a hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. the chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
Answers
According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
[tex]\frac{AQ}{EQ} = \frac{BQ}{DQ} = \frac{AB}{ED} = \frac{3}{5}[/tex]
Also,
[tex]\frac{\frac{AD - PQ}{2} }{PQ + 5} = \frac{3}{5}[/tex]
and [tex]\frac{3 - PQ}{\frac{AD + PQ}{2} } = \frac{3}{5}[/tex]
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
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Related Questions
Which number produces a rational number when added to 0.6?
Answers
Answer:
D is the answer
Step-by-step explanation:
please make my answer as brainelist
judy measured a summer camp and made a scale drawing. the scale she used was 19 centimeters : 8 meters. in the drawing, the sand volleyball court is 38 centimeters long. what is the length of the actual volleyball court?
Answers
As per the drawing scale, the actual length is 16m.
What is a drawing scale?
A length at full size: The length at the scale hired this is the identical period is how the size of works is expressed as a ratio. drawing, for example, would be 1:1.A drawing or representation of a authentic aspect that has been scaled up or down out of its original size at the same time as last proportionate to a actual item is called a scale drawing. Scale ratio refers to the share in which a drawing of such an object is shrunk or increased.Given scale is,
19:8
Therefore,
To determine the, actual length,
[tex]\frac{19}{8} =\frac{38}{actual\ length}[/tex]
⇒ actual length = [tex]\frac{38}{19}*8[/tex] = 16m.
Hence, as per the drawing scale the actual length is 16m
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is it true a cylinder is a polyhedron where two faces are parallel and congruent and the remaining faces are parallelograms
Answers
It is "false" that a cylinder is a polyhedron where two faces are parallel and congruent and the remaining faces are parallelograms. Its is a prism.
What is a prism?A polyhedron of two polygonal faces in parallel planes & parallelograms on the other faces is called prism.
Some features regarding the prism are-
A prism is a type of polyhedron with two parallel and congruent faces known as bases, and the other faces were indeed parallelograms. The base is the pair of identical shapes in a prism; there seem to be two bases on a prism that really are congruent and parallel. These bases are N-sided and polygonal. Prisms abound in our surroundings, such as the locker in our bedroom and skyscrapers.Prisms come in a variety of shapes, including Rectangular Prisms, Pentagon shaped Prisms, Triangular Prisms, Pyramids as Prisms, and Hexagonal Prisms. They each are given their own polygon as a base and parallelogram faces.To know more about the prism, here
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write the standard form of a complex number using a for the real part and b for the imaginary coefficient
Answers
The standard form the Complex number having real part "a" and imaginary part"b" is a+ib.
Complex number:
Basically, a Complex number is made up of two numbers: a real number and an imaginary number. A+iB, where an is a real number and ib is an imaginary number, is a Complex number. A and B are real numbers.
As a result, a Complex number is just a straightforward way to describe the addition of two integers, a real number and an imaginary number. It is divided into two parts: a pure actual component and a pure fictitious part.
Therefore,The standard form the complex number having real part "a" and imaginary part"b" is a+ib.
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Answer:It’s a+bi
Step-by-step explanation:
Simplify each expression for x=6 a. 12x^0(x^-4) b. 14(x-2)
Answers
After solving the expressions we get the value for each of it as:
a. 1/108
b. 7/18
Given:
a. 12x⁰(x⁻⁴)
Apply the multiplication property of exponents.
when variables multiply, the powers are added.
12x⁰⁻⁴
12x⁻⁴
substitute the value of x = 6 in the above term.
12(6)⁻⁴
12 × 1/6⁴
12 × 1/1296
1/108
b. 14(x⁻²)
The algebraic technique for resolving simultaneous linear equations is called the substitution method. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.
directly substitute the value of the x in the expression.
14(6)⁻²
14 × 1/6²
14 × 1/36
7/18
hence after evaluating expressions we get the values as 1/108 and 7/18.
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Answer the 2 questions in photo [ Brainliest + easy points ]
Answers
Answer:
14. 41
15. 4
Step-by-step explanation:
I used Substitution.
2(14)+13 = 41
3(2) - 2 = 4
Answer: EF = 29 units and KM = 22 units
Step-by-step explanation: For the first one, we just add EF and FG, x+14 and 14, and make it equal to EG, 2x+13. We then get x+28 = 2x+13, x = 15. EF = x + 14 and then sub in 15 for x to get 29.
For KM, same deal as the first one. KL and LM, 6 and 2x, equals to KM, 3x-2. 2x+6 = 3x - 2. x = 8. KM = 3x - 2. sub in 8 for x and then we get 22.
Question
Evaluate.
−26.6
-----------
−1
Enter your answer in the box.
Answers
The value of the expression given as −26.6/−1 is 26.6
How to evaluate the expression?The expression is given as
−26.6
-----------
−1
Rewrite the above expression properly as follows
So, we have
−26.6/−1 or −26.6 ÷ −1
This is so because the expression is a quotient expression
So, we have
−26.6/−1
Express −26.6 as -13.3 - 13.3
So, we have the following equation
−26.6/−1 = (−13.3 −13.3)/−1
Expand the expression
So, we have
−26.6/−1 = (−13.3)/−1 + (−13.3)/−1
Evaluate the quotients in the above equation
So, we have
−26.6/−1 = 13.3 + 13.3
Evaluate the quotients in the above equation
So, we have
−26.6/−1 = 26.6
Hence, the value of the expression given as −26.6/−1 is 26.6
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in college basketball, some teams get most of their points from just one player, and other teams are more balanced in scoring. consider the following facts about the scoring distributions for some ncaa division i basketball teams. each team has 121212 players. at baylor university, there are 666 players who each score 121212 points per game, and there are 666 players who each score 000 points per game. at the university of maryland, 111 player scores 585858 points per game, 111 player scores 141414 points per game, and the rest of the players score 000 points per game. at dartmouth college, 444 players score 555 points per game, 444 players score 666 points per game, and 444 players score 777 points per game.
Answers
At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. The mean number of points per player per game is the same at all 3 schools.
Given that in Baylor's University that there are 6 players who each score 12 points per game, and 6 players who each score 0 points per game.
The scores are 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12.
Mean = Sum/Count = 72/12 = 6.
Median is the average between the nth and (n+1)th term.
(0+ 12)/2 = 6
In Maryland university 1 player scores 58 points per game, 1 player scores 14 points per game, and the rest of the 10 score 0 points per game,
58, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Mean = Sum/Count = 72/12 = 6.
Median is 0
In Dartmouth, university, 4 players score 5 points per game, 4 players score 6 points per game, 4 players score 7 points per game.
The scores are
5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7
Mean = Sum/Count = 72/12 = 6
Median =(6+6)/2= 6
At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
The mean number of points per player per game is the same at all 3 schools.
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Johns weekly salary is $478.25. his employer is changing the pay period to semimonthly. What is johns annual salary?
What will johns semimonthly salary be to the nearest cent
Answers
Based on the fact that the employer is changing the pay period to semimonthly, John's semimonthly salary to the nearest cent is $956.50
John's annual salary can be found to be $24,869
How to find the semimonthly salary?If a person is paid semimonthly, it means that they are paid twice a month or every two weeks.
This means that John's semimonthly salary is:
= 478.25 x 2
= $956.50
In a year, John's annual salary will be:
= 478.25 x 52 weeks
= $24,869
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february $1$, $2008$ is a friday. the last friday of february $2008$ will be february $x$, $2008$. if $2008$ is a leap year, what is the value of $x$?
Answers
x= 29 which is Friday of that Month.
As 1st February 2008 is Friday
By adding 7 to the date we will get the next Friday Date of that month
i.e., 1 + 7= 8
i.e., 8 is Friday
Again if we will add 7 in 8 then we will get another Friday
so by adding again i.e., 8 + 7= 15 which is again Friday
Then 15 + 7 = 22 which is Friday.
adding again we will reach final to final answer 22+ 7 = 29 which is Friday
after adding 29 with 7 we will get 36 and as we know there are only 30/31 days in a month.
So, by adding 7 to the date we will reach the next week.
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find the solution to this equation: 4x-2(x-3)=-7+5x+4
Answers
Answer:
x=3
Step-by-step explanation:
4x-2x+6=-7+5x+4
2x+6=-7+5x+4
2x+6-6=5x-3-6
2x=5x-9
-3x=-9
x=3
BEED URGENT HELPPP!
(please help me answer these 3 questions, picture attached)
Questions:
1. what is the area of the whole rectangle?
( area = length * width )
2. what is the area of the shaded rectangle?
3. what is the area of the unshaded part of the rectangle? (area of the whole rectangle - area of the shaded part)
Answers
Answer: See below
Step-by-step explanation:
1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:
(4x-4)(x+1)= 4x^2 -4
2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:
(2x+2)(x-1)= 2x^2-2
3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:
4x^2-4 - 2x^2 -2 = 2x^2 - 6
3. Use your estimates to find out how many times more massive Jupiter is than
Mercury. Express your answer in standard form (without using a power of 10). Show
your work. (4 points)
Answers
Jupiter is 5,751.51 times more massive than Mercury.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The mass of the planet Jupiter is given below.
1,898,000,000,000,000,000,000,000,000 kg.
The scientific notation is:- 2 x 10²⁷ kg.
The mass of the planet Mercury is given below.
330,000,000,000,000,000,000,000 kg.
The scientific notation is:- 3.30 x 10²³ kg.
Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have
Jupiter / Mercury = 2 x 10²⁷ / 3.30 x 10²³
Jupiter / Mercury = 5,751.51
Your question was incomplete, but the complete question was given below.
The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.
The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.
Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).
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pls help me solve this question
Answers
Answer: 57.75 m or about 57.8m
Step-by-step explanation:
Carl used 24 blocks to build a tower. Each block is a cube with side length of 2 inches. Use the formula v = s3 to find the volume of a cube. What is the volume of the tower?
Answers
Answer:
184
Step-by-step explanation:
Which is faster?
The number of bacteria colonies doubling every 80 minutes
Or
The number of bacteria colonies quadrupling after 4 hours (once?)
Answers
Answer:
A. the number of bacteria colonies doubling every 80 minutes.
Step-by-step explanation:
A. 2 cells = 80 mins
B. 4 cells = 80 mins
how to check;
multiply both sides by 2 in equation A
2 × 2 = 80 × 2
4 cells = 160 mins
change the mins into hours
4 cells = 160 ÷ 60
4 cells.= 2 hrs 40 mins
coagulate results
equation A. is 4 cells = 2hrs 40 mins
equation B. is 4 cells = 4 hrs
therefore equation A. is faster
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5. Reem paid £62 for a bicycle.
She sold it later for £46.
What was her percentage loss?
Answers
Step-by-step explanation:
[tex] \frac{46}{62} \times 100 = 74.19 percent \\ 100 - 74.19 = 25.81 \: percent \\ her \: loss \: was \: 25.81 \: percent[/tex]
Toni rows a boat 4.5 km/h upstream and then turns around and rows 5.5 km/h back downstream to her starting point. If her total rowing time is 1.5 h, for how long does she row upstream?
Express your answer to the nearest minute. Make the table, write equations and solve.
Answers
Answer:Q
Step-by-step explanation:1+2-3+4=1
Help for BRAINLIEST! Find BC
Answers
The length of the segment BC is equal to 5√3 π / 3.
What is the length of a missing side of a geometric system?
Herein we find the a geometric system formed by a circle and an inscribed right triangle formed by two right triangles. By a quick inspection we find the following measures:
AD = 10π, m ∠ BCD = 60°, m ∠ BDC = 30°, m ∠ BDA = 60°, m ∠ BAD = 30°
Then, by 30-60-90 right triangle theorem we find that:
DB = (1 / 2) · AD
DB = (1 / 2) · 10π
DB = 5π
DB = √3 · BC
BC = (√3 / 3) · DB
BC = 5√3 π / 3
The length of the segment BC is equal to 5√3 π / 3.
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nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
Answers
The given statement is true because it is the definition of nonlinear optimization.
it is the branch of mathematics with deals with the basic mathematical operators called arithmetic operators are addition, division, multiplication and subtraction.
Here,
The nonlinear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is nonlinear, is true, Since its the basic definition of nonlinear optimization.
Thus, the given statement is true.
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Find the measure of LAOC
m LAOC =
Classify LAOC
Answers
The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.
What is an Acute Angle?An angle that has a measure that is less than 90 degrees is classified as an acute angle.
Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.
30 degrees is less than 90 degrees and can therefore be termed an acute angle.
Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.
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Describe the graph of the Celsius-Fahrenheit relationship
Answers
Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
When the input is of 0, the output is of 32, hence the intercept is of 32.When the input changes by 10, the output changes by 18, hence the slope is of 18/10 = 1.8.Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
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Remote Interior and Exterior Angles in Triangles
Answers
Answer:
∠ 2 = 60°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 remote interior angles.
123° is an exterior angle of the triangle , then
∠ 2 + 63° = 123° ( subtract 63° from both sides )
∠ 2 = 60°
Answer:
60
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180° so we can write the following equation to find the value of missing angle:
∠2 + 63 + 57 = 180 add like terms
∠2 + 120 = 180 subtract 120 from both sides
∠2 = 60
please simplify! i do not understand, work shown please!
Answers
[tex]2xy \sqrt[3]{3y {}^{ \: 2} } [/tex]
express the following equation in the form y=mx+c and identify the gradient:
2y=7x-5
5x-3y=4
10-2x+3y=0
Answers
Answer:
y = 7/2x - 5/2 ; gradient is 7/2
y = 5/3x - 4/3 ; gradient is 5/3
y = -2/3x - 10/3; gradient is -2/3
Step-by-step explanation:
2y = 7x-5
2y/2 = (7x - 5)/2 y = 7/2x - 5/25x - 3y=4
(5x-3y) -5x = 4 -5x -3y = -5x + 4-3y/-3 = (-5x+4)/-3 y= 5/3x - 4/310 - 2x+3y = 0
(10-2x+3y) -10 = 0 - 10-2x + 3y = -10(-2x + 3y) + 2x = -10 + 2x 3y = 2x -10 3y/3 = (2x - 10)/3 y = 2/3x -10/3NOTE: The gradient is the slope
x3+y3+z3=k does anyone get this anyone?
Answers
Answer:
k = x^3+y^3+z^3
Step-by-step explanation:
Solve for k by simplifying both sides of the equation, then isolating the variable.
Hope this helps.
A number z divided by 4 is 12
Answers
Answer:
z divided by 4 is 12
48 divided by 4 is 12
Help me please i cant do this
Answers
Answer: Can you give choices that in the problem
Step-by-step explanation:
Find the center and radius of 2x^2 + 2y^2 - 12x + 8y - 24 = 0
Answers
When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.
The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]
The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]
Where (-g,-f) is the coordinates of the circle
The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]
Divide the equation by 2
[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]
Compare the equation with general form
2g= -6
g= -3
2f= 4
f= 2
The center of the circle (-g,-f) = (3,-2)
The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]
Substitute the values in the equation
r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]
[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]
=6.08 units
Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.
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Please help math 30 points
Answers
Answer:
298781
Step-by-step explanation: