rational numbers and integers
Asked and answered elsewhere.
brainly.com/question/9247314You obviously don't mind using "technology" (Brainly) to answer these questions. A graphing calculator can do quadratic regression on the sequence and tell you its formula.
If you want to do it by hand, you can write the equation
.. y = ax^2 +bx +c
and substitute three of the given points. Then solve the resulting three linear equations for a, b, and c.
.. 4 = a +b +c
.. 7 = 4a +2b +c
.. 12 = 9a +3b +c
Subtracting the first equation from the other two reduces this to
.. 3 = 3a +b
.. 8 = 8a +2b
The latter can be divided by 2, so reduces to
.. 4 = 4a +b
Subtracting the first of the reduced equations from this, you have
.. 1 = a
so
.. 3 = 3*1 +b
.. 0 = b
and
.. 4 = a + b + c = 1 + 0 + c
.. 3 = c
And your equation is
.. y = x^2 +3 . . . . . . as shown previously
Regarding your (1/10 divided by 2/5): I'm going to regard this as
(1/10) divided by (2/5).
First, write
1
---
10
Invert the fraction 2/5 and then multiply 1/10 by 5/2:
1(5)
-------- = 1/4, after reducing 5/10.
10(2)
Thus, <span>−34+(1/10÷2/5) yields -34 + 1/4, or -33 3/4.</span>