For this exercise it is important to know that, in Dilations:
1. When the scale factor is greater than 1, the Image (the figure obtained after the transformation) is an enlargement.
2. When the scale factor is greater than 0 but less than 1, the Image is a reduction:
And the scale factor is:
Since:
It is a reduction.
You can identify that the rule of this transformation is:
Answer:
FG = 7
Step-by-step explanation:
5x+2+3x-1=9
8x+1=9
8x = 8
x = 1
FG = 5(1)+2 = 7
Answer:
a) The recursion formula is .
b) .
Step-by-step explanation:
a) Let us explore the recurrence. A plane with only one line is divided in two regions, so . If we add another line under the restrictions of the problem, .
Notice that each line intersects the other n-1 lines, because there are no parallel lines. Assume we have n-1 lines and regions in the plane. If we add a new one we will have the previous plus n new regions. Because, for each line crossed by the new one there are a new region. Therefore,
.
b) The method here is to develop the recurrence and find some pattern. Hence, using the formula for , and we obtain
Notice that for each step back in the recurrence we add a new term in th sum. If we repeat the procedure n-1 times we will have
Using that :
Here the smart step is to split the first 2 in 1+1, in order to obtain the sum of the first n natural numbers, and the expression for this last sum it is well known. Therefore,
V(4,-2)
In the vertex form, the h value is the x and the k value is the y.
So if the vertex (4,-2) is also (h,k)
You can just simply replace the h and k in (x-h)^2+k.
Which gives us...
f(x)=(x-4)^2-2.