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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.
Answer:
The equation is equal to
Step-by-step explanation:
Let
x -----> the number
we know that
The equation that represented the problem is equal to
Solve the quadratic equation by graphing
The solution are x=-2 and x=4
see the attached figure
therefore
The number can be -2 or 4
Step-by-step explanation:
To write the equation in LaTeX in form y = ab^x or for y = abx .........(1)
(a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x can be written in mathematical form as
; y = 342x
on comparing with equation (1) we get a =3 and b =4
⇒y = 34^x or
(b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 can be written in mathematical form as
; y = 342x
on comparing with equation (1) we get a =0.5 and b =5
⇒y =
(c)LaTeX: y=8^{x+2} y = 8 x + 2 can be written in mathematical form as
on comparing with equation (1) we get a =64 and b =8
y =
(d)LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}} can be written in mathematical form as
=
=
on comparing with equation (1) we get a =3 and b =3
y =