About Use the given equations in a complete proof of each theorem. Your proof should be expressed in complete English sentences. (a) Theorem: If a, b, and c are integers such that a3|b and b2|c, then a6|c.

(b) Theorem: If m and n are integers such that m|n, then m|(5n3 - 2n2 3n).

(c) Theorem: If n is an odd integer, then 4 divides n2-1.

(d) Theorem:The sum of the squares of any two consecutive integers is odd.

step-by-step explanation:

try remembering the steps

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.