

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:
9
in²
Step-by-step explanation:
The area (A) of an equilateral triangle is calculated as
A =
( s is the length of a side )
Here s = 6, thus
A =
=
= 9
in²
Answer:
a=1/2b, 2a=b
Step-by-step explanation:
Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.
Answer:
19.9 miles
Step-by-step explanation:
In this problem we have:
is the distance travelled during the 1st day
is the distance travelled during the 2nd day
is the distance travelled during the 3rd day
is the distance travelled during the 4th day
We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

Which can be rewritten using the general formula:

This means that

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

So, the distance travelled on the 7th day is 19.9 miles.
Answer:
1.75
Step-by-step explanation:
0.009÷0.004-
=
2.25-0.5=
1.75