A regular heptagon has a radius of approximately 27. 87 cm and the length of each side is 24. 18 cm. What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides. 1,173 cm2 2,125 cm2 2,359 cm2 4,250 cm2.
Answers
To find the area, the heptagon can be considered as consisting of seven
triangles, each having a side of the heptagon as its base.
The area of the heptagon is approximately 2,125 cm².Reasons:
The radius of the heptagon, r = 27.87 cm
Length of each side, s = 24.18 cm
Required:
The approximate area of the heptagon
Solution:
The area of the heptagon can be considered as consisting of seven triangles
From Pythagorean theorem, we have;
\(\displaystyle Height \ of \ each \ triangle, \ h = \mathbf{\sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}\)
\(\displaystyle Area \ of \ each \ triangle, \ A = \mathbf{ \frac{s}{2} \times h}\)
Which gives;
\(\displaystyle Area \ of \ heptagon, \ A_{heptagon} =7 \times \frac{s}{2} \times h = \mathbf{7 \times \frac{s}{2} \times \sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}\)
Plugging in the values gives;
\(\displaystyle Area \ of \ heptagon, \ A_{heptagon} = 7 \times \frac{24.18}{2} \times \sqrt{27.87^2 - \left(\frac{24.18}{2} \right)^2 } \approx \mathbf{2,125.15}\)
The area of the heptagon given to the nearest whole number is therefore;
\(A_{heptagon}\) ≈ 2,125 cm²Learn more about finding the area of a regular polygon here:
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Answer:
B
Step-by-step explanation:
Trust
Related Questions
Bernies monthly phone plan can be reprented by the expresion $ 0.10x + $20 where x represents the number if minutes use. If he talked for 300 minutes lat month, how much was his phone bill
Answers
Answer:
Step-by-step explanation:
0.10(300) + 20
30 + 20 = $50
Decrease 64 g by 12 1/2%
please help i need step by step explanation
Answers
Step-by-step explanation:
100% --> 64g
1% --> 64g ÷ 100 = 0.64g
100% - 12.5% = 87.5%
87.5% = 0.64g x 87.5
= 56g
Write the meaning of each algebraic expression. Then, evaluate the algebraic expression for the given value. 5x - 4 if x= 3
Answers
Answer:
\(11\)
Step-by-step explanation:
\(5 \times x - 4\)
\(5 \times 3 - 4\)
\(15 - 4\)
\(11\)
Help pleaseeee I need it ASAP
Answers
Answer:
Option D:Diagonals of a square bisect each other
Step-by-step explanation:
The diagonals of a square are equal and bisect each other at right angles and making the bisected parts equal.
I know
You are designing a candle-making kit. Each kit will contain 25 cubic inches of candle wax and a mold for making a model of the pyramid-shaped building at the Louvre Museum in Paris, France. You want the height of the candle to be 2 inches less than the length of each side of the candles square base. What should the dimensions of your candle mold be?
Answers
Hope this helped : )
Please help, 100 points
If a polynomial has integral coefficients with 3 + i and 1 + \(\sqrt{3}\) as roots, then what other roots must it have?
1. 3 – i
2. \(1 - \sqrt{3}\)
3.\(-1 + \sqrt{3}\)
4.. –3 + i
5. no other roots
Answers
The other root of the polynomial is 1 - √3.
What are roots of a polynomial?The roots of a polynomial are the values of the independent variable at which the polynomial is zero.
How to find the root the polynomial must have?If a polynomial has integral coefficients with 3 + i and 1 + √3 as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.
So, since 1 + √3, the conjugate is also a root.
The conjugate is 1 - √3.
So, the other root is 1 - √3.
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What expressions are equivalent to 3x+5x+8 and 4x+4x
Answers
=8x :))))))))
you roll two six-sided dice at the same time. what is the probability the second dice landed on an even number given the first one landed on an odd number?
Answers
The probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
Step-by-Step Explanation:Let A be the event that the first dice rolls an odd number, and let B be the event that the second dice rolls an even number. We want to find P(B|A), which is the probability of B given A. This can be found using the formula:P(B|A) = P(A and B) / P(A) We know that P(A) = 1/2, as half the numbers on a six-sided dice are odd.
To find P(A and B), we need to find the probability that both dice roll the desired numbers simultaneously. Since we know that the first dice rolled an odd number, only half of the numbers are possible for the second dice to be even. Therefore, P(A and B) = 1/2 x 1/2 = 1/4. So:P(B|A) = P(A and B) / P(A) = (1/4) / (1/2) = 1/2 or 0.5. Therefore, the probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
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Write an equation/inequality to represent the description. *
Answers
Provided in the question, total number of people that can be accommodated in the theatre are 471.
Now, 254 people are seatedp is the number of people who can enter the theatre of the movie.Then, according to the question there are two possibilities. The number of people is less than the total number of People who can be accommodated.
\(1) \: p + 254 < 471\)
Or, they can be equal to the number of people.
\(2) \: p + 254 = 471\)
Combining both the inequations, We get
\( \boxed{ p + 254 \leqslant 471}\)
So, the correct option is Option D
━━━━━━━━━━━━━━━━━━━━
Please help provide the product in standard form !!
Answers
Answer:
x^3+4x^2+5x+2
Step-by-step explanation:
Plz can someone help me show work for these two problems!!
3x + y = 13
2x - y = -1
Answers
Answer:
3x +y = 13
Or, x=13-y/3......eqn(i)
Now putting the value of x
2x - y = - 1
Or, 2(13-y/3) - y = - 1
Or, 26 - 2y /3 - y = -1
Or, 26 - 2y - 3y = - 3
Or, 26 - 5y = - 3
Or, - 5y = - 3 - 26
Or,y = - 39/ (- 5)
Or, y = 7.8~
HELP ASAP WHAT IS IT!!!
Answers
Answer:
A :)
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A large box P containing 15 cans of biscuits weighs 23 kg and weighs 500g when empty. A box containing 8 cans of the same biscuits Q weighs 12.3kg. Box Q What is the mass when the box is empty?
Answers
Answer:
300 g
Step-by-step explanation:
weight of a can of biscuits= (23- 0.5)/15= 1.5 kg
weight of 8 cans= 1.5 * 8= 12 kg
mass of the empty box Q= 12.3- 12= 0.3 kg= 300 g
Answer:
300 g or 0.3 kg
Step-by-step explanation:
23 kg - 500g = 22.5 kg
each can of biscuits weighs 22.5 ÷ 15 = 1.5 kg
if the box Q weighs 12.3kg when there's 8 box of biscuits then
8 × 1.5 = 12 kg is the weight of biscuits and the remaining 300 g is box Q's weight
Find the length of a rectangle that has a width of 3.9 cm and an area of 25.311 cm².
Answers
Answer:
Length = 6.49 cm
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in units squared,l is the length,and w is the widthSince we're already given the area and width and want to find the length, we can first rewrite the area formula in terms of l:
A/w = l
Now, we can plug in 25.311 for A and 3.9 for w to solve for l, the length:
25.311 / 3.9 = l
6.49 cm = l
We can check that 6.49 is the correct length by plugging everything into the regular area formula and checking that we get 25.311:
25.311 = 6.49 * 3.9
25.311 = 25.311
6-x^2 what is it
please answer correctly to be awarded brainliest
Answers
Answer:
i think the question might be incorrect or the question is incomplete
This isn’t really solvable rationally if that’s what your trying to do but irrationally:
sqrt means square root
(-x + sqrt6) (x + sqrt6)
= -x^2-sqrt6x+sqrt6x+6
= -x^2 + 6
so x = -sqrt6 and sqrt6
hope this helped
What is the constant of proportionality in this equation?
у= 5/2 x
Answers
Answer:
5/2
Step-by-step explanation:
The constant of proportionality in the equality is 5/2. Later on, you will learn that the constant of proportionality is slope, or m.
Which of the following represents the factorization of the polynomial below?2x2 +11x +5O A. (2x+5)(x+1)O B. (2x + 2)(x+5)C. (2x + 1)(x+5)O D. (2x+5)(x+2)
Answers
The correct option is C which is (2x+1)(x+5).
Factorise...
3x2 - 6x
Answers
How to solve your question- 3 2 − 6
Grouping
The Common factor- 3 2 − 6 3 ( 2 − 2 )Rewrite in factored form- 3 ( 2 − 2 ) 3 ( − 2 ) ⋅Solution- 3 ( − 2 ) ⋅
Given the polynomial find any actual rational roots
x^3+x^2+4x+4=0
Answers
https://brainly.com/question/7356967 the correct answer is there Part 1A:
Given
Part 1B:
Given
Using rational roots theorem, we can see that the possible roots of the the given equation are:
By substituting the possible roots, we can see that x = 1 is a root, thus x - 1 is a factor.
We can get the other factors by using sythetic division to divide by x - 1.
Step-by-step explanation:
x^3+x^2+4x+4=0
x³+x²+4x=-4
x(x²+x+4)=-4
either
x=-4
or
x²+x+4=-4
x²+x+4+4=0
x²+x+8=0
comparing with ax² +bx+c
a=1
b=1
c=8
x={-1±√{1²-4×1×8}}/2×1
x={-1±√{-31}}/2
Determine whether the relationship is an inverse variation or not. Explain
X y
2 630
3 420
5 252
.A.The product xy is constant, so the relationship is an inverse variation.
B.The product xy is not constant, so the relationship is an inverse variation.
C.The product xy is not constant, so the relationship is not an inverse variation.
D.The product xy is constant, so the relationship is not an inverse variation
Answers
The correct answer is option A: "The product xy is Constant, so the relationship is an inverse variation."
To determine whether the relationship between the values of x and y in the given table is an inverse variation or not, we need to examine the behavior of the product xy.
Let's calculate the product xy for each pair of values:
For x = 2, y = 630, xy = 2 * 630 = 1260.
For x = 3, y = 420, xy = 3 * 420 = 1260.
For x = 5, y = 252, xy = 5 * 252 = 1260.
From the calculations, we can observe that the product xy is constant and equal to 1260 for all the given values of x and y.
Based on this information, we can conclude that the relationship between x and y in the table is an inverse variation. In an inverse variation, the product of the variables remains constant. In this case, regardless of the specific values of x and y, their product xy consistently equals 1260.
Therefore, the correct answer is option A: "The product xy is constant, so the relationship is an inverse variation."
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solve the following equation step by step 7-x=5
Answers
Answer:
x=2
Step-by-step explanation:
add the x onto the other side so it is positive : 7=5+x
then subtract the 5 from both sides so you can isolate the x : 2=x
rewrite the equation: x=2
☆ Hello ☆
The value of x is 2.
\( \red{ \sf \underline {\underline{Explantation: }}}\)
¿What are equations?
The equations represent an equality between two mathematical expressions that have at least one variable called unknown.
\( \sf \:Solution:\)
\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - x = 5}}\\\boldsymbol{\mathsf{ - x = 5-7}}\\\boldsymbol{\mathsf{ - x = -2}}\ \\ {\mathsf{ x = 2}}\end{gathered}\)
\( \bf \:Verification:\)
\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - 2 = 5}}\\\boldsymbol{\mathsf{ 5=5}}\end{gathered}\)
\(\green{ \sf \: The \: result \: is} \: \red{\longmapsto} \blue 5\)
18. If (2x-3) is a factor of 2x4 - 3x² + 15x - 15k,
find the value of (3k - √5 k).
Answers
Answer:
Well, here it means that if we set 2x-3 to zero, it becomes x over two dimensions. If we set the question form to zero and set x to two over two
k is obtained 19 to 12, now put this k in what you want
Is 6,9, 12 a right triangle, acute triangle or obtuse triangle???
Answers
Answer:
acute triangle
Step-by-step explanation:
acute triangle is degree is 0to 90 degree
QUESTION 6
Which of the following is the correct description of the graph shown?
a.) Figure A'B'C'D' is the image of figure ABCD under a rotation of 90°clockwise about the origin
b.) Figure A'B'C'D' is the image of figure ABCD under a rotation of 45° counterclockwise about the origin.
c.) Figure A'B'C'D' is the image of figure ABCD under a rotation of 90°
counterclockwise about the origin
d.) Figure A'B'C'D' is the image of figure ABCD under a rotation of 180
about the origin
Answers
From 24 grams to 96 grams ( percent change )
Answers
Answer:
i think it is 300%
Step-by-step explanation:
for A boy walk at 8km/h quarter of an hour and he travelled the rest by bus at 28km/h for 12h. What was the total direction travelled
Answers
The boy traveled a total distance of 338 kilometers.
To solve this problem
We can start by calculating the boy's walking distance.
Distance = speed x time.
The boy walked for 0.25 hours, or one-quarter of an hour. The distance covered on foot is calculated as follows:
Distance = 8 km/h x 0.25 h = 2 km
Next, we can determine how far a bus travels. The boy covered the following distance in 12 hours by bus at a speed of 28 km/h:
Distance = Speed x Time
Distance = 28 km/h x 12 hours = 336 km.
The sum of the distances walked and traveled by bus represents the total distance traveled:
Total distance = 2 km + 336 km = 338 km
Therefore, the boy traveled a total distance of 338 kilometers.
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what is the mean value of the following scores: 12, 25, 15, 27, 32, 8?
Answers
The mean value of the scores is 19.83, based on their sum and quantity of numbers.
The mean or average is calculated using the formula -
Mean = sum of all the numbers ÷ quantity of numbers.
We see that there are six numbers and hence the quantity of numbers will be 6.
Sum of all the numbers = 12 + 25 + 15 + 27 + 32 + 8
Performing addition on Right Hand Side of the equation
Sum of all the numbers = 119
Now calculating the mean of the scores by keeping the values in formula -
Mean = 119/6
Performing division on Right Hand Side of the equation
Mean of scores = 19.83
Hence, the average of scores is 19.83.
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can you please tell me which one it is and why. thank you
Answers
Answer
its A the answer is on quizzes
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
rational numbers do not have unending numbers trailing it
ex: 1, 1/4 13/2
irrational numbers do not end
(pi, square root of 2)
Use the given information to find the left- and right-hand Riemann sums for the following function. If necessary, round your answers to five decimal places.
f(x)=x^2+3
a=−10,b=8, and n=17
Left-Hand Riemann Sum = Right-Hand Riemann Sum =
Answers
The left -hand Riemann sums is (1.05)[f(-10) + f(-10 + 1.05) + f(-10+ 2(1.05)) + ... + f(-1 + 16(1.05)] and the right-hand Riemann sums is (1.05)[f(-10 + 1.05) + f(-1 + 2(1.05)) + f(-1 + 3(1.05)) + ... + f(8)]
Since the given function is : f(x)=x^2+3 and the given points are a=−10,b=8, and n=17 .
We know by the formula Δx = (8 - (-10)) / 17 = 1.05.
So, the Left sum = (1.05)[f(-10) + f(-10 + 1.05) + f(-10+ 2(1.05)) + ... + f(-1 + 16(1.05)] and Right sum = (1.05)[f(-10 + 1.05) + f(-1 + 2(1.05)) + f(-1 + 3(1.05)) + ... + f(8)]
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Rewrite 2(3x)+7+8 in simplest form
Answers
Answer:
\(6x+15\)
Step-by-step explanation:
\(2\left(3x\right)+7+8\)
\(\mathrm{Add\:the\:numbers:}\:7+8=15\)
\(=2\cdot \:3x+15\)
\(\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6\)
\(=6x+15\)
Hence, the correct answer is: \(6x+15\)
Answer:
\(\huge\boxed{\sf{6x+15}}\)
Step-by-step explanation:
Hello.
Let's solve this problem.
First, multiply 2 times 3x:
6x
Now, add 7 plus 8:
15
Write the expression:
6x+15
Can this expression be simplified any further?
No.
Why?
Because variables and constants are not like terms.
In this case, the variable is x, and the constant is 15.
I hope it helps
Have a nice day.
\(\boxed{imperturbability}\)