Write 8/74 in simplest form

simplify (x^3)^5

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]

Solve the exponential equation for x.

∆abc is mapped onto ∆a'b'c' which is then mapped onto ∆a"b"c". ∆abc and ∆a"b"c" are shown in the diagram. a. describe the sequence of transformations from ∆abc to ∆a"b"c". b. describe a single transformation from ∆abc to ∆a"b"c". c. what is the relationship between ∆abc and ∆a’’b’’c’’? explain your reasoning.