Answer:
"No, the relationship is NOT proportional"
Step-by-step explanation:
<u>Complete Question:</u>
Of the 75 boys in the 7th grade class, 25 participate in at least one sport. Of the 120 girls in 7th grade class 30 participate in at least one sport. Is this relationship proportional?
We have to see the ratio of each and if they are equal (after reducing), we can say they are proportional.
Boys:
25 participate in atleast 1 sport and there are total of 75. Hence, ratio is
25 : 75 = 1 : 3
Girls:
30 particiapte in atleast 1 sport and there are toal of 120. hence ratio is:
30 : 120 = 1 : 4
So, the relationship is NOT proportional
Answer:
y = 12-(61) is the answer !!
Answer:
1. They consist primarily of variables.
2. They are often called formulas.
4. They often describe real-world relationships.
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.
y' = 2ax + b
Now that we where the derivative, we can set it equal to 0.
2ax + b = 0
We also know that at the extreme value, x = -1/2. We can plug that in as well.

The 2 and one-half cancel each other out.


Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.
a(-0.5)^2 + a(-0.5) + 10 = 0
0.25a - 0.5a + 10 = 0
-0.25a = -10
a = 40
b = 40
To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.
80x + 40
Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.
LESS THAN:
80(-1) + 40 = -40
GREATER THAN:
80(0) + 40 = 40
The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.
4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.
y' = 2ax + 1
2a(3) + 1 = 0
6a = -1
a = -1/6
So now plug the a value and x=3 into the original function to find the extreme value.
(-1/6)(3)^2 + 3 + 3 = 4.5
The extreme value is 4.5