Answer:
I. m = 2401
II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]
Step-by-step explanation:
I. Determination of m
x ∆ y = x² − 2xy + y²
2 ∆ − 5 = √m
2² − 2(2 × –5) + (–5)² = √m
4 – 2(–10) + 25 = √m
4 + 20 + 25 = √m
49 = √m
Take the square of both side
49² = m
2401 = m
m = 2401
II. Simplify ((n+1) ∆ y)/n
We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:
x ∆ y = x² − 2xy + y²
(n+1) ∆ y = (n+1)² – 2(n+1)y + y²
(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²
(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1
(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1
(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1
(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1
(n+1) ∆ y = (n – y + 2)(n – y) + 1
((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n
((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]
Answer:
y=-1/2x+3/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-1)/(5-1)
m=-2/4
m=-1/2
y-y1=m(x-x1)
y-1=-1/2(x-1)
y=-1/2x+1/2+1
y=-1/2x+1/2+2/2
y=-1/2x+3/2
We first find the zeros of the function , the zeros of the function are those at which points the graph of the function crosses or touches the x axis
here we can see in the graph that graph crosses the x axis at two points , 1 and 7
So the zeros of the function are
x=1 and x=7
It means the factor are
(x-1) and (x-7)
So the factorization is given by
(x-1)(x-7)
