6(x+5)² + 5(x+5)-4 = 0
(x+5)(x+5) = x(x+5)+5(x+5) = x² + 5x + 5x + 25 = x² + 10x + 25
6(x²+10x+25) + 5(x+5) - 4 = 0
6x² + 60x + 150 + 5x + 25 - 4 = 0
6x² + 60x + 5x + 150 + 25 - 4 = 0
6x² + 65x + 171 = 0
<span>u = (x + 5)</span>
Answer:
x^2/12 - y^2/4 = 1
Step-by-step explanation:
As the diretrices have simetrical values of x and have y = 0, the center is located at (0,0)
The formula for the diretrices is:
x1 = -a/e and x2 = a/e
And the foci is located at (a*e, 0) and (-a*e, 0)
So we have that:
a/e = 3
a*e = 4
From the first equation, we have a = 3e. Using this in the second equation, we have:
3e*e = 4
e^2 = 4/3
e = 1.1547
Now finding the value of a, we have:
a = 3*1.1547 = 3.4641
Now, as we have that b^2 = a^2*(e^2 - 1), we can find the value of b:
b^2 = 3.4641^2 * (1.1547^2 - 1) = 4
b = 2
So the equation of the hyperbola (with vertical diretrices and center in (0,0)) is:
x^2/a^2 - y^2/b^2 = 1
x^2/12 - y^2/4 = 1
Both ratios are equivalent due to the fact that 11/22 as a simplified fraction makes 1/2 and 14/28 also makes 1/2 if simplified.
There are 3 odd numbers out of 6 numbers and 7 B's out of 28 so
required probability = 3/6 * 7/28 = 1/2 * 1/4 = 1/8 Answer
