Put this equation into slope intercept form 6x+12y=9

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

8 0

y = - $\frac{1}{2}$ x + $\frac{3}{4}$

The equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 6x + 12y = 9 into this form

subtract 6x from both sides

12y = - 6x + 9 ( divide all terms by 12 )

y = - $\frac{6}{12}$ x + $\frac{9}{12}$ ( which simplifies to )

y = - $\frac{1}{2}$ x + $\frac{3}{4}$

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Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: