Answer:
x = 1/3 + sqrt(5/2)/3 or x = 1/3 - sqrt(5/2)/3
Step-by-step explanation:
Solve for x:
6 x^2 - 4 x = 1
Divide both sides by 6:
x^2 - (2 x)/3 = 1/6
Add 1/9 to both sides:
x^2 - (2 x)/3 + 1/9 = 5/18
Write the left hand side as a square:
(x - 1/3)^2 = 5/18
Take the square root of both sides:
x - 1/3 = sqrt(5/2)/3 or x - 1/3 = -sqrt(5/2)/3
Add 1/3 to both sides:
x = 1/3 + sqrt(5/2)/3 or x - 1/3 = -sqrt(5/2)/3
Add 1/3 to both sides:
Answer: x = 1/3 + sqrt(5/2)/3 or x = 1/3 - sqrt(5/2)/3
Answer:
Step-by-step explanation:
red balls=3
blue balls=4
total balls=3+4=7
probability of selecting 3 red balls=3/7 ×2/6×1/5=1/35
selecting 1 red ball=3/7
after selecting there are two red balls and total balls are 6
so now P=2/6
and so on .
One form of the equation of a parabola is
y = ax² + bx + c
The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)
Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)
Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1
The equation is
y = -x² + 5x - 6
Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6
y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.
Answer: y = -(x - 2.5)² + 0.25
Answer:
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