When you have a point A and then transform it using a linear transformation (like rotation, reflections, etc.), we mark it as A' to say, "This is the point which corresponds to A after the transformations were applied". This establishes a link between the two, even though they may appear to be unrelated to someone looking at the graph.
Answer:12 9/10
Step-by-step explanation:
A) $27,000.00 - $5,000.00 =$22,000.00
B) $31,500
C) $4,150
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If 
, then 
.
Let's simplify that.
Distribute with 
:
Combine the end like terms 
:
Use 
identity for 
:
Combine like terms 
and 
:
We are given 
.
So we have that 
.
The vertex happens at 
.
Compare 
to 
to determine 
.
Let's plug it in.
So the 
coordinate is 5.
Let's find the corresponding 
coordinate by evaluating our expression named 
at 
:
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is 
where the vertex is 
.
Let's put 
into this form.
We are given .
We will need to complete the square.
I like to use the identity 
.
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.
Answer:
D/2=r
Step-by-step explanation:
Since we want r to be by itself what we can do is divide 2 on both sides so 2 can cancel out on 2r and when you divide on both sides your left with d/2=r
