Answer:
Let
be the time for the
th task.
We know these times have a certain structure:
- Any 3 adjacent tasks will take half as long as the next two tasks.
In the form of an equations we have

- The second task takes 1 second

- The fourth task takes 10 seconds

So, we have the following system of equations:

a) An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.
Here is the augmented matrix for this system.
![\left[ \begin{array}{cccccc|c} 1 & 1 & 1 & - \frac{1}{2} & - \frac{1}{2} & 0 & 0 \\\\ 0 & 1 & 1 & 1 & - \frac{1}{2} & - \frac{1}{2} & 0 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & 10 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccccc%7Cc%7D%201%20%26%201%20%26%201%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%200%20%26%200%20%5C%5C%5C%5C%200%20%26%201%20%26%201%20%26%201%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%200%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%201%20%26%200%20%26%200%20%26%2010%20%5Cend%7Barray%7D%20%5Cright%5D)
b) To reduce this augmented matrix to reduced echelon form, you must use these row operations.
- Subtract row 2 from row 1
. - Subtract row 2 from row 3
. - Add row 3 to row 2
. - Multiply row 3 by −1
. - Add row 4 multiplied by
to row 1
. - Subtract row 4 from row 3
.
Here is the reduced echelon form for the augmented matrix.
![\left[ \begin{array}{ccccccc} 1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 & - \frac{1}{2} & - \frac{1}{2} & -11 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & 10 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccccccc%7D%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%2015%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%200%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%201%20%26%200%20%26%200%20%26%2010%20%5Cend%7Barray%7D%20%5Cright%5D)
c) The additional rows are

and the augmented matrix is
![\left[ \begin{array}{ccccccc} 1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 & - \frac{1}{2} & - \frac{1}{2} & -11 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\ 0 & 0 & 0 & 0 & 0 & 1 & 20 \\\\ 1 & 1 & 1 & 0 & 0 & 0 & 50 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccccccc%7D%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%2015%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%200%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-%20%5Cfrac%7B1%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%201%20%26%200%20%26%200%20%26%2010%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%26%2020%20%5C%5C%5C%5C%201%20%26%201%20%26%201%20%26%200%20%26%200%20%26%200%20%26%2050%20%5Cend%7Barray%7D%20%5Cright%5D)
d) To solve the system you must use these row operations.
- Subtract row 1 from row 6
. - Subtract row 2 from row 6
. - Subtract row 3 from row 6
. - Swap rows 5 and 6.
- Add row 5 to row 3
. - Multiply row 5 by 2
. - Subtract row 6 multiplied by 1/2 from row 1
. - Add row 6 multiplied by 1/2 to row 3
.
![\left[ \begin{array}{ccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 & 0 & 0 & 44 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\ 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\ 0 & 0 & 0 & 0 & 0 & 1 & 20 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccccccc%7D%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%200%20%26%200%20%26%200%20%26%2044%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%201%20%26%200%20%26%200%20%26%2010%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%200%20%26%201%20%26%200%20%26%2090%20%5C%5C%5C%5C%200%20%26%200%20%26%200%20%26%200%20%26%200%20%26%201%20%26%2020%20%5Cend%7Barray%7D%20%5Cright%5D)
The solutions are:
.
Answer:
6x+6y-5 distributive property
Step-by-step explanation:
6(x+y)-5
Distribute using the distributive property
6x+6y-5
Not quite sure what you’re asking for but i can offer a couple(and by that i mean two) “answers” depending on what you need.
Usd>Yen~1->.009
Gym B costs 50%less
If the question is trying to compare hours to usd then Gym A is the most accurate representation of USD to Yen
Is This Elementary School HomeWork Or High School HomeWork