Awoman is 3 times as old as her son.8 years ago the product of their ages was 112. find their present ages

Son 12 and woman 36 years old.

Step-by-step explanation:

Let the age of the woman now be 3x years,  then her son's age = x years.

8 years ago the woman's age was (3x-8) and her son's age was (x- 8) years, so:

(3x - 8)(x - 8) = 112

3x^2 - 32x + 64 = 112

3x^2 - 32x - 48 = 0

3x^2 - 36x + 4x  - 48 = 0

3x(x - 12) + 4(x - 12) = 0

(3x  + 4)(x  - 12 ) = 0

x = -1.33... ,  12 .  ( We ignore the negative value).

So the son's age is 12 and the woman's age is 36.

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )