David's : y = 12,350 - (240x)
Amanda's : y = 12,350 + (240x)
David's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings
Answer:
y = -3x + 9
Step-by-step explanation:
y = mx + b where m is the slope and b is the y intercept
The hypotenuse is on the same line as BC but twice as long. So extend that line up and it will cross the y axis at (0,9). 9 will be your y intercept.
To find the slope start at C and count up 9 and to the left 3 to get to B.
So the slope is rise/run or 9/(-3) = -3.
Final equation would be y = -3x + 9
9514 1404 393
Answer:
(c) 162 cm
Step-by-step explanation:
The centroid divides a median into parts with the ratio 1:2, so RL:LD = 1:2. Then RL:RD = 1:(1+2), and RD = 3RL.
RD = 3·54 cm
RD = 162 cm
Answer:
Connect the arcs to make a perpendicular bisector
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>.
