Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 + 6 + 62 + ... + 6n - 1 = 
What will be an ideal response?
First, we show that the statement is true when n = 1.
For n = 1, we get 1 (or 6[(1) - 1]) = =
= 1.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for . That is, we need to show that
So we assume that is true and add the next term, 6k, to both sides of the equation.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Find the real solutions, if any, of the equation. Use the quadratic formula.5x2 + 20x - 25 = 0
A.
B.
C.
D.
The data table has been generated by a linear, quadratic, or cubic function f. All zeros of f are real numbers located in the interval By making a line graph of the data, conjecture the degree of f.
A. 1 B. 2 C. 3 D. 4
Write the percent as a decimal. Round to the nearest thousandth if the division does not terminate. %
A. 780 B. 0.078 C. 0.0078 D. 0.78
Find the square root. Do not use a calculator. Do not refer to a table of square roots.
A.
B. 14
C. 38,416
D. 196