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OverLord2011 [107]
2 years ago
15

if the sum of a number and seven is doubled, the result is eight less than the number. Find the number

Mathematics
2 answers:
Kipish [7]2 years ago
5 0

Answer:

-22

Step-by-step explanation:

The result is eight less than the number means that

the result = number - 8

( x + 7 ) * 2 = x - 8

=> 2x + 14 = x - 8

=> x = -22

Alexeev081 [22]2 years ago
4 0

Answer: -18

Step-by-step explanation:

Let the number be represented by x.

If the sum of a number and seven is doubled, the result is four less than the number. The expression would be

2(x + 7) = x - 4

We would open the bracket on the left hand side of the equation by multiplying each term inside the bracket by 2. It becomes

2x + 14 = x - 4

Subtracting 14 and x from the left hand side and the right hand side of the equation, it becomes

2x + 14 - 14 - x =x - x - 4 - 14

x = - 18

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Find the sum of the geometric series 512+256+ . . .+4
mario62 [17]

\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}

\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}

so is the 8th term, then, let's find the Sum of the first 8 terms.

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}

\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}}  \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}}  \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020

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Step-by-step explanation:

There are many equivalent ratios but I chose this one because the c value is 2.

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3 years ago
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kifflom [539]
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Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and
Lina20 [59]

According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:

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A similar example is given at brainly.com/question/14544759

8 0
3 years ago
Is the graph below proportional or non-proportional? How do you know?
Alex

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4 0
3 years ago
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