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
5.)
A ball is thrown into the air with an initial velocity of 96 feet per second. Given the formula below wheret,
represents time in seconds and s(t), the height of the ball, when will the ball hit the ground?
s(t) = -16t? + 960
Show full work
Answers
Answer: The ball will hit the ground 6 seconds after it has ben thrown, at t = 6s.
Step-by-step explanation:
The equation for the height of the ball should be:
s(t) = (-16ft/s^2)*t^2 + 96ft/s*t
When s(t) = 0ft, means that the ball is in the ground
This represents the height of the ball as a function of t, the time in seconds.
We can see that at t = 0s:
s(0s) = (-16ft/s^2)*(0s)^2 + 96ft/s*(0s) = 0ft
Then at the time 0 seconds, the ball is in the ground, so we must look at the other root of the equation
(-16ft/s^2)*t^2 + 96ft/s*t = 0ft
To find it, we can use the Bhaskara equation, in this case is:
[tex]t = \frac{-96ft/s +- \sqrt{(96ft/s)^2 - 4*(-16ft/s^2)*0} }{-2*16ft/s^2} = \frac{-96ft/s^2 +-96ft/s^2}{-32ft/s^2}[/tex]
Then we have the two solutions:
t = (-96ft/s + 96ft/s)/(-32 ft/s^2) = 0s (the one that we already found)
And the other one is:
t = (-96ft/s - 96ft/s)/(-32ft/s^2) = 6s
Then:
s(6s) = 0ft
This means that the ball will hit the ground at t = 6 seconds.
The time required to hit the ground is required.
The time taken by the ball to reach the ground is 2.45 seconds.
The equation is
[tex]s(t)=-16t^2+96[/tex]
At the ground [tex]t=0[/tex]
so,
[tex]0=-16t^2+96\\\Rightarrow 16t^2=96\\\Rightarrow t=\sqrt{\dfrac{96}{16}}\\\Rightarrow t=2.45\ \text{s}[/tex]
The time taken by the ball to reach the ground is 2.45 seconds.
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(Pls help me! I don’t understand!) it’s as image btw
Answers
what is 535 divided by 30 with a remainder?
Answers
Answer:
17 with the remainder of 25
Step-by-step explanation:
Given directed line segment AB determine point X on the graph such that X partions the segment A to B in a ratio of 1:4 and given its coordinates A(5,1) and b(-5,4)
(NEED THIS ASAP!!)
Answers
Answer:
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
Step-by-step explanation:
When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,
the coordinates of point are given by:
[tex](x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})[/tex]
Given points are:
(x1,y1) = (5,1)
(x2,y2) = (-5,4)
Putting the values in the formula
[tex]X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})[/tex]
Hence,
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
which of the following is not equivalent to the rational number 12/5
1) 2.4
2) 9/4
3) 2 2/5
4) 36/15
Answers
Answer:
2) 9/4
Step-by-step explanation:
12/5 in decimal form is 2.4. As a mixed number, 12/5 is 2 2/5. And, 12/5 is just a reduced form of 36/15. So, the only answer it can be is answer 2: 9/4
Select the expression that is NOT equivalent to 2 × (3 + 6).
A. 6 + 12
B. (2 × 3) + (2 × 6)
C. (2 × 6) + (2 × 3)
D. (2 × 3) + (3 × 6)
Answers
B. 18
C. 18
D. 24
Answer:
D
Step-by-step explanation:
in answer D, the values would equal "6" and "18" which is not equivalent to the given equation
Help!! Please help with this question.
Answers
Answer:
The slope seems to be 4.
Step-by-step explanation:
The line seems to be starting at (3,0) and if you use the rule rise/run, it goes up (rises) 4 units and moves over (runs) 1 unit. You then rewrite this as 4/1 and you get 4 as the slope!
Answer:
The slope is 4
My logic:
Slope is delta y over delta x so if you take any 2 points on that graph and get the x and y of each point and find the change of the two x and the two y and put the change in y over the change in x. you get slope. like so= 16/4 or 4
5 men build a wall in 10 days how long will it take one man
Answers
Answer:
50 days?
Step-by-step explanation:
Answer:
i think it is 2 because
10 divide by 5 = 2
1 x 2 = 2
2 days
Consider quadrilateral ABCD shown.
Answers
Answer:
a=(2,8) b=(8,8)
c=(8,2) d=(2,2)
Step-by-step explanation:
Answer:
this quadrilateral would be a square because all of the sides are equal.
A linear function contains the following points. (0,-4) (4,4) What are the slope and y-intercept of this function?
Answers
Answer:
slope = 2
y-intercept= -4
Step-by-step explanation:
slope = y2- y1/ x2-x1
slope = 4-(-4) / 4-0
slope = 2
using (4,4) for (x,y)
y= mx+b
4= 2(4)+b
b= -4
Recidivism occurs when a person continues to commit criminal behavior even after having been punished. A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. Construct a 99% confidence interval for the proportion of cases of recidivism.A. (0.331, 0.567)B. (0.188, 0.332)D. (0.289, 0.431)E. (0.069, 0.111)
Answers
Answer:
Option (C) [0.2574 , 0.2626]
Step-by-step explanation:
Of 250 convicts, there are 65 cases of recidivism.
- Construct a 99% confidence interval for the proportion of cases of recidivism.
This calls for first finding the proportion of cases of recidivism. This will be 65/250 = 0.26
You are 100% confident that the proportion of cases of recidivism is 0.26
You will be 99% confident that the recidivism cases are between:
99% of 0.26 = 0.2574
1% of 0.26 = 0.0026
[0.26 - 0.0026] , [0.26 + 0.0026] = [0.2574 , 0.2626]
This should be OPTION C, as that option is missing in the list of options.
Wich equation describes this graph?
Answers
Answer:
The correct equation for the graph is B.) y = x- 3
Answer:
B
Step-by-step explanation:
the right answer us B is that right
Circle circumference
Will mark brainliest
Answers
47.1
43.96
these are the answers
BLANK% of 50 shirts is 2 shirts.
Answers
Answer:
4%
Step-by-step explanation:
2/50 is 4....I believe.
whats the sum of the numbers in the 15th row of pascals triangle
Answers
Answer:
2,3,5,7,11,and 13
Step-by-step explanation:
Hope this helped :))
The sum of the numbers in the 15th row of pascals triangle are 2,3,5,7,11,and 13
What is Pascal triangle?Pascal triangles contains coefficient of 's expanded form's terms.
Thus, 1 is the value in the first row of Pascal triangle.
The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.
For nth row, and its rth term(all counted from 0-indexing(that means, counting of index starts from 0), then that term in Pascal triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
........
The sum of row n is 2^n, thus the row number with a particular sum;
2^n = sum
n·log(2) = log(sum)
n = log(sum)/log(2)
The sum of the numbers in the 15th row of pascals triangle
2,3,5,7,11,and 13
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1
Find the average of
1/3
And
1/4
Answers
Answer:
7/6
Step-by-step explanation:
1/3+1/4
4/12+3/12=7/12
7/12 divided by 1/2
7/12 times 2 as when dividing fraction, multiply by reciprocal.
14/12
7/6
A cold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours. If cold water pipe is turned on and hot water pipe is turned on 3 hours later then how long will it take them to fill the pool together?
Answers
answer = 5
Step-by-step explanation:
A cold water pipe can fill a swimming pool in 4 hours
And a hot water pipe in 6 hours.
If cold water pipe is turned on and hot water pipe is turned on 3 hours later
6-4 = 2
2+3 = 5
5 answer
Answer:
0.6 of an hour
Step-by-step explanation:
A cold pipe takes 4h hours so we can assume ¼ of our job is done in one hour.
After 3 hours go by with the cold pipe on, we have ¼ of the job left.
Now we have our hot pipe, which takes 6 hours for the entire pool, so we can assume that it has a rate of ⅙ per hour. Now since these two pipes are working together we can add them.
⅙ + ¼ = ⁵/₁₂
Now we divide.
Since at the start 3 hours had gone by with the cold pipe that would have been ¾ of our time so, 1 - ¾ = ¼
¼ ÷ ⁵/₁₂ = ⅗ or 0.6 of an hour
What is the x-intercept of the line?
(-38,40)
(-23,30)
(-8,20)
Answers
The answer fam is.......... 22
please help me solve this
Answers
Answer:
A) 7 and 8
Step-by-step explanation:
root of 7 is 2.64575..... then when u multiply by 3
3*2.64575=7.93725
Find the lengths of the sides of the triangle PQR. P(3, â3, â3), Q(9, 0, 3), R(12, â6, â3) |PQ| = |QR| = |RP| = Is it a right triangle?
a. Yes
b. No
c. Is it an isosceles triangle?
Answers
Answer:
a. Yes
Step-by-step explanation:
Instead of handing out candy like a well-adjusted person on Halloween, grumpy, anti-social Professor Sosa decides to stand on top of a 400 ft building and toss candy treats onto the ground below. If he drops a bag of candy corn, how long will it take for it to land on the ground? What will the velocity of the bag be when it hits the ground?
Answers
Answer: The bag of candy corn will take 5 seconds to land on the floor and it will hit it with velocity of 49m/s.
Step-by-step explanation: A free falling object has only Gravitational Force acting on it, so acceleration will be due to gravity, which has magnitude
g = 9.8m/s².
As Professor Sosa drops the bag, its initial velocity and time are 0.
The building has a height of 400ft, so adjusting units: y = 121.92 m and [tex]y_{0}[/tex] = 0.
For this problem, going down will be the positive reference.
Then:
[tex]y=y_{0}+v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]\Delta y=v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]121.92=\frac{9.8}{2}t^{2}[/tex]
[tex]t=\sqrt{\frac{121.92*2}{9.8} }[/tex]
t ≈ 5
It will take 5s for the candy corn bag to land on the ground.
Acceleration is the change in velocity per change in time, so:
[tex]g=\frac{\Delta v}{\Delta t}[/tex]
As initial velocity and time are 0 and rearraging it:
v = g.t
v = 9.8*5
v = 49
The bag will hit the ground with velocity of magnitude 49 m/s.
if the graph of an exponential function is increasing is the domain always all real numbers
Answers
Answer:
D) The domain of the function is all real numbers
Step-by-step explanation:
Given g (x) = -x + 3, find g(1)
Answers
Answer:
2
Step-by-step explanation:
g (x) = -x + 3
g(1) = -(1) + 3
= 2
Hope this helped! If so, plz mark brainliest.
HELPPPP WITH THIS QUESTION PLEASEEE!!!
Answers
Answer:
I believe it is A.
Let me know if this helps!
Lisa takes a night walk after dinner every night. She walks 1/4 mile in 2 minutes. How how does she walk in 10 minutes? (write-in decimal form)
Answers
Answer:
1.25 miles
Step-by-step explanation:
Lisa takes a night walk after dinner every night.
She walks 1/4 mile in 2 minutes.
Distance = 1/4 mile
Time, t = 2 minutes
For covering 1 mile,
1/4 mile = 2 minutes
In 1 minute she will cover [tex]\dfrac{1}{8}\ \text{mile}[/tex]
For 10 minutes, she will cover [tex]\dfrac{10}{8}\ \text{mile}\ or\ 1.25\ \text{miles}[/tex]
So, she will cover 1.25 miles.
What 90
4 l is
3
?
You have 41 students three are absent what percentage of students are absent?
Answers
Answer:
Step-by-step explanation:
If 41 students is in the roll (total), then
[tex]\frac{3}{41}[/tex] = [tex]\frac{x}{100}[/tex] ⇒ x = [tex]\frac{3*100}{41}[/tex] ≈ 7.3 %
Plz i need an accurate answer help me plz
Answers
Answer:
Plug in the values 1, 2, 3, 4, 5, one at a time into the function (replacing x with the number). Then calculate the result for each. Sum the results and divide it by the number of values (5).
Solve for X. PLEASE HELP
Answers
Answer:
xxtentacion for life
Step-by-step explanation:
9 + 7 = 8 + x
16 = 8 + x
x = 8
A bottle of juice that says it holds 2 cups only holds 1 cup 5 ounces. The bottle of juice holds how many ounces less than it should. This represents what percentage error
Answers
Answer:
A bottle of juice that says it holds 2 cups actually only holds 1 cup 5 ounces. The bottle of juice holds
3 ounces less than it should. This represents a 18.75 percent error.
Step-by-step explanation:
4.3.AP-10
Question Help
On a team, 7 girls and 5 boys scored a total of 91 points. The difference between the number of points scored by the 7 girls and the number of points scored by the
5 boys is 21. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each
boy
Answers
Answer:
u want step by step?
Step-by-step explanation: