Answer: The system of equations is:
x + 2y + 2 = 4
y - 3z = 9
z = - 2
The solution is: x = -22; y = 15; z = -2;
Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.
The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a <u>Row</u> <u>Echelon</u> <u>Form,</u> which satisfies the following conditions:
- There is a row of all zeros at the bottom of the matrix;
- The first non-zero element of any row is 1, which called leading role;
- The leading row of the first row is to the right of the leading role of the previous row;
For this question, the matrix is a Row Echelon Form and is written as:
![\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%262%5C%5C0%261%263%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}4\\9\\-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C9%5C%5C-2%5Cend%7Barray%7D%5Cright%5D)
or in system form:
x + 2y + 2z = 4
y + 3z = 9
z = -2
Now, to determine the variables:
z = -2
y + 3(-2) = 9
y = 15
x + 30 - 4 = 4
x = - 22
The solution is (-22,15,-2).
Answer:
yes
Step-by-step explanation:
this is because we are eliminating the same shape so the same amount of weight from both sides, therefore the mobile still balances
<h2>
Answer:</h2>
The cost in dollars is:
$ 1.8144
<h2>
Step-by-step explanation:</h2>
It is given that:
The 60-W lamp is operated continuously for 1 week.
We know that:
1 week=7 days
and 1 day=24 hours
This means that:
1 week=24×7
i.e. 1 week= 168 hours
Also, 1 kW=1000 W
This means that:
1 W=0.001 kW
Hence,
60-W=0. 060 KW
i.e. Power= 0.60 KW
Hence, the energy consumed is:
Energy=Power×Time
i.e.
Energy=0.060×168
i.e.
Energy=10.08 KWh
Also, cost of 1 KWh=18 cents
We know that:
1 cent=0.01 dollar
This means that:
18 cents=0.18 dollar
i.e.
Cost of 1 KWh=$ 0.18
Hence, cost of 10.08 KWh is: $ (0.18×10.08)
i.e.
Cost of 10.08 KWh is: $ 1.8144
Answer:
66.6
Step-by-step explanation:
because 5000/75 equals 66.6 and ooooo spooky season