Answer:
The width of the red tile would be
inches.
Step-by-step explanation:
Given blue tile has a length of
inches, and a width of
inches.
Also, length of similar tile is
inches.
Let us assume
as the width of red tile.
It is given in the question that both tiles are similar.
So, their area will be the same.
Area of blue tile would be 
Area of red tile would be 
The area of blue tile would be equal to area of red tile.


So, the width of the red tile would be
inches.
Answer:
x = 15
Step-by-step explanation:
A full circle = 360°
Therefore,
(8x - 10)° + (6x)° + (10x + 10)° = 360°
Solve for x
8x - 10 + 6x + 10x + 10 = 360
Add like terms
24x = 360
Divide both sides by 24
x = 360/24
x = 15
we know that
if two lines are perpendicular, then the product of their slopes is equal to minus one
so

Step 1
<u>Find the slope of the given line</u>
we have

Solve for y
Divide by
both sides


the slope of the given line is 
Step 2
<u>Find the slope of a line that is perpendicular to the given line</u>
we have



substitute the value of m1

therefore
<u>the answer is</u>
the slope is 
LCM 14 & 24 = 168
then use the highest exponents for the variables
answer = 168x^6y^6z^8
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>.