Answer:
C
Step-by-step explanation:
If x = a is a zero of f(x) then (x - a) is a factor of f(x)
Here the zeros are x = 6 and x = - 4 then the corresponding factors are
(x - 6) and (x - (- 4) ) , that is (x - 6) and (x + 4)
Then f(x) is the product of the factors
f(x) = a(x - 6)(x + 4) ( a is a multiplier )
If a = 1 , then
f(x) = (x - 6)(x + 4) ← is a possible choice → C
the answer is 89
Step-by-step explanation:
it does not matter if the number is negative the absolute value is the number inside the lines
Answer:
and 
Step-by-step explanation:
The first system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
Answer:
Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.
<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that
. Thus, A↔A.
<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that
. In this equality we can perform a right multiplication by
and obtain
. Then, in the obtained equality we perform a left multiplication by P and get
. If we write
and
we have
. Thus, B↔A.
<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have
and from B↔C we have
. Now, if we substitute the last equality into the first one we get
.
Recall that if P and Q are invertible, then QP is invertible and
. So, if we denote R=QP we obtained that
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.