If Cassie has 20 and wants to keep 11 then we would subtract 11 from 20.
So 20 - 11 is 9.
Her sister will get 9 bracelets.
Hope this helps!
Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point 
in the plane is 
, but we know that 
and 
share the same critical points, so we need only worry about minimizing 
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that 
is a critical point. The Hessian for the target function is
which is positive definite for all 
, so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is 
.
5c+10a=3570
c+a=512
...
a=512-c
so ...
5c + 10(512-c)=3570
Answer:
104°
Step-by-step explanation:
If segments NO and NM are congruent, then angles NMO and NOM are congruent. So, their supplements, angles NML and NOP are congruent. That is ...
∠NML ≅ ∠NOP = 104°
∠NML = 104°
Answer:
Given that,
My cupcake recipe makes $12$ cupcakes and requires $1\frac12$ sticks of butter. I can only buy whole sticks of butter.
Therefore, 1 whole sticks of butter is enough to make $100$ cupcakes.
