Answer:
There should be 2 teachers and 21 students on each bus.
Step-by-step explanation:
1 Backpack + 3 Textbooks + 2 Notebooks = 10.5 pounds
His Backpack Weighs 2.5 pounds
Answer:
80
Step-by-step explanation:
If we assume the triangles are similar and are isosceles, and that BK is an altitude, then we can work the problem.
Triangle OKN will be similar to triangle BKA, so ...
AN : AK = BO : BK = 1 : 3
Then ...
AN : AK : KC = 1 : 3 : 3
In terms of ratio units, ...
AN = 1
AC = 3+3 = 6
NC = 6-1 = 5
This means NC : AC = 5 : 6. The triangle perimeters will have the same ratio.
perimeter(NMC) = 5/6·perimeter(ABC) = 5/6·96
perimeter(NMC) = 80
Answer: 1/20
Step-by i hope you have a great day
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

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