Quadrant 2 because it goes to the left because the X is negative then up because the Y is positive.
dividing 11.5 by 5 gives you the unit rate, then you just multiply that answer by 2 and you should be okay
Answer:
P ( -1, -3)
Step-by-step explanation:
Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)
We will calculate coordinates of the point P which divides line segment AB in the following way:
xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1
xp = -1
yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3
yp = -3
Point P( -1, -3)
The function appears to be L(legos) = T(tower)^3
L = T^3
This checks out for t =1,2,3,4
The 100th tower would have 100^3 legos.
100^3 = 1,000,000.
The 100th tower would have 1 million cubes
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>.
