Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.

a)

It could be expressed as:

Hence, the radius of circle is: √3≈1.732 units

b)

It is represented as:

Hence, the radius of circle is: 3√2≈4.242 units

c)

on converting to standard form

Hence, the radius of circle is: 3√5≈6.708 units

d)

on dividing both side by 4 we obtain:

Hence, radius of circle is: √23=4.796 units

e)

on dividing both side by 5 we obtain:

Hence, radius of circle is: √5=2.236 units

f)

which could also be represented as follows:

Hence, the radius of circle is: ≈ 10.817 units

g)

It could also be written as:

Hence, the radius of circle is: ≈ 6.782 units

            The ascending order is:

        a → e → b → d → c → g → f

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72