely getting Brainlest thank you so much for your answer. YOU ARE A LIFE SAVER. :D XD.
Please give him/her Branliest ;D
Related Questions
Flying against the wind, a jet travels miles in hours. Flying with the wind, the same jet travels miles in hours. What is the rate of the jet in still air and what is the rate of the wind
Answers
Answer:
Velocity in still air: 760 mi/ hr
Velocity against the wind: 210 mi/ hr
Step-by-step explanation:
Given
See attachment for complete question
Required
The rate in still air
The rate of the wind
From the question, the velocity (v) against the wind is:
[tex]v =\frac{distance}{time}[/tex]
[tex]v =\frac{3040}{4}[/tex]
[tex]v_1 =760mi/hr[/tex]
The velocity with the wind is:
[tex]v_2 = \frac{8260}{7}[/tex]
[tex]v_2 = 1180mi/hr[/tex]
Let:
[tex]x \to[/tex] velocity in still air
[tex]y \to[/tex] velocity of the wind
So, we have:
[tex]x - y = 760[/tex]
[tex]x + y = 1180[/tex]
Add both equations
[tex]x + x -y + y = 760 + 1180[/tex]
[tex]2x = 1940[/tex]
Divide by 2
[tex]x = 970[/tex]
Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]
[tex]970 - y= 760[/tex]
Make y the subject
[tex]y = 970 - 760[/tex]
[tex]y = 210[/tex]
The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28
Answers
Answer:
21 + x < 28
Step-by-step explanation:
27 is in fact greater than 28 if you where to input 6 into the x spot, this is the only one that's a true expression.
SOMEONE PLEASE HELP ME OUT!!!!
Answers
Answer:
40/30
Step-by-step explanation:
Since tan∅= o/a, 40 is opposite, and 30 is adjacent to angle A, 40/30 is the ratio for tanA.
Answer:40/30
Step-by-step explanation:
....
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}
Answers
Answer:
(-12,2)
Step-by-step explanation:
x^2 + 10x = 24
x^2 + 10x + (10/2)^2 = 24 + (10/2)^2
10/2 = 5
5^2 = 25
x^2 + 10x + 25 = 24 + 25
x^2 + 10x + 25 = 49
(x + 5)^2 = 49 Take the square root of both sides
(x + 5) = sqrt(49)
x + 5 = +/- 7
x = +/- 7 - 5
x = +7 - 5 = 2
x = -7 - 5 = -12
Answer:
{ -12 , 2}
Step-by-step explanation:
x² + 10x = 24
In order to complete the square, the equation must first be in the form x² + bx =c.
x² + 10x = 24Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x² + 10x + 5² = 24 + 5²expand exponents.
x² + 10x + 25 = 24 + 25Add 24 and 25
x² + 10x + 25 = 49Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².
( x + 5 )² =49Take the square root of both sides of the equation.
[tex] \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} [/tex]
simplify
x + 5 = 7x + 5 = +/- 7Subtract 5 from both sides.
x + 5 - 5 = 7 - 5
x = 2x + 5 - 5 = +/- 7 -5
x = -7 - 5 = -12Solve for x. Thank you
Answers
Answer:
x = sqrt(3)
Step-by-step explanation:
Use Thales theorem
x²=3(4-3)x²=3(1)x²=3x=√3I NEED HELP WITH THIS ONE TOO !!
Answers
Answer:
40°
100 + 80 = 180
60 + 80 = 140
140+ 40 = 180
Step-by-step explanation:
Answer:
m<C+m<D=100 degrees m<D=40 degrees
Step-by-step explanation:
Evaluate the function. f(x)=−x^2 −6x+12 Find f(4)
Answers
1. How to find f(4)?
I explained how to find f(5) in your previous question. It is exactly the same. We substitute x = 4 in the equation.2. Substitution and Evaluate
[tex] \large{f(4) = - {(4)}^{2} - 6(4) + 12} [/tex]
Follow BODMAS/PEMDAS rules as well! Exponent first.
[tex] \large{ f(4) = - 16 - 24 + 12} \\ \large{f(4) = - 40 + 12} \\ \large{f(4) = -2 8}[/tex]
3. Final Answer
f(4) = -28.Marking brainliest
I’m getting a belly piercing soon and this guy asked this question but I’m not sure what he means? Someone help
Answers
Answer:
Say I want a
Step-by-step explanation:
Ask what do you mean
Write an expression for each statement: A truck has a total of a pounds of fruit which were packed in n boxes. How many pounds of fruit are in each box?
Answers
Answer:
The answer is "[tex]\text{Total number of boxes} =\frac{a}{n \ boxes}[/tex]"
Step-by-step explanation:
Total pounds carried by the vehicle are "a" pounds.
This will be spread into many boxes, each containing "n" pounds.
It implies that:
[tex]\text{Total pounds = box number} \times \text{amount of pounds from every box} \\\\a = \text{box number} \times n\\\\\text{Box number} = \frac{a}{n \ boxes}[/tex]
David is now 4 years more than twice the age of Henry. If Henry will be 18 in 3 years, how old was David 2 years ago?
Answers
Answer:
i think its 10.5
Step-by-step explanation:
Answer:
David was 32 two years ago
Step-by-step explanation:
D = 2H + 4
H = 15
D = 30+4
D = 34
David was 32 two years ago
sketch the graph of y² = -2x + 5
Answers
Answer:
[tex] {y}^{2} = - 2x + 5[/tex]
Step-by-step explanation:
vertex = [tex]( \frac{5}{2} \: ,0)[/tex]
Hope it is helpful....1.) What is the domain and range of the function in the graph?
2.) What is the average rate of change over the interval [1, 0]?
Answers
Answer:
Domain → (-∞, ∞)
Range → (-2, ∞)
Step-by-step explanation:
1). Domain of a function is defined by the input values (set of x-values) and Range of the function is defined by the output values (set of y-values).
From the graph attached,
Function is defined for all real values of x.
Therefore, domain of the function will be (-∞, ∞).
On y-axis values of the function vary from -2 (excluding 2) to positive infinity.
Therefore, range of the function will be (-2, ∞).
2). Average rate of change of a function in the interval (a, b) is defined by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
By using this expression we can find the average rate of change in the given interval.
Please give the correct interval for which the average rate of change is to be calculated.
please write your answer with explanation
Answers
Answer:
Step-by-step explanation:
If cost price (CP) is greater than selling price (SP) , then the item is sold for loss.
Loss = CP - SP
Loss% = [tex]\frac{loss}{CP}*100[/tex]
If SP is greater than Cp, then the item is sold for a profit.
Profit =SP -CP
Gain % = [tex]\frac{gain}{CP}*100[/tex]
a) CP = $50 ; SP = $30 ; CP > SP, loss
Loss = 50 - 30 = $ 20
Loss % = [tex]\frac{20}{50}*100=20*2[/tex]
= 40% loss
b) CP = £ 5000 ; SP = £6250 ; SP > CP , Profit
Profit = 6250 - 5000 = £ 1250
Profit % = [tex]\frac{1250}{5000}*100=25[/tex]
25% Profit
Solve the equation sin(x - 20°) = cos(42º) for x, where 0
Answers
Answer:
[tex]x = 68[/tex]
Step-by-step explanation:
Sine are Cosine are Complementary Angles.
We can use this formula
[tex] \sin(x) = \cos(y) [/tex]
when x+y=90.
Add the expressions in the parentents to 90 and solve for x.
[tex]x - 20 + 42 = 90[/tex]
[tex]x + 22 = 90[/tex]
[tex]x = 68[/tex]
The answer is
[tex]x = 68[/tex]
Find the equation of a line that is perpendicular to y = -3x – 1 and passes through the point
(3,2).
Give your answer in the form y = mx + b.
Answers
y = 1/3x + 1
Calcule as expressões:
a) (-1/2)² + 2/5 =
b) (-1/2)³ + 1 =
c) (2/5)² x (-1/2)³ =
d) 2 x (-1/3)² - (1/2) =
e) 1 + (+2/5) – ( ½)² =
Answers
Step-by-step explanation:
a, 1/4+2/5=13/20
b,-1/8+1=7/8
c, 4/25×-1/8=-1/50
d, 2×1/9-1/2=2/9-1/2=-5/18
e, 1+2/5-1/4=7/5-1/4=23/20
9. Consider the line y = 4x+9. If a second line is perpendicular to this one, what is its slope? please show your work, i will mark brainliest!
Answers
Answer:
Slope of the line perpendicular to the given line = [tex]- \frac{1}{4}[/tex]
Step-by-step explanation:
If two are lines are perpendicular to each other,
the product of their slopes = - 1 .
That is ,
[tex]m_ 1 \times m_2 = -1[/tex]
Slope of the given line :
[tex]m_ 1 = 4[/tex]
Hence slope of the line perpendicular to it :
[tex]4 \times m_ 2 = - 1 \\\\\frac{4}{4} \times m_2 = - \frac{1}{4} \\\\1 \times m_2 = - \frac{1}{4}\\\\m_ 2 = \frac{-1}{4}[/tex]
The slope of the line perpendicular to the equation y = 4x + 9 is m = -1/4
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = 4x + 9 be equation (1)
The equation is of the form y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = 4
Now , the second line is perpendicular to the line A , the product of slopes of the lines will be -1
So , m₁ x m₂ = -1
4 x m₂ = -1
Divide by 4 on both sides of the equation , we get
m₂ = -1/4
Therefore the value of m₂ is -1/4
Hence , the slope of the line is m₂ = -1/4
To learn more about equation of line click :
https://brainly.com/question/14200719
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Determine the value of x.
4.375 units
4.59 units
13.95 units
15 units
Answers
Answer:
13.95 units
Step-by-step explanation:
[tex] \sin \: 35 \degree = \frac{8}{x} \\ \\ \therefore \: x \: = \frac{8}{\sin \: 35 \degree} \\ \\ \therefore \: x \: = 13.9475744 \\ \\ \therefore \: x \: = 13.95 \: units[/tex]
Convert the percentage into a fraction,
3%=
100
Answers
Answer:
3% = 0.03 = [tex]\frac{3}{100}[/tex]
Answer: 3/100
Step-by-step explanation:
3%=0.03=3/100
Have a great day!!
Which of the following is the graph of the quadratic function y= x2 - 4x + 4
A. Graph D
B. Graph B
C. Graph A
D. Graphic
SUBMIT
Answers
Answer:
graph c
Step-by-step explanation:
it is the longest one
Please need a help !!
Need explanation
Urgent
Answers
If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? With four hard disk drives, the probability that catastrophe can be avoided is
Answers
Answer:
[tex]P(Atleast\ 1) = 0.9999992[/tex]
Step-by-step explanation:
Given
[tex]p = 3\%[/tex] --- rate of hard disk drives failure
[tex]n = 4[/tex] --- number of hard disk drives
See comment for complete question
Required
[tex]P(Atleast\ 1)[/tex]
First, calculate the probability that the none of the 4 selected is working;
[tex]P(none) = p^4[/tex]
[tex]P(none) = (3\%)^4[/tex]
[tex]P(none) = (0.03)^4[/tex]
Using the complement rule, the probability that at least 1 is working is:
[tex]P(Atleast\ 1) = 1 - P(none)[/tex]
This gives:
[tex]P(Atleast\ 1) = 1 - 0.03^4[/tex]
[tex]P(Atleast\ 1) = 0.9999992[/tex]
What value of n makes the equation true?
Answers
Answer:25
Step-by-step explanation: Subtract 7 from 2, you get -5. then multiply both sides of the equation by -5 ( to make -1/5n to n) and you get n=25
Explanation
The circle below is centered at (4, q) and has a radius of 3. What is the equation.
Answers
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (4, - 1 ) and r = 3 , then
(x - 4)² + (y - (- 1) )² = 3² , that is
(x - 4)² + (y + 1)² = 9 → C
What is the answer for this equation
Answers
Answer:
the answer is -5,-7,-10,-14,-19
What is the square root of -1
Answers
Answer:
i.
Step-by-step explanation:
.
Answer:
[tex]\sqrt{-1}=i[/tex]
The square root of -1 (i)
---------------------------------
~HOPE IT HELP
~HAVE A GREAT DAY!!
What is the solution of 5/2x-7=3/4x+14
Answers
Answer:
D. x = 12
Step-by-step explanation:
if you plug 12 in
the solutoon says 23 = 23 which is correct
Answer:D 12
Step-by-step explanation:
I took the test
Please help me! ❤️ I got stuck on this and really need some help
Answers
Answer:
0,-4
-2.65,2.62
2.65,2.62
Step-by-step explanation:
[tex]0^2 = 0\\-2.65^2 =7.0225\\ 2.65^2 =7.0225[/tex]
[tex]y = x^2 - 4[/tex]
-4, 3.0225
[tex]-4^2 = 16\\3.0225^2=9.1355[/tex]
[tex]2 ^{2x + 1} - 9.2 ^{x} + 4 = 0[/tex]
pleas I need this answer. I want to submit it now.
Answers
[tex]\displaystyle\bf 2^{2x+1}-9\cdot 2^x+4=0 \quad ; \qquad \boxed{ 2^x=t \; ; \; 2^{2x}=t^2} \\\\2t^2-9t+4=0 \\\\D=81-32 =49 \\\\ t_1=\frac{9+7}{4} =4 \\\\ t_2=\frac{9-7}{4} =\frac{1}{2} \\\\1) \ 2^x=4 \Longrightarrow x_1=2 \qquad 2) \ 2^x=2^{-1}\Longrightarrow x_2=-1 \\\\Answer: \boxed{x_1=2 \quad ; \quad x_2=-1}[/tex]
You want to buy juices while shopping at ShopRite but are stuck between buying a bottle of apple juice and orange juice. The apple juice is 2 Liters and costs $3.00 while the orange juice is 3 Liters and costs $3.99. Which juice bottle is the better deal?
Answers
Answer:
Orange juice
Step-by-step explanation:
The bottle of apple juice costs 3 dollars for 2 liters, and the bottle of orange juice costs 3.99 dollars for 3 liters. To see which bottle has the better deal, we need to make the liters the same so we can compare them.
We can divide the 2 liters for 3 dollars ratio by 2 to get that 1 liter of apple juice costs 1.5 dollars, and we can divide the orange juice ratio by 3 to get that 1 liter of orange juice costs 1.33 dollars. We see that for 1 liter, orange juice is cheaper, so it is the better deal.
