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3 years ago

9:45 on Tuesday Questions

Mathematics

1 answer:

Serga [27]3 years ago

3 0

Answer:

Neither

Step-by-step explanation:

-12x + 3y = 3

y = 4x + 1

y = mx + b

The second equation given is set up in the correct form already (y = 4x + 1)

We have to convert the first equation into the same format

-12x + 3y = 3

Isolate the y

3y = 3 + 12x

Divide the 3 from the y and the other side

y = 1 + 4x

y = 4x + 1

This is the same as the first equation

They can only be parallel if their slope (m or 4 in this case) is the same and their y-intercepts (b or 1 in this case) are different. Since the equations are the exact same and do not fit the y-intercept criteria for parallel, they cannot be parallel. If they were perpendicular, their lines must cross. This means they have to contain reciprocals or opposite slopes. Our slope here for both of them is 4 or 4/1. Since neither are the opposite (which would be 1/4), it is not perpendicular. Therefore, the answer is neither

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Answer:

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Step-by-step explanation:

About the easiest way to do this for small values of n is to compute each of the terms using the given recurrence relation.

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_____

<em>Alternate solution</em>

You recognize that the recurrence relation describes a geometric sequence with a first term of 4 and a common ratio of -3. The n-th term of a geometric sequence is ...

$a_n=a_1\cdot r^{n-1} \qquad\text{for first term $a_1$ and common ratio $r$}$

Then the 4th term will be ...

$a_4=4\cdot(-3)^{4-1}=4\cdot(-27)=-108$

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