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
During one hour of television there are two shows on. That would be the ratio 1:2. We need to find 3:?. Since 1×3 is 3, we multiply the second number by 3 as well. 2×3 is 6. So the ratio would be 3:6.
Hey there!
ORIGINAL EQUATION:
|x + 2| = 3
TRANSLATE:
x + 2 = 3 or x + 2 = -3
SOLVING for: x + 2 = 3
SUBTRACT 2 to BOTH SIDES
x + 2 - 2 = 3 - 2
CANCEL out: 2 - 2 because it give you 1
KEEP: 3 - 2 because help solve for the current x-value
NEW EQUATION: x = 3 - 2
SIMPLIFY IT!
x = 1
Thus, your answer is: x = 2
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SOLVING for: x + 2 = -3
SUBTRACT 2 to BOTH SIDES
x + 2 - 2 = -3 - 2
CANCEL out: 2 - 2 because it give you 0
KEEP: -3 - 2 because it help solve for the current x-value
NEW EQUATION: x = -3 - 2
SIMPLIFY IT!
x = -5
Thus, your answer is: x = -5
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Therefore, your answer is: x = 1 or x = -5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
Step-by-step explanation:
The formula of a distance between two points:
We have the points (1, -5) and (-3, 6). Substitute:
