A line passes through the points (2, -2) and (-6.2), The point (a, -4) is also on the line. What is the value of a?
1 answer:
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An arithmetic sequence takes the form
where
is the common difference between terms. You can solve for 
in terms of any of the previous terms of the sequence:
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
and the 11th term is 
, you have the following system of equations.
Solving this system for the two unknowns yields
and 
.
So, the sequence is given explicitly by
where
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
Solving this system for the two unknowns yields
So, the sequence is given explicitly by
Answer:
Leon is correct. (Option 1)
Step-by-step explanation:
Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.
Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.
we have to explain whether or not Leon is correct.
As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem
⇒
Let a, b, c forms a Pythagorean triplet
Multiplied by 4 on both sides
⇒
⇒
Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.
∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Hence, Leon is correct.