Answer:
The parabola's axis of symmetry is x = -6
Step-by-step explanation:
Parabola general equation:
y = a*(x - r1)*(x - r2)
Equation given:
y = (-1/4)*(x + 2)*(x + 10)
a = -1/4
r1 = -2
r2 = -10
To check if the parabola passes through the point (2, 10) it is necessary to replace x = 2 and check the y-value, as follows:
y = (-1/4)*(2+ 2)*(2 + 10) = -12
Then, point (2, 10) is not included in the parabola.
If a > 0 then the parabola opens upward; if a < 0 then the parabola opens downward. Then, the parabola opens downward
Axis of symmetry:
h = (r1 + r2)/2
h = (-2 + -10)/2 = -6
Then, The parabola's axis of symmetry is x = -6
To find Parabola's vertex, replace with the axis of symmetry:
y = (-1/4)*(-6 + 2)*(-6 + 10) = 4
Therefore, the parabola has a vertex at (-6, 4)
Answer:
Length of first piece = 1.7058823 ft
Length of second piece = 4(1.7058823) = 6.82352941 ft
Length of third piece = 12(1.7058823) = 20.47058823 ft
Step-by-step explanation:
As given, Total length of the board = 29 ft
Let the board is divided into 3 pieces
Suppose that the length of first piece = x ft
As given, the second piece is 4 times longer than the first
⇒Length of second piece = 4x ft
Also given, the third piece is 3 times longer than the second.
⇒Length of third piece = 3(4x) = 12x ft
Now,
As total length of board = 29
⇒ x + 4x + 12x = 29
⇒ 17x = 29
⇒ x =
= 1.7058823 ft
∴ we get
Length of first piece = 1.7058823 ft
Length of second piece = 4(1.7058823) = 6.82352941 ft
Length of third piece = 12(1.7058823) = 20.47058823 ft
Answer:
-26
Step-by-step explanation:
6x-6=60
Add 6 to both sides
6x=60
Divide 6 into 60
X=10