5. Nancy counted the number of butterflies in her garden every month and recorded the data in the table below:. 3 4 Number of Months 1 2 Number of Butterflies 5 10 40 20 Write a recursive formula that represents the number of butterflies in Nancy's garden. an-an-1 (6) az Write an explicit formula that represents the number of butterflies in Nancy's garden. an-ai (r)n-1

Mr. walker gave his class the function f(x) = (x + 3)(x + 5). four students made a claim about the function. each student’s claim is below. jeremiah: the y-intercept is at (15, 0). lindsay: the x-intercepts are at (–3, 0) and (5, 0). stephen: the vertex is at (–4, –1). alexis: the midpoint between the x-intercepts is at (4, 0). which student’s claim about the function is correct?

Ineed in figuring out this problem.

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.