Answer:
-24 a^2 b^7
Step-by-step explanation:
Simplify the following:
-8×3 a^2 b^4 b^3
Hint: | Combine products of like terms.
3 a^2 b^4 (-8) b^3 = 3 a^2 b^(4 + 3) (-8):
-8×3 a^2 b^(4 + 3)
Hint: | Evaluate 4 + 3.
4 + 3 = 7:
-8×3 a^2 b^7
Hint: | Multiply 3 and -8 together.
3 (-8) = -24:
Answer: -24 a^2 b^7
Answer:
D. Their intersection point is the only point where the same input into both functions yields the same output.
Step-by-step explanation:
The intersection point of 2 graphed lines represents the solution.
At this point, for both lines, there is the same x value (input) and the same y value (output) because both of the lines have that point in common.
So, if those 2 lines were to be graphed, the intersection point would represent the only point with the same input and output for both functions.
D is the correct answer.
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
Answer:
It can never be a prime number.
Step-by-step explanation:
This is because the product of the two prime numbers are divisible by those two numbers, therefore going against the definition of a prime number. For example 3 and 5 are prime numbers and their product is 15. 15 can be divided by 3 and 5 so it is not a prime number.
Hope this helps.
Step-by-step explanation:
<em>I think you have forgotten to attach the question. </em>
<em>Anyways....</em>
In order to find the area of a circle use the formula:
π
Where r is the radius
For example the radius is 3cm. The area of the circle will be:
π × 
Since you have taken pi as 3.142...
3.142 ×
3.142 × 9
= 28.278
In order to find the answer to 1 decimal place, check the number next to the number right after the decimal. Is it a number greater than or equal to 5? then add +1 to the number.
= 28.3 
