Answer:
Step-by-step explanation:
BC=AD
3x-1=x+5
3x-x=5+1
2x=6
x=3
BC=3×3-1=8
CD=2x=2×3=6
perimeter=2(8+6)=2(14)=28
Answer:
3/12: terminating; 2/9: repeating
Step-by-step explanation:
3/12=0.25 terminating as it has a finite number of digits after the decimal point.
2/9=0.222.... repeating decimal as its number is repeated indefinitely.
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>.
<h3><u>The unknown number is equal to 4.</u></h3>
8x - 27 = 5
Add 27 to both sides.
8x = 32
Divide both sides by 8
x = 4
Answer:
The last option
Step-by-step explanation:
You take the middle 2 numbers, add them up, and divide by 2.
