Answer:

Step-by-step explanation:
-Amy walks a distance of 7/8 mile
-Tom walks a distance of 4/8 mile.
#We immediately notice that Amy has walked a longer distance than Tom.
We subtract Tom's distance from Amy's to find how much further Amy walked;

Hence, Amy has walked 3/8 miles further than Tom has.
Answer:
x = 6 2/3 The supplementary pair of angle is 78 degree and z = 112degree = 180 degree First step is where we can also see z its opposite angle is vertical opposite angle to 112 degree given and label as vertical angle - where we see a line through the 180 degree line at any angle we can call the pair supplementary- Pairs OR sets of angles an only be called consecutive when they are grouped with a set of parallel line across a straight line and it is only because they add up to 180 they could be either terms so as there isn't parallel shown ; <u>we know we an call a pair of angles upon a straight line supplementary.angles. </u>
Step-by-step explanation:
6 x +38 (+112) = 180 degree as angles on a straight line add up to 180 6 x +38 (+112) = 180 6 x +140 = 180 6 x + 140- 140 = 180-140 6 x = 40 x = 40/6 x = 6.66666667 x = 6 2/3 <u> </u><u>Proof (6( 6 2/3)) + 38 + 112 = 180</u> = (40+38)+112 = 180 = 78 +112 = 180 Proves the supplementary angle is 78 degree.
Answer:
10
Step-by-step explanation:
Hope it helps!
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:
-5
Step-by-step explanation: