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:
5
Step-by-step explanation:
There are 3 feet in a yard, so 420 feet is 420/3 = 140 yards.
The total number of yards Edith needs is ...
65 yd + 580 yd = 645 yd
So, the total number of balls of yarn Edith needs is ...
(645 yd)/(140 yd/ball) ≈ 4.61 balls
Edith needs to buy 5 balls of yarn to make her projects.
You have to make an equation that i forgot what was called but you just take
x+y=10 and multiply it by -2 so the y’s can cancel out
so you’ll end up with:
-2x-2y= -20
(+) x+2y=14
you’ll get : x = -6
then you plug in -6 for x, solve for y and your coordinates will be
(-6 , 10)
Answer:
Step-by-step explanation:
Answer:
1. There are _______ quarter notes in a whole note.
2. There are_______ half notes in a whole note.
3. There are________ quarter notes in a half note.
4. There are________ quarter notes in two half notes.
5. There are ______quarter notes in three half notes.
6. A whole note equals________ half notes
7. A whole note equals________ quarter notes. 8. A half note equals______ quarter notes.
9. Two half notes equal_______quarter notes. 10. Four quarter notes equal_______ whole note.
