Substitute this into the parabolic equation,
We're told the line 
intersects 
twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know
We can tell from the quadratic equation that has its vertex at the point (3, 6). Also, note that
and
so the furthest to the right that extends is the point (5, 2). The line passes through this point for 
. For any value of 
, the line passes through either only once, or not at all.
So 
; in set notation,
If you would like to know what is the unit price for the hair shampoo, you can calculate this using the following steps:
500 ml ... $2.10
100 ml ...$x = ?
500 * x = 2.10 * 100 /500
x = 2.10 * 100 / 500
x = $0.42
The unit price for the hair shampoo is $0.42.
60-41 1/2=18 1/2 18 1/2 divided by 1/2=37/2*2 (cross cancel 2s)=37
Answer:
12 x^4 + 18 x^3 - 9 x^2 thus D is the correct answer.
Step-by-step explanation:
Expand the following:
3 x^2 (4 x^2 + 6 x - 3)
3 x^2 (4 x^2 + 6 x - 3) = 3 x^2 (4 x^2) + 3 x^2 (6 x) + 3 x^2 (-3):
3 4 x^2 x^2 + 3 6 x^2 x - 3 3 x^2
3 (-3) = -9:
3 4 x^2 x^2 + 3 6 x^2 x + -9 x^2
3 x^2×6 x = 3 x^(2 + 1)×6:
3 4 x^2 x^2 + 3×6 x^(2 + 1) - 9 x^2
2 + 1 = 3:
3 4 x^2 x^2 + 3 6 x^3 - 9 x^2
3×6 = 18:
3 4 x^2 x^2 + 18 x^3 - 9 x^2
3 x^2×4 x^2 = 3 x^4×4:
3×4 x^4 + 18 x^3 - 9 x^2
3×4 = 12:
Answer: 12 x^4 + 18 x^3 - 9 x^2
