Answer:
2x^2 -x +1 = 0
Step-by-step explanation:
For roots α and β, the original equation can be factored as ...
f(x) = 2(x -α)(x -β)
If we add 1 to each of those roots, the factors become ...
g(x) = 2(x -(α+1))(x -(β+1))
This can be rearranged to be ...
g(x) = 2((x -1) -α)((x -1) -β)
That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.
2(x -1)² +3(x -1) +2 = 0
2x^2 -x +1 = 0
Answer:
(x + 1)² + (y - 6)² = 50
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r =
with (x₁, y₁ ) = (- 1, 6) and (x₂, y₂ ) = (- 6, 1)
r =
=
=
=
(h, k ) = (- 1, 6 ), then
(x - (- 1))² + (y - 6)² = ( )² , that is
(x + 1)² + (y - 6)² = 50 ← equation of circle
Answer:
number o students bought pennants = 18
number of student bought fancy ones=12
Step-by-step explanation:
Let x be the number o students bought pennants
and y be the number of student bought fancy ones
total 30 students
Plain pennants cost $4 each and fancy ones cost $8 each.
Substitute 30-x for y in second equation
Subtract 240 from both sides
divide both sides by -4
x=18
number o students bought pennants = 18
number of student bought fancy ones=12