Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Side links are : 3m, 4m, 5m
The perimeter of a triangle = (a + b + c)
Perimeter 1= (3 + 4 + 5) = 12m
If the side links are multiplied by 4 :
3*4 = 12 m
4*4 = 16m
5*4 = 20m
Perimeter2 = (12 + 16 + 20) = 48 m
Comparing the perimeters:
Perimeter 1 = perimeter 2
12 = 48
Hence, perimeter also increases by 4 folds
The axis of symmetry is the fold line that splits the parabola down the middle.
Now, since a parabola is symmetrical, every point, except the vertex, will have a mirror image of another point if we folded the parabola over the axis of symmetry.
So if we know the axis of symmetry is x = 3 and one of our points
has the coordinates (5, 0), the other point will have the coordinates (3, 0).
The axis of symmetry is always halfway between the x-intercepts.
Answer:
This means that, when the price of a book from a publisher is $60, the bookstore will sell it for $88 to the students.
Answer:
(a) (-∞, -8) (-6, -4) (-2, ∞)
(b) -6, -2
(c) negative
(d) 5
Step-by-step explanation:
(a) A function is "decreasing" when the y-value decreases as the x-value increases.
⇒ the function is decreasing over these intervals : (-∞, -8) (-6, -4) (-2, ∞)
(b) Local maxima are the points on the function where it reaches a maximum.
⇒ maxima at x = -6 and x = -2
(c) negative
(d) 5
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
