Maths-
General
Easy
Question
Make and test a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.
The correct answer is: 6(6 - 3)/2 = 9
We will consider a pentagon
![](data:image/png;base64,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)
We observe that there are 5 diagonals in a pentagon.
Now, for an “n” sided-polygon, the number of diagonals can be obtained by the following formula:
Number of Diagonals = n(n-3)/2
This formula is simply formed by the combination of diagonals that each vertex sends to another vertex and then subtracting the total sides. In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways.
Now by subtracting n with nC2
ways, the formula obtained is
n(n-3)/2.
For example, in a hexagon, the total sides are 6.
So, the total diagonals will be 6(6-3)/2 = 9.
We observe that there are 5 diagonals in a pentagon.
Now, for an “n” sided-polygon, the number of diagonals can be obtained by the following formula:
Number of Diagonals = n(n-3)/2
This formula is simply formed by the combination of diagonals that each vertex sends to another vertex and then subtracting the total sides. In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways.
Now by subtracting n with nC2
ways, the formula obtained is
For example, in a hexagon, the total sides are 6.
So, the total diagonals will be 6(6-3)/2 = 9.
Related Questions to study
Maths-
Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Maths-General
Maths-
Make and test a conjecture about the square of even numbers.
Make and test a conjecture about the square of even numbers.
Maths-General
Maths-
Make and test a conjecture about the square of odd numbers.
Make and test a conjecture about the square of odd numbers.
Maths-General
Maths-
Make and test a conjecture about the sign of the product of any two negative integers
Make and test a conjecture about the sign of the product of any two negative integers
Maths-General
Maths-
Identify the value of c that makes the trinomial factorable using the perfect square pattern.
![x squared plus 24 x plus c](data:image/png;base64,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)
Identify the value of c that makes the trinomial factorable using the perfect square pattern.
![x squared plus 24 x plus c](data:image/png;base64,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)
Maths-General
Maths-
Is the expression
factorable using integer coefficients and constants? Explain why or why not?
Is the expression
factorable using integer coefficients and constants? Explain why or why not?
Maths-General
Maths-
Given four 6 collinear points, make a conjecture about the number of ways to connect different pairs of points
Given four 6 collinear points, make a conjecture about the number of ways to connect different pairs of points
Maths-General
Maths-
Identify the missing terms.
![x squared plus 11 x plus 24 equals left parenthesis ? plus 3 right parenthesis left parenthesis x plus ? right parenthesis](data:image/png;base64,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)
Identify the missing terms.
![x squared plus 11 x plus 24 equals left parenthesis ? plus 3 right parenthesis left parenthesis x plus ? right parenthesis](data:image/png;base64,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)
Maths-General
Maths-
Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.
Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.
Maths-General
Maths-
Describe the pattern in the numbers 5, 15, 45, 135, ... and write the next three numbers in the pattern
Describe the pattern in the numbers 5, 15, 45, 135, ... and write the next three numbers in the pattern
Maths-General
Maths-
Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure.
![](data:image/png;base64,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)
Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure.
![](data:image/png;base64,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)
Maths-General
Maths-
What is the factored form of
![6 x squared minus 60 x plus 150](data:image/png;base64,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)
What is the factored form of
![6 x squared minus 60 x plus 150](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
The area of a rectangular rug is
. Use factoring to find possible dimensions of the rug. How are the side lengths related? What value would you need to subtract from the longer side and add to the shorter side for the rug to be a square?
The area of a rectangular rug is
. Use factoring to find possible dimensions of the rug. How are the side lengths related? What value would you need to subtract from the longer side and add to the shorter side for the rug to be a square?
Maths-General
Maths-
Tom has a large cone-shaped pinata hung from a tree. The height and radius of the pinata are 8 inches and 1 foot respectively. What is the volume of the pinata? Round your answer to two decimal places. (use π = 3.14)
Tom has a large cone-shaped pinata hung from a tree. The height and radius of the pinata are 8 inches and 1 foot respectively. What is the volume of the pinata? Round your answer to two decimal places. (use π = 3.14)
Maths-General