9514 1404 393
Answer:
y = 3x^2 +30x +69
Step-by-step explanation:
Transformations work this way:
g(x) = k·f(x) . . . . vertical stretch by a factor of k
g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)
__
So, the translation down 2 units will make the function be ...
f(x) = x^2 ⇒ f1(x) = f(x) -2 = x^2 -2
The vertical stretch by a factor of 3 will make the function be ...
f1(x) = x^2 -2 ⇒ 3·f1(x) = f2(x) = 3(x^2 -2)
The horizontal translation left 5 units will make the function be ...
f2(x) = 3(x^2 -2) ⇒ f2(x +5) = f3(x) = 3((x +5)^2 -2)
The transformed function equation can be written ...
y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)
y = 3x^2 +30x +69
__
The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came <em>before</em> the vertical scaling.
Answer:
The estimated impact of the experiment of offering test preparation classes is:
= 8 scores (in performance improvement).
Step-by-step explanation:
Average standardized-test score for the first 10 high schools = 69
Average standardized-test score for the second 10 high schools = 70
After 6 months:
Average standardized-test score for the first 10 high schools offered test preparation classes = 78
The change in the average standardized-test score for the first 10 high schools = 9 (78 - 69)
Average standardized-test score for the second 10 high schools not offered test preparation classes = 71
The change in the average standardized-test score for the second 10 high schools not offered the prep = 1 (71 - 70)
The estimated impact of the experiment of offering test preparation classes is:
= 9 - 1
= 8.
Answer:
Step-by-step explanation:
Let 
be the length of the longer side of the smaller rectangle and 
be the length of the shorter side of the smaller rectangle
When you look at the combined rectangle from top to bottom, you can see that 
. Therefore, 
This is the same for 
. Thus, 
When you look from right to left, you can see that 
. Using this, we can represent 
in terms of 
.
Now, we can find the ratio of 
:
<u>This question was quite hard to explain.</u>
<u>If you have any questions about the solution, feel free to ask.</u>
<u>Please have a look at the diagram below to get a better understanding of the solution.</u>
Answer:
yes, they are proportional
Step-by-step explanation:
A proportion is a relation that can be modeled by a straight line through the origin. The equation will have the form ...
y = kx
where x is the independent variable, y is the dependent variable, and k is a constant of proportionality.
__
If you start with the equation relating distance, rate, and time:
d = rt
and you fix the time at 50 seconds, then the equation becomes ...
d = 50t
This is the equation of a proportion with a constant of proportionality of 50. It tells you the distance run is proportional to the rate you run. When this equation is graphed, it is a straight line through the origin.
D=57 and r=30, then by the formula d=r*t
57=30*t.
dividing 30 on both sides we get, t= 57/30
t=1.9
