If you expand out the brackets you get this,
(4+5i)(a+2i) = 4a + (5a)i + 8i - 10
The -10 comes from 5i * 2i.
Squaring i becomes -1.
Let's group the real stuff together,
and imaginary separately,
(4a - 10) + (5a + 8)i
For this to be purely imaginary,
the real part needs to be zero.
Therefore 4a - 10 = 0
Solve for a.
The answer is 2/25, this should be hepful!
Answer:

Step-by-step explanation:
we know that
The profit is equal to the number of dolls multiplied by the selling price minus the number of dolls multiplied by the cost of each doll minus the cost of the promotion of the dolls
To make a profit, the number of dolls multiplied by the selling price minus the number of dolls multiplied by the cost of each doll must be greater than the cost of the promotion of the dolls
Let
d -----> the number of dolls
The linear inequality that represent this problem is

Adds 20d both sides

Rewrite
