In attempting to solve the system of equations and , John graphed the two equations on his graphing calculator. Because he saw o
1 answer:
Answer:
The correct answer is NO.
Step-by-step explanation:
John is graphing two lines with equations say ax + by + c = 0 and dx + ey +f =0 on his graphing calculator.
For John to get a unique solution the coefficients should follow the following condition . So when he plots the lines he get an intersecting pair of lines.
For John to get no solution the coefficients should follow the following condition . When we plot in this case we get two parallel lines.
For John to get an infinite many solution the coefficients should follow the following condition . And when we plot the lines in this case we get one line superimposed on the other.
Since after graphing, John sees only one line, the lines must have superimposed on one another giving John an infinite number of solutions.
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Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.
Explanation:
1)
The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.
If , then a+b\in Z.
Therefore, an integer added to an integer is an integer, this statement is always true.
2)
A polynomial is in the form of,
Where are constant coefficient.
When we subtract the two polynomial then the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.
3)
If a polynomial divided by a polynomial then it may or may not be a polynomial.
If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.
For example:
Then , which a polynomial.
If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.
For example:
Then , which a not a polynomial.
Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.
4)
As we know a polynomial is in the form of,
Where are constant coefficient.
When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.