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Step-by-step explanation:
Answer:
In order to have a consistent linear system represented by the augmented matrix:
the value of h must be:
Step-by-step explanation:
A system is consistent if it has a solution, this solution can be unique or a set of infinite solutions.
First, you take the augmented matrix and find the equivalent row echelon form using Gaussian-Jordan elimination:
To do this, you have to multiply the 1st row by 3 and add it to the 2nd row, the resulting matrix is:
Now, write the system of equations:
The only way this system has a solution is if 5+3h=0, then, to satisfy this, the value of h must be:
Answer:
Exponential form: 5^3
Expanded form: 5*5*5
Standard form: 125
Step-by-step explanation:
The exponential form is when we use the ^ symbol. The base is the number before the ^ and the exponent is the number after the ^. When five is cubed, the base is 5 and the exponent is 3.
Therefore, the exponential form is 5^3. We can also write it with a little 3 on the top right corner of the 5, that is .
On the expanded form we use multiplications. The exponent number tells us how many times to multiply the base number by itself. When 5 is the base and 3 the exponent, we have to multiply 3 times the number 5 by itself. That is 5*5*5.
The standard form is the result of the calculations we wrote before. The easiest way is to get it from the expanded form.
5*5*5 = 25*5 = 125