Can someone please help me

The 31st term is 367

Step-by-step explanation: An arithmetic sequence is derived such that every term is calculated by adding a common difference to the previous term.

The first term has been given as 12. And the value of the nth term shall be defined by the formula

nth term = a(n - 1) + 7. So in order to calculate the unknown term, simply substitute the term for n.

To calculate the 31st term, we apply the formula as follows

nth = a(n - 1) + 7

31st = 12(31 - 1) + 7

31st = 12(30) + 7

31st = 360 + 7

31st = 367

Therefore, the 31st term is 367

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this