To make the reciprocal of a fraction, swap the numerator and denominator.
The reciprocal of 3/4 is 4/3.
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To make the reciprocal of an integer, write it as a fraction, then proceed as above. Example: (reciprocal of 2) = (reciprocal of 2/1) is 1/2.
Not surprisingly, the reciprocal of a number x is written 1/x.
Answer:
x = 121.5
Step-by-step explanation:
- Write it out: 6x = 729
- Divide each side by 6 to cancel out the 6 next to x. It should now look like this: x = 121.5
Answer:
9 TV ads and 20 radio ads
Step-by-step explanation:
He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x + 500y
The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y
The system that represents this is
![\left \{ {{3000x+500y=37000} \atop {10000x+2000y=130000}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B3000x%2B500y%3D37000%7D%20%5Catop%20%7B10000x%2B2000y%3D130000%7D%7D%20%5Cright.)
And the augmented matrix is
![\left[\begin{array}{cc|c}3000&500&37000\\10000&2000&130000\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D3000%26500%2637000%5C%5C10000%262000%26130000%5Cend%7Barray%7D%5Cright%5D)
First we divide the first row by 3000 and the second by 10000:
![\left[\begin{array}{cc|c}1&1/6&37/3\\1&1/5&13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C1%261%2F5%2613%5Cend%7Barray%7D%5Cright%5D)
Then we multiply the second row by (-1) and we add the first row:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&-1/30&-2/3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%26-1%2F30%26-2%2F3%5Cend%7Barray%7D%5Cright%5D)
Now we multiply the second row by -30:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
Finally, to the first row we add the second one multiply by (-1/6):
![\left[\begin{array}{cc|c}1&0&9\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%260%269%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
So, x = 9 and y = 20
That means 9 TV and 20 radio ads will contact 130,000 voters using the allocated funds
I think there are 3 time zones
The tax most likely is represented by 0.08(50h), as it is the smallest amount of the expression.
50h will result in a much larger number, which is probably the actual service fee.