maths f.2

1.a. simplify the ratio 1/3:1/2:1/5
= 30/3 : 30/2 : 30/5
=10:15:6

b. a sum of $465 is shared by John, Tom and Ann. Given that John's amount:Tom's amount : Ann's amount=1/3:1/2:1/5, how much does each of them get?
From a), 1/3:1/2:1/5 = 10:15:6

John will get 465 x 10/(10+15+6) = $150
Tom will get 465 x 15/(10+15+6) = $225
Ann will get 465 x 6/(10+15+6) = $90


2.if the sum of the interior angles of a regular n-sided polygon is 1800度, find
(a) the value of n,
Angle sum of polygon = 180(n-2)
180(n-2) = 1800
(n-2) = 10
n = 12

so it is a 12-side polygon

(b) the size of each exterior angle.
sum of exterior angles = 360 degree
each exterior angle = 360 / 12 = 30 degree

3.expand 9(4x-y/3) (4x+y/3)
9(4x-y/3) (4x+y/3)
=3(4x-y / 3) 3 (4x+y/3)
=(4x-y)(4x+y)
=(4x)² - (y)²
=16x² - y²


*please show the process, thanks.