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Blizzard [7]
3 years ago
13

Someone help and please make sure it’s right :)

Mathematics
1 answer:
pashok25 [27]3 years ago
4 0

Answer:

9

Step-by-step explanation:

11x  + 1 + 7x + 17 = 180   \:  \:  \:   \: 18x + 18 = 180 \:  \:  \:  \:  \:  \:  \: 18x = 180 - 18 \:  \:  \:  \:  \:  \:  \:  \:18x = 162 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 162 \div 18 = 9

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Find the value of x such that 365 based seven + 43 based x = 217 based 10.
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We need to find the base x in the following equation:

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First, lets convert 365 from base 7 to base 10. This is given by

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where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

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Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

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where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

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Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

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and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

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