Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all natural numbers. (Hint: 
What will be an ideal response?
When 
, so the statement is true when 
. Assume the statement is true for some natural number k. That is, 
for some integer m. Then,
.
So the statement is true for 
. Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers.
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Solve the equation.
y - (y - 
) = 
( y + 5)
A. - 
B. 
C. - 
D. 
Graph the system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points.
A. bounded;
corner points (3, 0), (0, 3),(0, 1), (1, 0)
B. no solution
C. unbounded;
corner points (0, 0), (0, 1), (1, 0)
D. unbounded;
corner points (3, 0), (0, 3)
Solve the problem.Estimate the minimum number of subintervals needed to approximate the integral
with an error of magnitude less than 10-4 using Simpson's Rule.
A. 18 B. 16 C. 20 D. 19
Graph the equation and give the coordinates of the vertex.y = (x + 3)2
A. (3, 0)
B. (-3, 0)
C. (0, 3)
D. (0, -3)