Answer:
a=√x3y5 or a=−√x3y5
Step-by-step explanation:
So the angle A on the first diamond corresponds with angle Q, angle B with angle S, angle C with angle R, and angle D with angle P. So if angle D correspond (equals) angle P then x+34=97 and if angle R corresponds with C then 3y-13=83. From there just do some basic algebra to find the x and y values.
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>.
In a triangle, the side opposite the largest angle is the longest one. So the answer is 8 inches.
X=6 and y=-9. Not sure if y is correct since I kind of rushed but I hope this helps!
