The simplified form of given expression is 
Answer: Option B
<u>Step-by-step explanation:</u>
Given expression:
To find the simplified form of the given expression
We know, x to the power 0 is equal to 1. i.e. 
. Therefore, it gets removed in the given expression.
As common ‘4’ in numerator and denominator also gets cancelled in the given expression
Bring negative exponents (in numerator) down (to denominator) to form positive exponents, we get the simplified form of given expression as below,
4 socks = 1 pair of jeans
2 jeans = 3 shoes
6 shoes = 1 coat
1 pair of jeans = 4 socks...so 2 jeans = 8 socks
so now we have 8 socks = 3 shoes.
if 3 shoes = 8 socks, then 6 shoes = 16 socks
so 16 socks = 1 coat
so 64 socks = 64/16 = 4 coats <===
A.
cannot be the power set of any set. Consult Cantor's theorem, which says that the cardinality of the power set of any set (even the empty set) is strictly greater than the cardinality of the set.
(No part b?)
c. Also not the power set of any set, because any power set must have
elements, where
is the cardinality of the original set. The cardinality of this set is 3, but there is no integer
such that
. This set would be a power set if
(that is, the set containing the empty set) were a member of it.
1st Avenue would be more difficult because it’s rise and run is for every one foot forward it is 3 feet up. Meanwhile avenue 16th would start at (3,1) and the rise and run would be for every 3 feet it would go up 1 foot.
Answer:
To Prove: Quadrilateral ABCD is a parallelogram.
Proof: In Δ ABE and ΔCDE
1. AE = EC and BE = ED [ Diagonals bisect each other]
2.∠ AEB = ∠ CED [ vertically opposite angles]
Δ ABE ≅ ΔCDE---------- [SAS]
∠ ACD ≅ ∠CAB [Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
6. The converse of alternate interior interior angle theorem states that if two parallel lines are cut by a transversal then alternate interior angles are equal.
7. In ΔBEC and ΔAED
∠BEC = ∠AED [ Vertical Angles Theorem ]
AE = EC and BE = ED [ Diagonals bisect each other]
⇒ ΔBEC≅ ΔDEA [ SAS criterion for congruence]
9. DBC ≅ BDA [ Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
As pair of triangles are congruent ∵ quadrilateral ABCD is a parallelogram.
Step 3 is m∠AEB = m∠CED
These pair of angles are vertically opposite angles of ΔAEB and ΔCED.
Option [D. Vertical Angles Theorem] is correct.
