Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 2 is a factor of 
What will be an ideal response?
Show S1 is true: 12 - 1 + 2 = 2; 2 is a factor of 2
Assume that Sk is true: 
; 2 is a factor of k2 - k + 2
Show that if Sk is true, then Sk+1 is true:
Sk+1 = (k + 1)2 - (k + 1) + 2 = k2 + k + 2 = (k2 - k + 2) + 2k
(k2 - k + 2) is Sk and 2 is a factor of 2k
Since 2 is a factor of Sk+1 is true, the statement is true for all values of n.
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Solve the problem.Let u = 5i + j, v = i + j, and w = i - j. Find scalars a and b such that u = av + bw.
A. 3.000 v + 2.000w B. 5v - w C. 0.3333 v + 0.5000 w D. 5v + w
Graph the hyperbola.(y - 1)2 - 9(x - 3)2 = 9
A. 
B. 
C. 
D. 
Answer the question.Paul's last four paychecks have been $1195.09, 
, 
, and 
. What is the average amount for these paychecks?
A. $1097.49 B. $1067.47 C. $1117.29 D. $1087.63
Write the vector v in the form ai + bj, given its magnitude 
and the angle ? it makes with the positive x-axis.
= 7, ? = 270°
A. v = -7i + 7j) B. v = -7i - 7j C. v = -7i D. v = -7j