Answer:
y = -1/2x + 2
Step-by-step explanation:
A line in slope-intercept form in y = mx + b
"m" is the slope
"b" is the y-intercept
x and y represent points on the graph
To write an equation, you need "m" and "b".
We already know m = -1/2
The point (0, 2) is the y-intercept. The y-intercept occurs when x = 0.
Points are in the form (x , y), so x = 0 and y = 2.
Therefore b = 2.
Substitute m = -1/2 and b = 2 into the equation:
y = mx + b
y = -1/2x + 2
Answer:
1
= -----------
6(x + 7)
Step-by-step explanation:
3x - 21 x^2 - 49
----------- ÷ -------------
18x - 18 x - 1
3x - 21 x - 1
----------- × -------------
18x - 18 x^2 - 49
Factor the top left:
3x - 21 = 3(x - 7)
Factor the bottom left:
18x - 18 = 18(x - 1)
Factor the new bottom right:
x^2 - 49 = (x + 7)(x - 7)
Multiply and simplify the faction:
3(x - 7) x - 1
----------- × -----------------
18(x - 1) (x + 7)(x - 7)
1
= -------------
6(x + 7)
54, 36, 24 are the 1st 3 element of a geometric progression with 2/3 as a common ratio: PROOF:
the 1st term is 54, (a₁= 54) the 2nd term a₂ = 24, then
(a₂ = a₁.r) or 36 = 54.r → r= 36/54 = 2/3. Same logique for the 3rd term.
So 2/3 is common ratio. We know that :U(n) = a.(r)ⁿ⁻¹. Then if a =54 and r = x (given by the problem), then f(x) = 54.xⁿ⁻¹
n, being the rank of any element of this geometric progression
