Answer:
Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
Y=4^4-100=16-100=-84
Result is -84
The volume of the balloon is 500 cubic inches after 20 seconds
<h3>How to determine the volume?</h3>
From the given graph, we have:
- Time on the x-axis
- Volume on the y-axis
Also from the graph, we have:
V(20) = 500
This means that:
The volume of the balloon is 500 cubic inches after 20 seconds
Read more about graphs at:
brainly.com/question/4025726
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Answer:
Step-by-step explanation:
Let the number of computers sold by Joe be represented by variable X
If Jonathan sold 5 times as many computers , it means he sold 5 times X= 5X
Total number of computers sold by both Jonathan and Joe = 78
Hence, X+5X =78
= 6X = 78
Divide both sides by 6 to solve for X;
X = 78/6
X = 13
And 5X = (5* 13) = 65
Therefore, Jonathan sold 65 computers while Joe sold 13
(10x - 65) degrees is equal to (9x - 49) degrees, therefore you can set them into an equation.
(10x - 65) = (9x - 49)
By subtracting 9x in both sides,
(10x - 9x) - 65 = (9x -9x) - 49
x - 65 = -49
By adding 65 in both sides,
x - 65 + 65= -49 + 65
x = 16
Next, to find the value of z, it’s important to know that the straight line has 180 degrees. Then you would substitute the x value you found into one of your equation and subtract it from 180.
10 (16) - 65 = 160 - 65 = 95
Now you know that (10x - 65) degrees is equal to 95 degrees,
180 - 95 = z = 85
Answer: x = 16
z = 85
