Answer:
1) (x + 3)(3x + 2)
2) x= +/-root6 - 1 by 5
Step-by-step explanation:
3x^2 + 11x + 6 = 0 (mid-term break)
using mid-term break
3x^2 + 9x + 2x + 6 = 0
factor out 3x from first pair and +2 from the second pair
3x(x + 3) + 2(x + 3)
factor out x+3
(x + 3)(3x + 2)
5x^2 + 2x = 1 (completing squares)
rearrange the equation
5x^2 + 2x - 1 = 0
divide both sides by 5 to cancel out the 5 of first term
5x^2/5 + 2x/5 - 1/5 = 0/5
x^2 + 2x/5 - 1/5 = 0
rearranging the equation to gain a+b=c form
x^2 + 2x/5 = 1/5
adding (1/5)^2 on both sides
x^2 + 2x/5 + (1/5)^2 = 1/5 + (1/5)^2
(x + 1/5)^2 = 1/5 + 1/25
(x + 1/5)^2 = 5 + 1 by 25
(x + 1/5)^2 = 6/25
taking square root on both sides
root(x + 1/5)^2 = +/- root(6/25)
x + 1/5 = +/- root6 /5
shifting 1/5 on the other side
x = +/- root6 /5 - 1/5
x = +/- root6 - 1 by 5
x = + root6 - 1 by 5 or x= - root6 - 1 by 5
Answer:
The number of supervisor in the factory is 9 .
Step-by-step explanation:
Given as :
The ratio of workers to supervisors and factories 32 : 2
let the number of workers = 32 x
And The number of supervisors = 2 x
The ratio of male workers to female workers is 6:5
Let The number of male workers = 6 y
And The number of female worker = 5 y
The number of female workers at the plant = 80
So, 5 y = 80
∴ y =
I.e y = 16
So, The number of male workers = 6 y = 6 × 16 = 96
Thus The Total number of worker in the factory = The number of male workers + The number of female workers at the plant
Or, The Total number of worker in the factory = 96 + 80 = 146
Now , Again
∵ The ratio of workers to supervisors in factories 32 : 2
So, The number of workers = 32 x
I.e 146 = 32 x
∴ x = = 4.5
So, The number of supervisors = 2 x = 2 × 4.5 = 9
Hence The number of supervisor in the factory is 9 . Answer