Let's follow the transformations that happen to A, to get to A' and A''.
Point A is at (-5, -2)
It moves to (-5, 2) which is where A' is located. Note the x coordinate stays the same while the y coordinate flips from negative to positive. This must mean we applied a reflection over the x axis.
That rule in general is 
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Now compare A'(-5,2) and A''(1,4). We can shift A' 6 units to the right and then 2 units up so we move from A' to A''.
Algebraically this is stated as 
Whatever the x coordinate is, add 6 to it. For the y coordinate, we add on 2.
Applying that rule to B'(-1,2) gets us to
which is the proper location of B''
The same applies to moving C' to C''
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In summary, we started off by reflecting over the x axis. Then we applied the translation rule of "shift to the right 6 units, shift up 2 units".
In terms of algebra, combining the rules 
and will have us end up with 
Y = (x + 4)(x - 2)
The x-intercepts:
0 = x + 4
0 = x - 2
x = -4
x = 2
The vertex:
y = (x + 4)(x - 2)
y = x^2 + 2x - 8
x = -b/2a
If ax^2 + bx + c, then:
a = 1
b = 2
c - 8
x -2/2(1)
x = -1
y = (-1)^2 + 2(-1) - 8
y = -9
The vertex is (-1, -9)
The x-intercepts are -4 and 2
Answer:
The student did not add 4 to all sides of the inequality
Step-by-step explanation:
2<-3x - 4<5
Add 4 to all sides
4 + 2< -3x - 4 + 4 < 5 + 4
6< -3x < 9
Divide all sides by the coefficient of x; -3
-2< x < -3
Remember, when dividing an inequality with a negative number, you must flip the sign
So, this becomes;
-2 > x > -3
Which variable depends or is affected by the quantity of the other variable?
-The number of cards Jonathan brings in is the dependent variable because it <em>depends </em>on the number of students in his class.
Hope this helps! :)
Answer:
B
Step-by-step explanation:
A division between two roots that have the same index can be rewritten as a division between the two terms with a unic root
