1) Never heard of someone referring to the Law of Levers before, must be showing my age. A system as you describe is at equilibrium when the net torque is equal to zero. Since torque is Fr=mgr so for this system we have a sum of:
27g*10+30g*x=0 The sum must be zero to be at equilibrium, dividing both sides by g you have:
270+30x=0
270=-30x
x=-9
The negative just indicates that the magnitude of 9 is on the opposite side of the fulcrum, so x=9ft in magnitude.
2) Inverse variation is of the form y=k/x, in this case we are given a point so we can solve for the constant, k, of variation...
y=k/x, and we are given y=-12 when x=5 so
-12=k/5
k=-60 so the equation is:
y=-60/x which can be expressed as
xy=-60
Answer:

Step-by-step explanation:
Given:
A mixture of green paint requires 3/4 pint yellow paint and 2/5 pint blue paint.
Question asked:
How many pints of yellow paint will be needed if the mixture contains one pint of blue paint ?
Solution:
We will easily find quantity of yellow paint, will be needed in the mixture, contains one pint of blue paint by using unitary method:
By using
blue paint, yellow paint requires = 
By using 1 pint blue paint, yellow paint requires = 

Thus,
pint yellow paint requires in the mixture with one pint of blue paint.
Use photomath. it shows the work too
Answer:
C. -5x − 3y = 0
Step-by-step explanation:
A(-3, 0) and B(-6, 5)
First we find the slope of line AB

Slope of the line parallel to AB = slope of line AB
When the lines are parallel then their slope are equal
So the slope of line parallel to AB = 
The line passes through the origin (0,0)
Use equation y-y1= m (x-x1)
m = -5/3 , x1=0 and y1=0


multiply the whole equation by 3
3y = -5x
Subtract 3x from both sides
0=-5x-3y
-5x - 3y =0
It would be 6 unless there is a line with a certain angle.