<span>let n+2=u
so, the equation became= [2/u]-[3/u]=5
=> [(2+3)/u]=5
=> 5/u=5
=> u=5/5=1
thus, u=1
we know u=n+2
so, n+2=1
=> n=1-2=-1
so, n=-1</span>
1.
1/4 is less then 2/4 or 1/2so if the denominator is equal it will be easier to multiply
Let's examine the given function first:
f(x) = x^2 + 1 is the same as f(x) = 1(x-0)^2 + 1.
The vertex of the graph of this function is at (0, 1).
Let x=0 to find the y-intercept: f(0)=0^2+1 = 1; y-int. is at (0,1) (which happens to be the vertex also)
Comparing f(x) = x^2 + 1 to y = x^2, we see that the only difference is that f(x) has a vertical offset of 1. So: Graph y=x^2. Then translate the whole graph UP by 1 unit. That's it. Note (again) that the vertex will be at (0,1), and (0,1) is also the y-intercept.
Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1,4) and (x₂, y₂ ) = (- 5, 3)
d = 
= 
= 
= 
≈4.12 ( to 2 dec. places )
To find the midpoint use the midpoint formula
[0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Using the same points as above then
midpoint = [0.5(- 1- 5), 0.5(4 + 3 ) ] = [0.5(- 6), 0.5(7) ] = (- 3, 3.5 )
So there is a real and imaginary axis
the midopint is just the average of them
average between the reals is (5-3)/2=2/2=1
average between imaginaries is (18i+2i)/2=20i/2=10i
center is 1+10i
