Given that (y+2), (y+3)and (2y^2+1) are consecutive terms of an arithmetic progression find the value of x

In an arithmetic sequence, the difference between any consecutive terms should be always the same, then we have:

(y + 3) - (y + 2) = D

(2*y^2 + 1) - (y + 3) = D.

From the first equation, we can find the value of D:

y + 3 - y - 2 = D

1 = D.

Replacing this in the second equation, we have:

(2*y^2 + 1) - (y + 3) = 1

Now we can solve this equation:

2*y^2 + 1 - y - 3 - 1 = 0

2*y^2 - y - 3 = 0.

The solutions of this quadratic equation can be found with the Bhaskara's equation:

Then the possible values of y are:

y = (1 + 5)/4 = 6/4

y = (1 - 5)/4 = -1

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

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step-by-step explanation: