Answer:
= 4n - 2
Step-by-step explanation:
There is a common difference d between consecutive terms in the sequence, that is
6 - 2 = 10 - 6 = 14 - 10 = 18 - 14 = 4
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 4 , thus
= 2 + 4(n - 1) = 2 + 4n - 4 = 4n - 2
We have the following system of equations:
y = -6x-6
y = x2-5x-6
Matching we have:
x2-5x-6 = -6x-6
Rewriting we have:
x2-5x-6 + 6x + 6 = 0
x2 + x = 0
Rewriting:
x (x + 1) = 0
The solutions are:
x = 0
x = -1
For x = 0
y = -6 (0) -6 = 0-6 = -6
y = -6
For x = -1
y = -6 (-1) -6 = 6-6 = 0
y = 0
The solutions are:
(x, y) = (0, -6)
(x, y) = (- 1, 0)
Answer:
The solutions of the system are:
(-1, 0) and (0, -6)
The given expression is
We extract the common factor 2x.
The first solution is 0.
Now, we solve the quadratic expression. We have to find two numbers whose product 20 and whose difference is 8. Those numbers are 10 and 2.
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