Answer:
concave pentagon I'm thinking
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>.
Answer:
$21.10=3.10+2m.
Step-by-step explanation:
If the total fare was $21.50, then that is what it will all have to equal out to.
They charged a pick-up fee of $3.10. Which means that no matter how far you go, you will pay that. Then an extra $2 per mile. If m is mile, then it would be 2m because it is $2 per extra mile. Then add the pick-up fee of $3.10 and you will get your answer of $21.50=3.10+2m.
Step-by-step explanation:
believe it or not, the area of any triangle is
baseline × height / 2
we have here 2 triangles, both with the same baseline (8 cm), but with 2 different heights : 6.5 cm and 4.6 cm.
so, their areas are
8 × 6.5 / 2 = 4 × 6.5 = 26 cm²
8 × 4.6 / 2 = 4 × 4.6 = 18.4 cm²
so, in total, the shaded region is
26 + 18.4 = 44.4 cm²
