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.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841