Find the area of a regular nonagon with a radius of 4
Answers
If it's a regular nonagon, each exterior angle has measure 360°/9 = 40°, so the supplementary interior angles each have measure 180° - 40° = 140°.
We can split up the nonagon into 9 congruent isosceles triangles whose longer side coincides with the radius of the circle. (The language in the question is a bit ambiguous; I think it's clearler to say the nonagon is itself circumscribed by the circle, so that each of its vertices lie on the circle. See attached image - not mine, but it's in public domain.)
As the image suggests, each triangle will have interior angles measuring 70°, 70°, and 40°.
We can use trigonometry to find the side length of the nonagon, i.e. the length of the shortest side of each triangle - I'll call it x. For example, using the law of cosines,
x² = 4² + 4² - 2 • 4 • 4 cos(40°) ⇒ x = 4√2 √(1 - cos(40°))
Then the perimeter of the nonagon is
9x = 36√2 √(1 - cos(40°)) in ≈ 24.623 in
The area of a triangle is 1/2 the product of its base and height. The base will be b = x, but to get the height we cut the isosceles triangle in half to produce a right triangle. We use trig again to determine its height h:
tan(70°) = h/(b/2) ⇒ h = 1/2 x tan(70°)
so each triangle contributes an area of
a = 1/2 bh = 1/4 x² tan(70°) ≈ 5.142 in²
and so the area of the nonagon is
9a = 9x²/8 tan(70°) ≈ 46.281 in²
Related Questions
Write (5 – 8i)2 in simplest a + bi form.
Answers
Answer:
10-16i
Step-by-step explanation:
use distrubutive property and treat i like a variable
Carter deposited $146.00 into a new savings account that earns 13% interest compounded
quarterly. How long will it take for the balance to grow to $239.00?
Round your answer to the nearest month.
___ years and ___ months
Answers
Answer:
it should be around 4 months I believe
Step-by-step explanation:
146.00(1+0.13/4)^(4×4)
What is the value of n?
Answers
8n + 64 = 16n + 32
8n = 32
N = 4
I think that’s right.
Find the value of p if the mean of the following distribution is 20.
X:- 15 17 19 20+p 23
F:- 2 3 4 5p 6
Answers
Answer:
X:-15 17 19 20+p 23 there is a difference of 2 between each number so p=1 .
F:-2 3 4 5p 6 there is a difference of one so p needs to be 1 .
Which kind of triangle must triangle XYZ be?
Answers
The type of triangle XYZ which is made, when the two line segments XY and ZY are tangent to circle, is an isosceles triangle.
What is the theorem of two tangents from external point?When the two tangent are drawn to a circle from an exterior point then according to this theorem-
The length of these two tangents is equal.Both the tangents subtend equal angle at the center of the circle.The angle between the two tangent is bisect by the line joining to the exterior point and the center.The figure of the circle O is attached below. Here, line segments XY and ZY are tangent to the circle.
As both the tangents are drawn from the same point, thus the length of XY and ZY is equal.
[tex]XY=YZ[/tex]
When the two sides of a triangle is equal, then it is known as the isosceles triangle.
Thus, the type of triangle XYZ which is made, when the two line segments XY and ZY are tangent to circle, is an isosceles triangle.
Learn more about the theorem of two tangents from external point here;
https://brainly.com/question/8705027
#SPJ1
12. In a language survey of students, it is found that 80 students know English, 60 know
French, 50 know German, 30 know English and French, 20 know French and German, 15 know English and German and 10 students know all the three languages. How many students know at least one language ?
Answers
Answer:
190 students
Step-by-step explanation:
Just focus on the first half of the problem: 80 english, 60 French, and 50 German. Added together this gives you 190
Calculate the percent
Answers
You recently discovered that your job provides a 30% matching towards your retirement. If you deposit $300 each month into a retirement account with an APR of 5.50%, what would you type in Excel to find the balance after 25 years?
Answers
Answer:
Total amount of every money dat I have deposited
Need help on one question
Answers
Answer:
write it so that we can know
now I can't see
What is the slope and y-intercept of this line?
y=−12x+7
slope: 12, y-intercept: −7
slope: −7, y-intercept: −12
slope: −12, y-intercept: 7
slope: 7, y-intercept: −12
Answers
Answer:
(c) slope: -12, y-intercept: 7
Step-by-step explanation:
The given equation is in the slope-intercept form:
y = mx +b
In this form, m is the slope, and b is the y-intercept.
__
Comparing the given equation to the form, we see ...
y = mx +b
y = -12x +7 ⇒ m = -12, b = 7
The slope is -12; the y-intercept is 7.
I need to know how to solve this
Answers
Answer:
it would be 3(16-8x) also know as A
Step-by-step explanation:
Let Vector a = LeftAngleBracket 3, 11, negative 8 RightAngleBracket. and Vector b = LeftAngleBracket 2, negative 3, c RightAngleBracket. . If Vector a minus vector b = LeftAngleBracket 1, 14, negative 3 RightAngleBracket., what is the value of c?
–11
–5
5
11
Answers
Answer:
c.5
Step-by-step explanation:
Pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answers
Answer:
orange one
Step-by-step explanation:
just the orange one since its 5 divided by 1 is 5
10 divided by 2 is 5
20 divided by 4 is 5
They answers are both correct
First you will look at the first pair of numbers then do some multiples of the numbers
Then compare them to the other points given and determine if you have a line from there
Dad is getting food ready for my birthday party! Including
me, there will be 18 people at the party. Dad is baking
cookies for us! He can bake 24 cookies per batch.
How many batches should I tell Dad to make so we can each
have 4 cookies?
Answers
Answer: Dad is getting food ready for my birthday party! Including
me, there will be 18 people at the party. Dad is baking
cookies for us! He can bake 24 cookies per batch.
How many batches should I tell Dad to make so we can each
have 4 cookies?
Step-by-step explanation:
Answer:
3 batches and a half = 84 cookies
Step-by-step explanation:
24 x 3= 84
84 divided by 19= 4.4
HGD
Matt and Mindy each built a rectangular prism that has a length of 5 units, a width of 2 units, and a height of 4 units. Matt used cubes that are 1 cm on each side. Mindy used cubes that are 1 in. on each side. What is the volume of each prism?
Answers
Answer:Matt’s is 40cm^3 and Mindy’s is 40in^3
Step-by-step explanation:5x2x4=40units^3
Answer:volume of rectangular prism is = whl= 2*4*5=40 unit³
the prism of the matt built will have the volume of 40cm³
where as Mindy will have 40in³
therefore,
1in=2.54cm
Mindy built volume= 40*2.54cm³= 101.6cm³
please help be answer this
Answers
Answer:
D
Step-by-step explanation:
[tex](2x +12)(2x + 8)[/tex]
[tex]4 {x}^{2} + 16x + 24x + 96[/tex]
[tex]4 {x}^{2} + 40x + 96[/tex]
519.6 x 10.86
by process.
Answers
Answer:
5642.856
Step-by-step explanation:
Multiply 5196 x 1086 without the decimal points
Then you will get the ans 5642856 then count how many decimal points are there altogether which is three points.
So go behind three numbers and put the point.
Final Answer - 5642.856
what is 36x - 28 equal
Answers
Answer:
[tex]36x-28[/tex]
Rewrite 36 as 4*9 & Rewrite 28 as 4*7
[tex]4\cdot \:9x-4\cdot \:7[/tex]
Now, u can factor out the common term 4
[tex]4\left(9x-7\right)[/tex]
What is the measure of angle ACB? (geometry)
Answers
Answer:
30°Step-by-step explanation:
The angle between two secants is half the difference of intercepted arcs.
m∠ACB = 1/2(mAB - mDE)Substitute the arc values and calculate
m∠ACB =1/2(80° - 20°) = 1/2(60°) = 30°Answer:
∠ACB = 30°
Step-by-step explanation:
Finding ∠ACB :
∠ACB = 1/2 x (∡AB - ∡DE)∠ACB = 1/2 x (80° - 20°)∠ACB = 1/2 x 60°∠ACB = 30°Help please please WILL MARK BRAINIEST
Answers
Let's consider the information given:
states that this is a regular polygon⇒ means that all the side lengths are equal
this is a hexagon since it has six sidesTo calculate the area of the hexagon:
⇒ must know the formula
[tex]Area = \frac{3\sqrt{3} }{2} s^2[/tex]
s: length of one side --> 7 unitsLet's solve: (remember we need to round the final answer to the nearest hundredth)
[tex]Area = \frac{3\sqrt{3} }{2} *7^2=73.5\sqrt{3} =127.306[/tex] ≈ 127.31 square units
Answer: 127.31 square units
Hope that helps!
What is 1/2 of 0.45x-1/4?
Answers
Answer:
0.45x−0.125
Step-by-step explanation:
0.45x-1/4
0.45x - 0.25 ÷ 2
0.45x−0.125
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answers
Answer:
(3, 2)
Explanation:
y = −2x + 8 ....equation 1y = x − 1 ....equation 2======================
substitute equation 2 into 1
x − 1 = −2x + 8x + 2x = 8 + 13x = 9x = 3find y
y = x − 1y = 3 − 1y = 2solution
(x, y) ⇒ (3, 2)Answer:
(3, 2)
Step-by-step explanation:
Given
Equation 1: y = -2x + 8
Equation 2: y = x - 1
Solving by Substitution
Substitute Equation 2 into Equation 1 and solve for x:
⇒ x - 1 = -2x + 8
Add 2x to both sides:
⇒ 3x - 1 = 8
Add 1 to both sides:
⇒ 3x = 9
Divide both sides by 3:
⇒ x = 3
Now substitute the found value of x into Equation 2 and solve for y:
⇒ y = 3 - 1
⇒ y = 2
Therefore, the solution is (3, 2)
If a point P is moving such that the lengths of the tangents drawn from P to the circles
[tex]x^2+y^2-4x-6y-12=0[/tex]
and
[tex]x^2+y^2+6x+18y+26=0[/tex]
are in the ratio 2:3 then find the equation of the locus of P.
Answers
Hello ~
My name is Irxdscent, and I will be answering your question today! :D
→ Answer :-[tex]\sf{(x_{1} \: - y_{1})[/tex]
→ Explanation :-[tex]\sf{Equations \: of \: the \: circles \: are:}[/tex][tex]\sf{S = x^2 \: + \: y^2 \: - \: 4x \: - \: 6y \: - \: 12 = 0}[/tex]
[tex]\sf{S_{1} = y^2 \: + \: y^2 \: + \: 6x \: + \: 18y \: + \: 26 = 0}[/tex]
[tex]\sf{P(x_{1}, \: y_{1}) \: is \: any \: point \: on \: the \: locus \: and \: PT_{1,} \: PT_{2} \: are \: the \: tangents \: from \: P \: to \: the \: two \: circles.[/tex]
[tex]\sf{Given \: condition \: is:}[/tex][tex]\sf{\frac{PT_{1}}{PT_{2}} = \frac{2}{3}[/tex][tex]\sf{3PT_{1} \: = \: 2PT_{2}[/tex][tex]\sf{3(x^2 \: + \: y^2 \: - \: 4x \: - \: 6y \: - \: 12) = 2(x^2 \: + \: y^2 \: + \: 6x \: + \: 18y \: + 26)[/tex]
[tex]\sf{3x^2 \: + \:3 y^2 \: - \: 12x \: - \: 18y \: - \: 36 = 2x^2 \: + \: 2y^2 \: + \: 12x \: + \: 36y \: + 52}[/tex]
[tex]\sf{x^2 \: + \: y^2 \: - \: 24x \: - \: 54y \: - \: 88 = 0}[/tex]
[tex]\sf{This \: is \: the \: locus \: P \: \sf{(x_{1} \: - y_{1})[/tex]
Hope It Helps! ~
~ Learn With Lrxdscent ~
[tex]\underline{Answer :}[/tex]
ɪ ʀ x ᴅ ꜱ ᴄ ᴇ ɴ ᴛ
"I have a 40% chance of being selected as the captain of the volleyball team and a 75% chance of being elected student body president." What is the probability that Cara will be selected as the captain of the volleyball team and will be elected student body president?
Answers
Answer:
30% chance of them both happening
Answer:
thats going to be and exact 85%!
I used the probability calculater on cal.net
Goran is running for president of the chess club, and he received 24 votes. There are 40 members in the club. What percentage of the club members voted for Goran?
Answers
Answer:
60%
Step-by-step explanation:
[tex]\sf Percentage=\left(\dfrac{Value}{Total\:value}\right) \times 100[/tex]
Given:
value = 24 votesTotal value = 40 membersSubstituting these into the formula:
[tex]\implies \sf \left(\dfrac{24}{40}\right) \times 100=0.6 \times 100 = 60 \%[/tex]
Therefore, 60% of the club members voted for Goran.
Solve the following problems.
Given: IL Perpendicular EJ at M
Prove: mEL + mll = 180°
Just need the proof!
Answers
Which pieces of information may be found on a person's credit report?
Select each correct answer.
credit card balance
late payments
person's address
income
household size
age
Answers
Answer:
credit card balance
late payments
income
Answer:
See below ~
Step-by-step explanation:
On a person's credit report, the following information may be found :
credit card balancelate paymentsperson's address1. Based on the current market rates for bonds of Frenza, Nelo, and Lika, which of the following bonds do lenders believe has the highest risk level? 2. If Frenza decided to issue new bonds with a contract rate of 11%, would these new bonds be sold at a discount or premium based on the current market rate for Frenza bonds? 3. Frenza is planning an $160,000 expansion to launch a new product line. Frenza currently earns $100,000 in net income, and the new product line will yield $50,000 in additional income before any interest expense. Frenza has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 8% annual interest, or (3) expand and raise $160,000 from equity financing. For each option 1, 2, and 3, compute (a) net income and (b) return on equity (Net income ÷ Equity). Ignore any income tax effects.
Answers
The net income and return on equity for the first part for Frenzo will be $100000 and 25%.
How to calculate the net income?The net income and return on equity for the first part will be:
Net income = $100000 - 0 = $100000.
Return on equity = (100000/400000) × 100 = 25%
The net income and return on equity for the second part will be:
Net income = $150000 - $12800 = $137200
Return on equity will be:
= (137200/400000) × 100
= 34.3%
The net income and return on equity for the third part will be:
Net income = ($150000 - 0) = $150000
Return on equity will be:
= (150000/560000) × 100
= 26.8%
Learn more about net income on:
https://brainly.com/question/15530787
Help?? um i can’t select multiple pics so..the other two Drop down menus say ..
A) (x - 5)(x - 1)
B) (x + 5)(x + 1)
C) x-1
D) x-5
—-
A) -1
B) 5
C) 2
D) -5
Answers
Answer:
Step-by-step explanation:
[tex]\frac{x^2 -3x-10}{x^2 -6x+5}[/tex] × [tex]\frac{x-2}{x-5}[/tex] = [tex]\frac{(x-5)(x+2)}{(x-5)(x-1)}[/tex] × [tex]\frac{x-2}{x-5}[/tex] = [tex]\frac{(x+2)(x-2)}{(x-1)(x-5)}[/tex] ( Domain is x ≠ 1 and x ≠ 5 )
The expression has an excluded value of x = 5
9. An airplane is 325 miles from the airport. To get to the present positionthe plane flew 205 miles due south from the airport and then flew due westTo the nearest mile, how far west didi the plane fly?
Answers
*explanation* : 325 x 205=