Answer:
Part 1) The constant of variation is 
part 2) The equation is 
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
Let
x -----> the number of square feet
y -----> the number of square yards
Three square yards are equivalent to 27 square feet
so
we have the point (27,3)
Part 1) What is the constant of variation?
The constant of variation or proportionality is equal to
substitute the values
Simplify
Part 2) What is the equation representing the direct variation?
we know that
substitute the value of k
Answer:
There are asymptotes at x = three-halves and x = negative one-third.
Step-by-step explanation:
f(x) = (x + 1)/ (6x^2 - 7x - 3)
= (x + 1)( / (6x^2 + 2x - 9x - 3)
= (x + 1) / (2x(3x + 1) - 3(3x + 1))
= (x + 1) / (2x - 3)(3x + 1)
Now x = 3/2 and x = -1/3 both make te denominator zero so these are both asymptotes.
A regular polygon is a closed figure
All its angles are equal in measure.
and all its sides are congruent
Answer: 
Step-by-step explanation:
Given the following expression:
You need to substitute the given values of "a" and "b" into the expression. Notice that these values are:
Then;
Now you must solve the multiplications:
The final step is to add the numbers. Therefore, you get the following answer:
From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
