Octagon ABCDEFGH with side lengthsABCDEFGII 10 and BC=DE FG = HA= 11 isformed by removing 6-8-10 triangles from the corners of a 23 x 27 rectanglewith side AH on a short side of the rectangle, as shown. Let J be the midpointof AH, and partition the octagon into 7 triangles by drawing segments JB,JC, JD, JE, JF, and JG. Find the area of the convex polygon whosevertices are the centroids of these 7 triangles.
Answers
Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.
What is a convex polygon?
A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.
Given,
AB = CD = EF = GH = 10
BC = DE = FG = HA = 11
Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.
Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.
The centroid of a triangle can be found using the formula,
Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]
For ΔJAB,
[tex]C_{1}[/tex] = (8/3 , -35/6)
For ΔJBC,
[tex]C_{2}[/tex] = ( 9 , -23/6)
For ΔJCD,
[tex]C_{3}[/tex] = ( 46/3, -35/6)
For ΔJDE,
[tex]C_{4}[/tex] = ( 18 , -23/2)
Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]
From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)
Area =
[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]
= 184 / 2
Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units
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Related Questions
What happens when you log an e?
Answers
When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.
For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.
In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.
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5 times a number,incrased by 8
Answers
Answer:
5 × x + 8
Would be the equation you are looking for.
Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])
Answers
Therefore , the solution of the given problem of triangle comes out to be A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).
Explain the triangle.The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.
Here,
The image A'B'C' is formed by our transformation rule, (+3,y-2)
So:
1. Describe the updated coordinates for points A', B', and C'?
In order to locate these new positions, we have:
A' (-23, 2-2) => A'(1, 0) (1, 0)
B' => (-23, 4-2) => B'(1, 2) (1, 2)
C'=> (0+3,0-2) => C'(3,-2) (3,-2)
2. Explain the qualities that would emerge if the respective vertices were linked together by lines.
We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.
The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.
Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.
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9/11 - 1/2 in it's simplest form
Answers
Answer:
7/22 or 0.31818...
Step-by-step explanation:
have a good day!! :)
which country are you from?
Answers
Answer:
Whom are you asking????
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Answer:
America
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
Answers
The distance between the girl and her bike is 25.00 ft.
What is distance?Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.
The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.
Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.
Therefore, the distance between the girl and her bike is 25.00 ft.
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Subtract 4 from 1/6 of 42
Answers
Here's link[tex]^{}[/tex] to the answer:
bit.[tex]^{}[/tex]ly/3gVQKw3
Answer:
42/6 = 7
7 - 4 = 3
Step-by-step explanation:
Talia attended a 5-day math camp that lasted 5/6 of an hour each day. How many total hours did Talia spend at math camp?
Answers
Answer:
Total hour Talia spend at math camp = 100 hour
Step-by-step explanation:
Given:
Number of days = 5 days
Per hour attended = 5/6 per hour
Find:
Total hour Talia spend at math camp
Computation:
Total number of hour per day = 24 hour
Total hour Talia spend at math camp = Number of days x Per hour attended x
Total number of hour per day
Total hour Talia spend at math camp = 5 x 5/6 x 24
Total hour Talia spend at math camp = 5 x 5 x 4
Total hour Talia spend at math camp = 25 x 4
Total hour Talia spend at math camp = 100 hour
a solid metal sphere of volume 1280cubic centimeters
is melted down and recast into 20 equal solid cubes.fund length of the side of each cube
a solid m or a solid m fear of volume
Answers
As we know the sphere has a volume of 1280 cubic centimeters, and it is being recast into 20 equal solid cubes.
The volume of each cube is the same, so we can divide the total volume of the sphere by the number of cubes to find the volume of each cube:
Volume of each cube = 1280 cm^3 / 20 = 64 cm^3
The volume of a cube is given by the formula: V = s^3, where s is the length of a side.
so, s^3 = 64 cm^3
solving for s, we get s = ∛64 = 4cm
So, the length of the side of each cube is 4 cm.
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 827 gallons, and you c
drain it at a rate of 48 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answers
Explanation below
According to the synthetic division below, which of the following statements are true? Check all that apply.
A. (x+2) is a factor of 5x2-16x + 12.
B. (x-2) is a factor of 5x2-16x + 12.
C. (5x2 - 16x+12) + (x - 2) = (5x-6)
D. (5x2-16x +12) + (x + 2) = (5x-6)
E. The number -2 is a root of F(x) = 5x2 - 16x + 12.
F. The number 2 is a root of F(X) = 5x2 - 16x+ 12.
Answers
Answer:
Correct answer just took the quiz
Step-by-step explanation:
The correct option for the given statement is that (x-2) is a factor of [tex]5x^{2} -16x+12[/tex].
What is a factor?It is a number by which the number whose it is a factor can be divided.
How to divide an equation?To check factor of an equation we need to divide it with so to check (x-2) a factor of [tex]5x^{2} -16x+12[/tex] we need to divide the equation by x-2
=( [tex]5x^{2} -16x+12[/tex])/x-2
=5x-6
So it is a factor of the given equation.
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What is a shape called with 1000000000 sides?
Answers
Answer:
Regular megagon
Step-by-step explanation:
Regular megagon is a shape called with 1000000000 sides.
Select the correct answer. which expression is equivalent to this quotient?
Answers
An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)
The correct answer is an option (B)
Consider given quotient.
[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]
Consider expression 5z + 15
We can write this expression as 5(z + 3) by taking out the common factor 5.
So given quotient would be,
[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]
As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.
For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.
So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]
We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,
(a/b) / (c/d) = (a/b) × (d/c)
So, given quotient would be,
[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]
= 5 / (z + 5)
Therefore, an equivalent expression is: 5 / (z + 5)
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PLA HELP WILL MARK BRAINLEST AND GIVE 100 points
Answers
Answer:
B) measures of variability
Hope this helped :)
Mike jogged 6 laps around a 0.25 mile track on Tuesday and 7 laps on Thursday. How many miles did he job on Tuesday and Thursday?
Answers
Answer: 3.25 miles
Step-by-step explanation:
Given
Mike Jogged 6 laps around a 0.25-mile track on Tuesday
7 laps on Thursday
Miles jogged on Tuesday is [tex]6\times 0.25=1.5\ \text{mile}[/tex]
Miles jogged on Thursday is [tex]7\times 0.25=1.75\ \text{miles}[/tex]
Total miles Jogged is [tex]1.75+1.5=3.25\ \text{miles}[/tex]
The sum of two numbers is -6. Their difference is 36. What is the smallest number?
Answers
Let first number be x.
Let second number be y.
According to question,
x+y=36…….(equation 1)
and
x-y=6…..(equation 2)
equation 2 can be written as , x=6+y……(equation 3)
Put equation 3 in equation 1,
6+y+y=36
6+2y=36
2y=36–6
2y=30
y=30/2
y=15
now, put y=15 in equation 1,
x+15=36
x=36–15
x=21
So, numbers are 21 and 15.
Find expressions for the possible dimensions of the rectangular prism.
V = 12y3 + 13y2 + 3y
Answers
Answer:
Step-by-step explanation:
The dimensions of a rectangular prism are length, width, and depth.
Volume = length * width * depth
Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.
How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.
V = y(3y2 + 16y + 5)
Then, factor what's left.
V = y(3y + 1)(y + 5)
The dimensions of the prism are y, (3y + 1), and (y + 5).
Answer:
The dimensions of a rectangular prism are length, width, and depth.
Volume = length * width * depth
Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.
How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.
V = y(3y2 + 16y + 5)
Then, factor what's left.
V = y(3y + 1)(y + 5)
The dimensions of the prism are y, (3y + 1), and (y + 5).
Step-by-step explanation:
it's this write ... comments plz have a nice day
Is the triangle formed by points A, B, and C a right triangle?
Answers
Answer:Yes
Step-by-step explanation: It is a right triangle as if you imagine it, you can see that is half of a square, holding a right angle within it.
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answers
The width of a rectangle measures (8p+5) centimeters, and its length measures (4p + 4) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle
Answers
Answer:
Perimeter = 24p + 18 cm
Step-by-step explanation:
Perimeter = 2[(8p+5)+(4p+4)]
simplify:
Perimeter = 16p + 10 + 8p +8
combine like terms:
Perimeter = 24p + 18
During lockdown down period people work very puzzled and their decided to play some game firstly they collect the 17 cards and write the numbers 1 to 17 put them in a box people make a bet from the chance of drawing the number either the prime or even number
etc.
Answers
From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Probability of drawing an even or prime number will be 15/17.
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.
N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Prime = {1,2,5,7,11,13,17}
Even = {2,4,6,8,10,12,14,16}
Pr(Prime) = 7/17
Pr(Even) = 8/17
Pr(Prime or even) = 7/17 + 8/17
Pr(Prime or even) = 15/17
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The game starts at 1830. They play four eight minute quarters, and half-time lasts for thirty minutes. What time should you tell your parents to pick you up? Give your answer in both 12 and 24 hour clock notation
Answers
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
What is time?the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.
Here,
Given : The game starts at 18:30
Thus,
They play for eight minutes quarters and half time last for 30 minutes.
So,
To find the time to pick up by your parents:
=> 8*4 + 30
=> 32 + 30
=> 62
Thus time after 62 minutes is 7:32
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
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Can someone help me with this.
Writing equations from graph
Answers
m=3-1/4-(-4)
=2/8
=1/4
—> y=1/4x+2
*not too sure if this is right but I hope it helps
70 years later from 1590
Answers
Answer: 1660
Step-by-step explanation: 70 + 1590 = QUICK MATHS
Answer:1660
Step-by-step explanation:
HELP ME ASAP AND I MEAN ASAP
Answers
Answer:
9miles
Step-by-step explanation:
Answer:
Step-by-step explanation:
Can you plase answer the question.
Answers
Answer:
I don't understand your language
Step-by-step explanation:
a sum of money is divided among two friends in the ratio 4:11 if the smaller amount is $420, determine the larger amount?
Answers
Answer:
1155
Step-by-step explanation:
let the ratio be 4x:11x
4x=420
x=105
11x=11*105
=1155
Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.
Answers
Answer:
The total cost of the science class trip to the zoo is $1200
Step-by-step explanation:
The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.
Does parallel programming always improve the performance of an application over sequential programming?
Answers
Parallel programming can improve the performance of an application over sequential programming in certain cases, but it is not a guarantee.
Explain about working of Parallel programming?Parallel programming allows for the use of multiple processors or cores to perform tasks simultaneously, which can improve the overall speed of an application. However, parallel programming can also introduce complexity and overhead, which can decrease performance. The potential for improved performance depends on the specific application and the design of the parallel implementation. Some applications may not benefit from parallel programming because they are not computationally intensive or because their data is not easily divided into parallelizable tasks. Additionally, the performance improvement also depends on the number of cores and the communication costs between them.
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hello please help i’ll give brainliest
Answers
Answer:
C.
Step-by-step explanation:
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