2 surfaces are 6 in by 9 in, meaning that their combined area is 2(54 in^2).
2 surfaces are 6 in by 18 in; combined area is 2(108 in^2).
2 surfaces are 9 in by 18 in; combined area is 2(162 in^2).
Add up these areas: A = 2(54+108+162) in^2 = 648 in^2 (answer)
For this case we have the following equations:
5y = 3-2x
5y-3 = -2x
2x + 5y = 3
2x + 5y-3 = 0
The standard form of the equations is given by:
Ax + By = C
Therefore, the equation written in its standard form is:
2x + 5y = 3
Where,
A = 2
B = 5
C = 3
Answer:
The equation that is the standard form is:
2x + 5y = 3
2 to the power of 14 means 2^14.
That would be 16384.
Answer:
The length of the sides of the square is 9.0015
Step-by-step explanation:
Given
The diagonal of a square = 12.73
Required
The length of its side
Let the length and the diagonal of the square be represented by L and D, respectively.
So that
D = 12.73
The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:
Solving further, we have
Divide both sides by 2
Take Square root of both sides
Reorder
Now, the value of L can be calculated by substituting 12.73 for D
(Approximated)
Hence, the length of the sides of the square is approximately 9.0015
We are to show that if X ⊆ Y then (X ∪ Z) ⊆ (Y ∪ Z) for sets X, Y, Z.
Assume that a is a representative element of X, that is, a ∈ X. By the definition of union, a ∈ X ∪ Z. Now because X ⊆ Y and we assumed a ∈ X, then a ∈ Y by the definition of subset. And because a ∈ Y, then a ∈ Y ∪ Z by definition of union.
We chose our representative element, a, and showed that a ∈ X ∪ Y implies that a ∈ Y ∪ Z and this completes the proof.
