Suppose we choose
and
. Then
Now suppose we choose
such that
where we pick the solution for this system such that
. Then we find
Note that you can always find a solution to the system above that satisfies
as long as
. What this means is that you can always find the value of
as a (constant) function of
.
area=legnth times width
we notice this is a special case
(a+b)(a-b)=a^2-b^2
area=(a+3b)(a-3b)=a^2-9b^2
area=a^2-9b^2
This works out beautifully. You COULD use long division here, but since your numerator is a quadratic, your first instinct should be to try and factor it. If you factor it, it works out to be (x - 3)(x + 2). Now it just so happens that when you do that, the (x - 3) in the numerator will cancel with the (x - 3) in the denominator leaving you with one sad and lonely (x + 2) as your answer.
Answer:
y = - 
x - 
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 4, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line
m = 
= - , thus
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 4, 2 ), then
2 = 
+ c ⇒ c = 2 - = -
y = - x - ← equation of line
<span>2 times 10 squared to the second power in standard notation
2 x(10^2)^2
=2x10^4
=20000</span>
