What is the diameter of the circle whose center is at (6,0) and passes through the point (2,-3)

10 units

Step-by-step explanation:

Use the distance formula(√(x1-x2)^2+(y2-y1)^2)

Thus, the radius of the circle is 5.  Because the diameter is 2r, the diameter = 2(5) = 10

Hope it helps <3

b²(2x+1)(x+2)

Explanation:
The given equation is:
2b²x² + 5xb² + 2b²
We can start by taking b² as a common factor, this will give us:
b² (2x² + 5x + 2)

Now, we have a trinomial quadratic equation that we need to factorize.
The general form of the quadratic equation is:
ax² + bx + c
The one we have is:
2x² + 5x + 2
By comparison:
a = 2
b = 5
c = 2

To get the factors, we will need to use the quadratic equation attached in the images.
By substitution, we would find that:
either x = -1/2.......> This means that the factor is (2x+1)
or x = -2........> This means that the factor is (x+2)

Now, back to our expression, we will replace the quadratic trinomial with its factored form to get the simplified expression:
b²(2x+1)(x+2)

Hope this helps :)