Let A = {15, 25, 35, 45, 55, 65} and B = {25, 45, 65}. What is A ∩ B?
1 answer:
Answer:
A∩B={}
B is a proper subset of A:
B⊂A
Step-by-step explanation:
A∩B means the intersection of the set A and the set B. In other words, is the set of elements contained in these both sets.
Given the set A and the set B:
{
}
{
}
You can indentify that the numbers common in both sets are: 25,45 and 65.
Therefore you get:
A∩B={}
Since all elements of B are in A, and A contains elements that are not in B, then B is a proper subset of A:
B⊂A
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Answer:
Perimeter = 18.7 units
Area = 13.5 units²
Step-by-step explanation:
Perimeter of ADEC = AD + DE + EC + AC
Length of AD = 3 units
By applying Pythagoras theorem in ΔDBE,
DE² = DB² + BE²
DE² = 3² + 3²
DE = √18
DE = 4.24 units
Length of EC = 3 units
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
AC² = 6² + 6²
AC = √72
AC = 8.49 units
Perimeter of ADEC = 3 + 4.24 + 3 + 8.49
= 18.73 units
≈ 18.7 units
Area of ADEC = Area of ΔABC - Area of ΔBDE
Area of ΔABC =
=
= 18 units²
Area of ΔBDE =
=
= 4.5 units²
Area of ADEC = 18 - 4.5
= 13.5 units²
