General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes 
. We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.
Question:
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
Answer: 13 dollars per hour
Step-by-step explanation:
The rate of change (ROC) for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x2, y2)
Point b = (2, 26) = (x1, y1)
Calculating the gradient or slope :
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
= 13 dollars per hour
Answer:
Option 4 is correct.
The equation 
is equivalent to 
Step-by-step explanation:'
Given equation:
First group the terms with x and those with y;
Next, we complete the squares.
We can do this by adding a third term such that the x terms and the y terms are perfect squares.
For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.
⇒
or
Add 360 on both sides we get;
Simplify:
Therefore, the given equation is equivalent to
Answer:
Check the explanation
Step-by-step explanation:
Write H(t) for the total sum spent in the United States on health care in year t, where t is measured in years since 2000.
The rate of increase of H(t) was projected to rise from $100 billion per year in 2000 to approximately $190 billion per year in 2010
(a) Find a linear model for the rate of change H'(t)
Slope of line is (190-100)/(2010-2000) = 90/10 = 9 billion dollars per yr
H'(t) - 190 = 9 (t-10) =
H'(t) = 9t + 100 billions dollars per year
(b) Given that $1,300 billion was spent on health care in the United States in 2000, find the function H(t).
H'(t) = 9t + 100 billions dollars per year TAKING INTEGRATION..
H(t) = 9t^2/2 + 100t + C given H(0) = 1300
H(0) = 1300 = C
H(t) = 9t^2/2 + 100t + 1300 billion dollars.
If they both do 7 hours, then the price will total out at $55.75 for both. Not sure if you have a formula from your book, but common sense/guestimating gets you that correct answer.
