A. for the circumference it is C=pi(d)=pi(2r)=pi(10)= 31.4 ft
b. for the area it is A=pi(r)^2=pi(5)^2=pi(25)= 78.5 ft squared
c. since the are is 78.5 ft squared multiply by $4.50= $353.25 to floor the circle.
Answer:
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. (OR) A face is a 2D shape that makes up one surface of a 3D shape, an edge is where two faces meet and a vertex is the point or corner of a geometric shape.
Step-by-step explanation:
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>.
It should be :
1/3(x + 18) = 7
1/3x + 6 = 7
1/3x + 6 - 6 = 7 - 6
1/3x = 1
x = 3
C. 10. you can calculate this by adding n to both sides to get 35=25+n and then subtracting 25 from each side to get n=10.
