

Multiply both numerator and denominator of
by the complex conjugate of the denominator, -2+9i.

Multiplication can be transformed into difference of squares using the rule:
.

By definition, i² is -1. Calculate the denominator.

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

Do the multiplications in
.

Combine the real and imaginary parts in -10+45i+6i+27.

Do the additions in
.

Divide 17+51i by 85 to get
.

The real part of
is
.

Answer:
18
Step-by-step explanation:
Answer:
33 chairs
Step-by-step explanation:
Answer:
25 seconds
Step-by-step explanation:
Hi there!
In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.
For machine A:

For machine B:

So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:

Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:

The <em>bolts</em> unit cancell each other and we are left with <em>seconds</em>

So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.
Greetings!