You are decorating the church for the christmas party. so far, you have used 12 1/2 yards of silver rope. you have 36 2/3 yards left. how much did you have to start with? it has to be improper fraction

The starting length of ribbon was yards.

Step-by-step explanation:

You have used 12 1/2 yards of silver rope. Converting this to improper fraction;

You have 36 2/3 yards left. Converting this to improper fraction;

So, in the starting the rope must have been :

LCM of 2 and 3 is 6.

=

=

Hence, the starting length of ribbon was yards.

$20.01

step-by-step explanation:

the sale price is (1.00 - 0.77)($87), or 0.23($87), or $20.01.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)