If an equation is a direct variation, then there is always something added or subtracted from the x term
1 answer:
Answer:
The given statement is false.
Step-by-step explanation:
Given statement:
"If an equation is a direct variation, then there is always something added or subtracted from the x term."
Consider 2 variables 'x' and 'y' such that 'y' varies directly with 'x'. Therefore, if two variables have direct variation, then they are related as:
, where, 'k' is a constant of proportionality.
Now, in the above relation, the variable 'x' is multiplied by 'k' but nothing is added or subtracted from the 'x' term.
If something is added to the 'x' term, then the relation is a linear variation and not a direct variation.
Thus, the given statement is FALSE.
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Consider the polynomial .
For this polynomial to be trinomial with a degree of 3. We have to identify the missing exponent of the 'y' term.
Let the missing exponent of the 'y' term be 0
So, the polynomial will be
=
= which is not a trinomial, which is a binomial.
So, the missing exponent of 'y' can'not be zero.
Let the missing exponent of the 'y' term be 2
So, the polynomial will be
=
= which is a trinomial of degree 4.
So, the missing exponent of 'y' can'not be '2'.
If we will take the missing exponent of 'y' more than 2, than the degree of the given polynomial will not be 3 anymore.
Let the missing exponent of the 'y' term be 1
So, the polynomial will be
=
= which is a trinomial of degree 3
So, the missing exponent of 'y' is 1.