Answer:
Multiply row 1 by 
.
Step-by-step explanation:
The augmented matrix of the system of linear equation is described below:
![\left[\begin{array}{cccc}2&1&-1&-8\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D2%261%26-1%26-8%5C%5C0%262%263%26-6%5C%5C-%5Cfrac%7B1%7D%7B2%7D%20%261%261%26-4%5Cend%7Barray%7D%5Cright%5D)
Where 
, if we need to create 
, we need to multiply row 1 by , that is to say:
![\left[\begin{array}{cccc}1&\frac{1}{2} &-\frac{1}{2} &-4\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B2%7D%20%26-%5Cfrac%7B1%7D%7B2%7D%20%26-4%5C%5C0%262%263%26-6%5C%5C-%5Cfrac%7B1%7D%7B2%7D%20%261%261%26-4%5Cend%7Barray%7D%5Cright%5D)
Hence, the correct answer is: Multiply row 1 by .
Answer:
1/4
Step-by-step explanation:
use the slope formula, (y2-y1)/(x2-x1) , or rise over run.
this would give you 2-(-1) divided by 6-(-6)
giving you 3/12, reducing to 1/4
9514 1404 393
Answer:
12 minutes
Step-by-step explanation:
Let c and h represent the filling times for the cold and hot taps, respectively. When the cold tap is 1/2 open, we presume that means the filling time becomes 2c.
In terms of baths per minute, the relationships are ...
1/c + 1/h = 1/3
1/(2c) +1/h = 1/(3 +1.8) . . . . . 1:48 min:sec is 1.8 minutes
Subtracting the first equation from twice the second, we get ...
2(1/(2c) +1/h) -(1/c +1/h) = 2(1/4.8) -(1/3)
1/h = 2/4.8 -1/3 = 1/12
h = 12
It takes the hot tap 12 minutes to fill the tub alone.
