Answer:
= r²−4r+3
Step-by-step explanation:
(r - 3) (r - 1)
(r x r) + (r x -1) + (-3 x r) + (-3 x -1)
r² + - r - 3r + 3
= r²−4r+3
Recall Euler's theorem: if 
, then
where 
is Euler's totient function.
We have 
- in fact, 
for any 
since 
and 
share no common divisors - as well as 
.
Now,
where the 
are positive integer coefficients from the binomial expansion. By Euler's theorem,
so that
She will use 42 purple beads.
Explanation
We will use a proportion to solve this.
The ratio of blue to purple beads is 4:3, or 4/3.
We know she uses 56 blue beads and an unknown amount, x, of purple beads. This gives us 56/x.
Together, we have
4/3 = 56/x
Cross multiply:
4*x = 3*56
4x = 168
Divide both sides by 4:
4x/4 = 168/4
x = 42
Ans: (6,-13)
Rationale:
Simply take your pre-image (point before applying transformation) of point B (4,-5) and apply the transformation to each point. Therefore, (x,y) = (4+2,-5-8) = (6,-13)
