Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 + 5 + 52 + ... + 5n - 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 5[(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, 5k, 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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Calculate the slope of the line.
A. -2
B. 
C. 2
D. - 
Provide an appropriate response.Using the following diagram, prove that ?ADB ~ ?BDC.
What will be an ideal response?
Solve the problem.An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic. The word tiles come in two sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?
What will be an ideal response?
Convert to an exponential equation.log4 16 = 2
A. 24 = 16 B. 42 = 16 C. 416 = 2 D. 162 = 4