Answer:
Step-by-step explanation:
4 gallons is 64 cups.
This means that it's 12 times f, then add that by 24. This f is a variable. It could be any number. First, try to find out what f equals. Then use that to find the answer.
It is 5 because any thing times 1 is that number
Answer:
for 
Step-by-step explanation:
Given
Shape: Triangle
Dimension: 3x + 2, x^2 and 2x

Required
Determine if it has equal sides
To do this, we simply substitute 4 for x in the given dimensions
<u>3x + 2</u>



<u>x^2 </u>


<u>2x</u>
<u></u>
<u></u>

for 
Step-by-step explanation:
(a)
Using the definition given from the problem
![f(A) = \{x^2 \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2 \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4] = f(A \cap B)\\](https://tex.z-dn.net/?f=f%28A%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B0%2C2%5D%5C%7D%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B1%2C4%5D%5C%7D%20%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccap%20f%28B%29%20%3D%20%5B1%2C4%5D%20%20%3D%20f%28A%20%5Ccap%20B%29%5C%5C)
Therefore it is true for intersection. Now for union, we have that
![A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]](https://tex.z-dn.net/?f=A%20%5Ccup%20B%20%3D%20%5B0%2C4%5D%5C%5Cf%28A%5Ccup%20B%20%29%20%3D%20%5B0%2C16%5D%5C%5Cf%28A%29%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccup%20f%28B%29%20%3D%20%5B0%2C16%5D)
Therefore, for this case, it would be true that
.
(b)
1 is not a set.
(c)
To begin with

Therefore

Now, given an element of
it will belong to both sets, therefore it also belongs to
, and you would have that
, therefore
.
(d)
To begin with
, therefore
