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).
900.9% would be 9.009 as a percentage.
It's 900% because it's a whole number and it's .9% because of the last 9 in the number (the thousandth - 3 digits after the decimal).
Answer:
formula for a circle: (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius.
1. Plug in center coordinates into formula
(x-3)^2 + (y-(-6))^2 = r^2
2. Plug in radius value
(x-3)^2 + (y-(-6))^2 = 5^2
3. Simplify:
(x-3)^2 + (y+6)^2 = 25
Answer:
x = -5
y = 2
Step-by-step explanation:
x = – 2y – 1
= -x - 2y - 1
-x - 2y = 1
x = – 5y + 5
= -x - 5y + 5
-x - 5y = -5
-x - 2y = 1
-x - 5y = -5
___________--
3y = 6
y = 6/3
<u>y = 2</u>
-x - 2y = 1
-x - 2(2) = 1
-x - 4 = 1
-x = 1 + 4
-x = 5
<u>x = -5</u>
The interval notation for numbers greater than 2 but less than or equal to 20 is (2,20]