Ming spent $15 at the movies. Then she earned $30 babysitting. She spent $12 at the bookstore. Now she has $18 left. How much mo
1 answer:
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Answer:
isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.
Step-by-step explanation:
Let denote a set of elements.
would denote the set of all ordered pairs of elements of
.
For example, with ,
and
are both members of
. However,
because the pairs are ordered.
A relation on
is a subset of
. For any two elements
,
if and only if the ordered pair
is in
.
A relation on set
is an equivalence relation if it satisfies the following:
- Reflexivity: for any
, the relation
needs to ensure that
(that is:
.)
- Symmetry: for any
,
if and only if
. In other words, either both
and
are in
.
- Transitivity: for any
, if
, then
. In other words, if
are both in
also needs to be in
The relation (on
) in this question is indeed reflexive.
,
, and
(one pair for each element of
) are all elements of
.
isn't symmetric.
but
(the pairs in
are all ordered.) In other words,
isn't equivalent to
under
even though
.
Neither is transitive.
and
. However,
. In other words, under relation
,
and
does not imply
.
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:
So one factor is (x-1) and now simplifying we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
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