2(3a+4)=6a+8 demonstrates the distributive property.
The Jacobian for this transformation is

with determinant
, hence the area element becomes

Then the integral becomes

where
is the unit circle,

so that

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

Then

Samantha : 240/12 = 20 glass beads per necklace
angelina : 231/11 = 21 glass beads per necklace
angelina uses 21 glass beads per necklace -- TRUE
samantha uses 1 glass bead for every 20 necklaces -- FALSE
angelina's necklaces have a unit rate of 20 glass beads per necklace -- FALSE
samantha's necklaces have a unit rate of 20 glass beads per necklace -- TRUE
samantha's necklaces have fewer glass beads then angelina's necklaces do -- TRUE
Answer:
222,678
Step-by-step explanation: