<h2>Evaluating Composite Functions</h2><h3>
Answer:</h3>
<h3>
Step-by-step explanation:</h3>
We can write how 
will be defined but that's too much work and it's only useful when we are evaluating with many inputs.
First let's solve for 
first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
Solving for :
Now we can solve for 
, since 
, 
.
Given:
Solving for 
:
Now we are can solve for 
. By now you should get the idea why 
.
Given:
Solving for :
Answer:
See photo
Step-by-step explanation:
We can fill out many of these pretty easily. Look at the picture below. (Black numbers represent what information they already gave us)
Now, for the actual math.
If a total of 46 seventh-graders were surveyed and 28 seventh-graders spent more than an hour on their phone, then that means that there would have to be 46-28=18 students that spend less than an hour on their phone.
If there are 43 total students that spend more than an hour on their phone, and 28 of those are seventh-graders, then there are 43-28=15 eighth-graders that spend more than an hour on their phone
Then, if there are 27 total eighth-graders, and 15 of those spend more than an hour, then that leaves 27-15=12 eighth-graders that spend less than an hour on their phone.
Lastly, figure out the total numbers.
There are 18 seventh-graders and 12 eighth-graders that spend less than an hour on their phone, so there is a total of 18+12 = 30 students that spend less than an hour on their phone.
There are a total of 46 seventh-graders and 27 eighth-graders that were surveyed, which is a total of 73 students surveyed.
Answer: B.
Step-by-step explanation:
See attached. We examine the equation and decide which situation, or problem, models it correctly.
Answer:
y=-1/2 x^2+3/2 x+9
Step-by-step explanation:
The equation of parabola is:
y=ax^2+bx+c
We know that parabola has three poibts
(6,0),(-3,0) and (1,10).
So we put these three points in equation:
a*36+b*6+c=0......(1)
a*9-3b+c=0........(2)
a+b+c=10........(3)
(1)-(2) we have:
27a+9b=0.....(4)
(2)-(3) we have:
8a-4b=-10.....(5)
4(4)+9(5) we got:
180a=-90
a=-1/2
From (4) we got: b=27/18=3/2
From (3) we got: c=10+1/2-3/2=9
So equation is:
y=-1/2 x^2+3/2 x+9
You can see the picture of parabola through three points.
