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3 years ago

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is

Mathematics

1 answer:

Damm [24]3 years ago

7 0

Answer:

$\frac{n(n-3)}{2}$

Step-by-step explanation:

Polygon Diagonals are a pattern that follows a specific rule which can be used through a specific formula. Remember that Math focuses on patterns to create equations that help to study them, and this case is not an exception.

The equation for polygon diagonals is

$\frac{n(n-3)}{2}$

Where $n$ refers to the number of sides of the polygon.

You see, a diagonal is defined as the union between two non-consecutive vertices. For a convex n-sided polygon, there are going to be n vertices, and we can draw $n-3$ from each vertex, then we multiply this by $n$ , because that's the total number of sides.

In the end, we divide by 2, because with the method described, we will have double number of diagonals.

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Prove triangle AOC is congruent to triangle BOD

marta [7]

Step-by-step explanation:

We are given two Triangles and we need to prove them congruent . In ∆AOC and ∆BOD , we have

$\to AC = BD ( given ) \\\\\to OD = OA \\\\\to \angle CAO =\angle BDO (Since\ BD || AC )$

Therefore by AAS congruent condition we can say that ,

$\implies\red{ \triangle AOC \cong \triangle BOD }$

Hence Proved!

8 0

3 years ago

How many solutions does y=-x^2-4x+7 have

Anastaziya [24]

Answer:

x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Step-by-step explanation:

Solve for x:

y = -x^2 - 4 x + 7

y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:

-x^2 - 4 x + 7 = y

Multiply both sides by -1:

x^2 + 4 x - 7 = -y

Add 7 to both sides:

x^2 + 4 x = 7 - y

Add 4 to both sides:

x^2 + 4 x + 4 = 11 - y

Write the left hand side as a square:

(x + 2)^2 = 11 - y

Take the square root of both sides:

x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

7 0

3 years ago

The romans marched 500 meters in 4 hours. For the next 4 hours they tripled their pace. What was the total distance traveled by

lara31 [8.8K]

Distance traveled during the first 4 hours: 500 m Note that the rate here was 125 m/hr.

Distance traveled during the next four hours: 3(125 m/hr)(4 hr) = 375 m

Total distance traveled: 500 m + 375 m = 875 m

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3 years ago

Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by co

VashaNatasha [74]

Answer: k = 4, k = -4 and k = 0.

Step-by-step explanation:

If we have y = sin(kt)

then:

y' = k*cos(kt)

y'' = -k^2*son(x).

then, if we have the relation:

y'' - y = 0

we can replace it by the things we derivated previously and get:

-k^2*sin(kt) + 16*sin(kt) = 0

we can divide by sin in both sides (for t ≠0 and k ≠0 because we can not divide by zero)

-k^2 + 16 = 0

the solutions are k = 4 and k = -4.

Now, we have another solution, but it is a trivial one that actually does not give any information, but for the diff equation:

-k^2*sin(kt) + 16*sin(kt) = 0

if we take k = 0, we have:

-0 + 0 = 0.

So the solutions are k = 4, k = -4 and k = 0.

4 0

3 years ago

State Year

slavikrds [6]

What’s the question.

4 0

3 years ago

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is​

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is