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dalvyx [7]
3 years ago
6

If x satisfies the equation 7x-8=90, what is the value of 6x+7

Mathematics
1 answer:
Furkat [3]3 years ago
3 0
7x=98
x=98/7
x=14

6*14+7= 91

hope this helped
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Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5
zaharov [31]

Answer:

31

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.

__________________________________________________________

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:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

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

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

7 0
2 years ago
The value of y directly varies with the value of x. If y equals 21when x is 14, what is the value of y when x = 20?
Karo-lina-s [1.5K]

Answer:

21×20÷14

=3×20÷2

=3×10

x=30

8 0
2 years ago
The following figure shows the first two steps of a proof of the Pythagorean theorem. Which of the following statements about th
weeeeeb [17]

Answer:

c^2>a^2+b^2

Step-by-step explanation:

6 0
3 years ago
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Is the square root of 400 rational or irrational
STatiana [176]

Rational number, because the Square root of 400 is 20, since 20 x itself is 400. Hope this helps!

6 0
3 years ago
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Sammie read at the rate of 25 pages per hour. Alex read at the rate of 1/2 of a pages per minute. Who was reading faster? By how
kompoz [17]

Answer:

Alex and 5 pages

Step-by-step explanation:

Sammie 25 pages per hour

Alex 1/2 pages per minute

You do 1/2x60=30 because you can find out how many pages he can read per hour.  Which is 30 pages per hour.  So Alex can read 30 pages per hour and Sammie can only read 25 pages per hour.  To find how many pages he reads faster per hour, you have to take 30 and subtract it by 25 to get 5 extra pages.  So Alex reads 5 pages faster per hour.  In the end, Alex reads faster than Sammie by 5 more pages per hour.

Hope this helps!  Please give brainliest.

3 0
2 years ago
Read 2 more answers
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