Answer:
x = -56
Step-by-step explanation:
x/7 = -8
Multiply each side by 7
x/7 *7 = -8*7
x = -56
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

0.5625 will be the answer to 9 divided by 16
Answer:
Step-by-step explanation:
I think you are trying to use synthetic division for
divided by x-3
First
x -3 = 0 , make it equal to 0 and add 3 to both sides
x = 3
Then we write all the coefficients and continue with
a pattern of multiply by 3 and add to the next coefficient.
See attachment.
You have to multiply by the complex conjugate so that you can clear the radical from the denominator.
Once you do the multiplication simplify the radical. There's still a common factor in -54, -18, & 75 so divide all those by 3.