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sweet [91]
3 years ago
5

Stind ca n!= 1*2*3*......n sa se arate ca nr 13!-11! se divide cu 31

Mathematics
1 answer:
Margarita [4]3 years ago
3 0
Hello : 
13! = 13×12×<span>11!
</span>13!-11!= (13×12×11! ) - <span>11!
           = </span>11! (13×12 -1)
           =11! (156 - 1)
           = 11! (  155)
            = 11!(31×5)
13!-11! = 31( 11!×5)

so : <span>13!-11! se divide cu 31</span>
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Find the value of x such that 365 based seven + 43 based x = 217 based 10.
Pepsi [2]

We need to find the base x in the following equation:

365_7+43_x=217_{10}

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

365_7=3\times7^2+6\times7^1+5\times7^0

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}

that is, 365 based 7 is equal to 194 bases 10.

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

43_x=4\times x^1+3\times x^0

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

43_x=(4x+3)_{10}

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

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

197+4x=217

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}

Therefore, the solution is x=5

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What is the reflection image of p(0, 0) after two reflections, first across x = -3 and then y = 4 ?
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The reflection point P' would be (-6, 8)
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Gavin and Caleb go to the movie theater and purchase refreshments for their friends. Gavin spends a total of $22.25 on 2 bags of
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Answer:

Drinks = 6.75

Popcorn= 1

Step-by-step explanation:

Let the popcorn = P

Let the drink = D

2*P + 3*D = 22.25         multiply this equation by 6

12*P + 4D = 39.00

<u>12P + 18D = 133.5</u>          Subtract these two equations

- 14D = - 94.50               Divide by -14

-14D/-14 = -94.5/-14        Do the division

D = 6.75

=========================

12P  +  4D = 39            Substitute for D

12P + 4*6.75 = 39        Combine

12P + 27 = 39               Subtract 27 from both sides

12P + 27-27=39-27      Collect like terms

12P = 12                        Divide by 12

12P/12 = 12/12

P = 1                               Answer

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