The convex heptagon has 14 distinct diagonals can be drawn
Step-by-step explanation:
A polygon is said to be a heptagon if it has 7 vertices, 7 sides and 7 angles. A heptagon is called a convex heptagon if the lines connecting any two non-adjacent vertices lie completely inside the heptagon
The formula of number of diagonals in any polygon is 
, where
- d is the number of the diagonals of the polygon
- n is the number of sides of the polygon
∵ The heptagon has 7 sides
∴ n = 7
∵ The number of diagonals = 
- Substitute n by 7 in the rule above
∴ The number of diagonals = 
∴ The number of diagonals = 
∴ The number of diagonals = 
∴ The number of diagonals = 14
The convex heptagon has 14 distinct diagonals can be drawn
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Answer:
48 dollars left
Step-by-step explanation:
120 divided by 10 is 12
12 times 6 equals 72
The length of the AC is x^2 + 4x - 12.
<h3>What is a parallelogram?</h3>
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
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Answer:
The three sides are 27 feet, 15 feet, 13 feet
Step-by-step explanation:
Let second side of a triangle be = a
Let one side be 12 feet shorter than the second side = (a - 12)
Let the third side be 2 feet shorter than the second side= (a - 12) - 2 =(a - 14)
Perimeter of triangle = Sum of length of all 3 sides
55 = a + (a - 12) + (a - 14)
55 = a + a + a - 12 - 14
55 = 3a - 26
55 + 26 = 3a
81 = 3a
a = 27
Length of one side, a - 12 = 27 - 12 = 15 feet
Length of second side, a = 27 feet
Length of third side, a - 14 = 27 - 14 = 13 feet
Answer:
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