An equilateral triangle and a regular hexagon have the same area. The ratio of the side length of the regular hexagon to the side length of the equilateral triangle can be written as m/√n. What is m+n?
Help me plz!
Answers
Answer:
7
Step-by-step explanation:
Let a and b be the sides of the equilateral triangle and the regular hexagon respectively as shown in figures (1) and (2).
The area of the equilateral having side a is
[tex]A_T= \frac {\sqrt3}{2}a^2\cdots(i)[/tex]
Now, join all the 6 corner points of the regular hexagon to the center of the hexagon as shown in figure (3).
As there are 6 equal sides, so angle subtended by each side at the center is 360/6=60 degrees.
Considering the triangle POR:
[tex]\angle POR= 60[/tex] degree [angle at center]
As sides PO=RO, so [tex]\angle OPR = \angle ORP = 60[/tex] degree.
Hence, triangle POR is an equilateral triangle.
Similarly, all the remaining 5 triangles are equilateral triangles.
So, the area of hexagon = 6 x Area of triangle POR
As the length of sides of the triangle POR is b,
so the area of the triangle POR [tex]= \frac {\sqrt3}{2}b^2[/tex].
Hence, the area of the regular hexagon,
[tex]A_H = 6 \times \frac {\sqrt3}{2}b^2\cdots(ii)[/tex]
As the equilateral triangle and a regular hexagon have the same area, so from the equations (i)and (ii), we have
[tex]A_T=A_H\\\\\frac {\sqrt3}{2}a^2=6 \times \frac {\sqrt3}{2}b^2\\\\\Rightarrow a^2=6b^2\\\\\Rightarrow \frac {b^2}{a^2}=\frac 1 6\\\\\Rightarrow \frac {b}{a}=\frac {1}{\sqrt 6}\cdots(iii)[/tex]
Given that the ratio of the side length of the regular hexagon to the side length of the equilateral triangle, b/a= m/√n.
On comparing with the equation (iii), we have
m=1 and n=6
Hence, m+n=1+6=7.
Related Questions
Please helpppp guyssssss
Answers
Answer:
the answer is B because the 30x how much they charge each hiur and the other one has a trend of 25 each hour so P charges 5 more .
Which of the following could be the perimeters of the three squares below?
A 12ft, 16 ft and 20 ft
B 20 ft, 16 ft and 24 ft
C) 40 ft, 80 ft and 120 ft
D 16 ft, 24 ft and 28 ft
Answers
Answer:
Option (A)
Step-by-step explanation:
Option (A).
Since, perimeter of a square = 4×(side)
Perimeters of 3 squares = 12 ft, 16 ft and 20 ft
Side lengths of three squares will be = [tex]\frac{12}{4}, \frac{16}{4},\frac{20}{4}[/tex]
= 3 ft, 4 ft and 5 ft
If these sides are the measures of the sides of the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
5² = 4² + 3²
25 = 16 + 9
25 = 25
True.
Therefore, these are the sides of the given right triangle.
Option (B).
Perimeters of three squares are 20 ft, 16 ft and 24 ft.
Sides lengths of three squares = [tex]\frac{20}{4},\frac{16}{4}, \frac{24}{4}[/tex]
= 5 ft, 4 ft and 6 ft
By Pythagoras theorem,
6² = 4² + 5²
36 = 61
False.
Therefore, these sides are not of the given right triangle.
Option (C)
Perimeters of the squares = 40 ft, 80 ft and 120 ft
Side lengths of the squares = 10 ft, 20 ft and 30 ft
If these sides are the sides of the given right triangle, they will follow the Pythagoras theorem.
By Pythagoras theorem,
(30)² = (10)² + (20)²
900 = 500
False.
Option (D)
Perimeters of the given squares are 16 ft, 24 ft and 28 ft.
Side lengths of these squares will be 4 ft, 6 ft and 7 ft.
If these sides form a right triangle they will follow the Pythagoras theorem.
By Pythagoras theorem,
7² = 4² + 6²
49 = 16 + 36
49 = 52
False.
Therefore, these are not the sides of a right triangle.
Option (A) will be the answer.
ILL GIVE BRAINLIEST!!! The average of x+6, 6x+2, and 2x+7 is 4x-7. What is x?
Answers
Answer:
yStep-by-step explanation:
Please help ASAP! Answer the questions like 1. 2. 3 pls
Answers
Answer:
1. 3, because 30 divided by 10 is 3.
2-6, What is the recipe? By understanding the OG recipe I can multiply every number by three.
You can put the recipe in the comments and I will edit this answer. :)
~PumpkinSpice1
3 is your lucky number
For question one, You need to multiply 10 by 3. To get this you can divide 30 by 10, this gives you the number you need to multiply 10 by, in this case its 3.
The next two questions are not able to be answered because I need the amount of oil or flour to determine how much to use for 30 cupcakes.
But, if you have 1 cup of oil for 10 servings, and you want 30 servings, like before, multiply by 3.
Same for flour, it doesnt matter how much of it you need, just multiply by 3 from the amount you use for 10 servings.
If your confused on 4, 5 and 6. Just remember, 3 is the lucky number.
As the standard deviation of outcomes for Martin Products increases, investing in Martin Products becomes riskier because:__________a. the range of outcomes having some probability becomes widerb. an outcome at or near the expected return of 10% becomes less likelyc. although the chances of some big gains increase, the chances for some big losses also increase.d. all of the above reasonse. none of the above reasons
Answers
Answer:
c. although the chances of some big gains increase, the chances for some big losses also increase.
Step-by-step explanation:
In the Martin Products, there is a probability that the investment could either succeed or fail. The standard deviation of the outcome carried out to determine the risks involved in investing in his products helps in trying to offer the investors the clearer picture of the risks involved.
Answer:
d. all the reasons above
Please help me solve this! If you could solve my other questions that haven't been solved that would be great!
Answers
Answer:
The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
In the complex fractions [tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c
To simplify it change ÷ to × and reciprocal c
[tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c = [tex]\frac{a}{b}[/tex] × [tex]\frac{1}{c}[/tex] = [tex]\frac{a}{bc}[/tex]In the complex fractions [tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex]
To simplify it change ÷ to × and reciprocal [tex]\frac{b}{c}[/tex]
[tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex] = a × [tex]\frac{c}{b}[/tex] = [tex]\frac{ac}{b}[/tex]Let us solve the question
∵ The complex fraction is [tex]\frac{\frac{8}{9}}{8}[/tex]
∵ [tex]\frac{\frac{8}{9}}{8}[/tex] = [tex]\frac{8}{9}[/tex] ÷ 8
→ Change ÷ to × and reciprocal 8
∴ [tex]\frac{8}{9}[/tex] ÷ 8 = [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex]
→ Cancel 8 up with 8 down
∴ [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{9}[/tex]
∴ The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is [tex]\frac{1}{9}[/tex]
Answer:
1
Step-by-step explanation:
In the fraction 8/9, 8 is the numerator and 9 is the denominator. When you ask "What is 8/9 simplified?", we assume you want to know how to simplify the numerator and denominator to their smallest values, while still keeping the same value of the fraction. We do this by first finding the greatest common factor of 8 and 9, which is 1.
(3x+5)+(2x+3)
Please show steps
Answers
Answer:
first you do the mutpiton in the first perentes then you do addition
Step-by-step explanation:
3x + 8 + 2x
(3x+2x) + 8
5x + 8
Your answer is 5x + 8
Please help me please
Answers
Answer:
the ham is the least expensive, the roast beef is most expensive
Step-by-step explanation:
hope this helps.
DUE IN 10 MINUTES!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
1/4
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.
The figure shows a right triangle with legs marked 40 and 9.
Answers
Answer:
41
Step-by-step explanation:
The Pythagorean Theorem:
[tex]x^2+y^2=z^2[/tex]
where x and y are two legs, and z is the hypotenuse
Plugging this in, we have
[tex]40^2 + 9^2 = 1681\\\sqrt{1681}=41[/tex]
Answer: Hypotenuse is 41
An internet site sells 75 feature type cell phones. The ratio of the number of smartphones to the number of feature phones is 3:5. How many cell phones are smart phones?
Answers
Does the graph represent a function? Why or why not?
10-
-10
10
-10-
O A. No, because it fails the vertical line test.
B. No, because it fails the horizontal line test.
O C. Yes, because it passes the vertical line test.
O D. Yes, because it passes the horizontal line test.
Answers
Answer:
no because it fails the vertical line test
what is 206 divided :) 6
Answers
Answer:
if you mean 206 divided by 6 than the answer will 34.3 (rounded)
Step-by-step explanation:
I used a calculator
Could anyone give a hand?
Answers
Answer: 73.5
first you work out the total area of this shape.
area: 105
this mean you can start working out the non-shaded area to do this you need to multiply 7cm with 6cm which is 42cm then you divide by 2 to get 21cm.
then to work ou the other non-shaded area in the left you multiply 3cm and 7cm together getting 21cm you then divide it and you get 10.5.
you then add 10.5cm and 21cm together to get 31.5cm, subtract that answer with the total area which gets the answer 73.5!
2. Melissa estimated that she would read 250 pages
last week. She read 290 pages. What is the
percent error of Melissa's estimate? Round to
the nearest whole percent.
I will give brainliest!!!
Answers
Answer:
Is it 11.6%?
Step-by-step explanation:
I divided 290/250
25) (1,-5) parallel to y = - 10x - 3
Answers
Here is the working
I'm going to k.m.s GOODBYE WORLD
Answers
Answer:
nooooo
Step-by-step explanation:
Answer:honestly i might too at some point but if you decide not to and want to talk about what happened, let me know. i'm not a therapist and i'm not the best with words, but i do like to listen to what others have to say and learn from their lives. i hope you choose to live, but i sadly cannot stop you.
Step-by-step explanation:
help please with #3
Answers
Answer: x = 2a over b + c
Step-by-step explanation:
1. Multiply both sides by two. This cancels out 2 and turns a into 2a. It should look like 2a = bx + cx
2) Since both b and c have x’s, we turn it into (b + c)x
3. Then divide both sides by b+c to get 2a over b + c = x
Find the product of (x - 3)2.
Answers
Answer:
2x-6
Step-by-step explanation:
Answer:
Step-by-step explanation:
(x - 3)^2 = x^2 - 3x - 3x + 9 = x^2 - 6x + 9
Finding the area, any help?
Answers
Answer:
Volume: x^6
Area: 6x^4
Step-by-step explanation:
volume: length x width x height
area: 6 sides of x^4 so 6x^4
What is the answer to 1/3x(15+6)?
Answers
Answer:
1/3×21
=7
Step-by-step explanation:
first step: solve the barket part
second step: Solve division or multiplication which first..Follow Rule:BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction.
A 115-inch is cut into two pieces. One piece is four times the length of the other. Find the lengths of the two pieces.
Answers
Answer:
Shorter piece: 23 inches
Longer piece: 92 inches.
Step-by-step explanation:
Since the longer piece is four times the length of the other, we multiply 23*4 and we get 92 inches.
Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights below 125 oz is:
A. .500
B. .159
C. .341
D. .841
Answers
Answer:
125 is 1 dev above, so it's 13.5 + 2.35,so it's B. 0.159And i think the proportion of infants with birthweights between 125 oz and 140 oz is :D. 0.136juanito has a rope 1.75 meters long. He needs to cut it into shorter ropes each 0.1 meter long
Answers
Answer:
17.5
Step-by-step explanation:
[tex]1.75 \div 0.1 = 17.5[/tex]
Which algebraic expression represents “Sarah has fives times as much homework today as yesterday”?
5 + h
5 h
h minus 5
StartFraction h Over 5 EndFraction
Answers
This is because the phrase “times” represents multiplication, therefore your answer would be 5 x h but you can represent that as just 5h.!
Answer:5h
Step-by-step explanation: i just did the quiz
Combine like terms: 4 - 3m - 1 + 2m
Answers
Answer:
-m+3
Step-by-step explanation:
4 - 3m - 1 + 2m
4-1-m
-m+3
Is (2, 10) a solution to this system of inequalities? y 7 X 1 y > 4x + 2
Answers
yes it is, 700 is greater than 10.
Slope is known as the run over the rise. True or False
Answers
Answer:
false. slope is calculated by rise over run
Answer:
FALSE
Step-by-step explanation:
Slope is known as the RISE OVER RUN.
Can I get brainliest? Plz!!!
WILL GIVE BRAINLIEST TO WHOEVER IS RIGHT
Answers
Answer:
lies you wont give brainliest
Step-by-step explanation:
A ladder is 2 metres long. It leans against a wall
so the base is 86 cm from the wall.
a Write 86 cm in metres.
b How far up the wall does the ladder reach?
Answers
Step-by-step explanation:
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