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tangare [24]
3 years ago
15

Solve 3 x - 9 x + 7 - 3 = -8.

Mathematics
1 answer:
erik [133]3 years ago
3 0

Answer: x=2

3x−9x+7−3=−8

Step 1: Simplify both sides of the equation.

3x−9x+7−3=−8

3x+−9x+7+−3=−8

(3x+−9x)+(7+−3)=−8

−6x+4=−8

−6x+4=−8

−6x+4−4=−8−4

−6x=−12

−6x

−6

=

−12

−6

x=2


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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

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Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

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and we can solve for b_n in terms of b_1=4:

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and so on down to

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We solve for a_n in the same way.

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Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
What is the y coordinate of the solution 3x+2y=12
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Answer:

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