Answer:
6. B. T(n) = -0.411n² +6.5n +27
7. C. The zeros, -18 and 18, can be found when 0 = (x +18)(x -18)
Step-by-step explanation:
6. Graphing, or thinking about the data in the table, you see that it is described by a curve that opens downward and has a peak in the vicinity of n=8.
Of the choices offered, the only ones that describe a downward-opening curve are the ones with a negative leading coefficient, B and C. Of those two, Choice C has a peak at n=0, leaving choice B as the only viable one.
This is confirmed by software that computes the regression formula for you. (see attached)
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7. You know that "the difference of squares" has a special factored form:
a² -b² = (a +b)(a -b)
This suggests that the function you have might be considered in terms of the difference of squares:
h(x) = x² -324 = x² -18²
So, its factoring would be ...
h(x) = (x +18)(x -18)
The zeros of the function are those values of x such that h(x) = 0. Hence, the zeros can be found when ...
0 = (x +18)(x -18)
Those values of x are -18 and 18, matching choice C.
