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3 years ago

Which of the following is the solution set of x2 + 8x + 12 = 0? (-2.-6 2.6

Mathematics

1 answer:

algol [13]3 years ago

6 0

To solve this polynomial equation, we first factor the left side.

To factor x² + 8x + 12 = 0, look for factors of 12 that add to 8.

These factors are 6 and 2 so we have (x + 6)(x + 2) = 0.

So either x + 6 = 0 or x + 2 = 0 and solving for

x in each equation, our answer is {-6, -2}.

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3 years ago

What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

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3 years ago