Rule needed: i^2 = -1
Standard form a + bi
(3 + 2i)(7 - 5i) FOIL
3 * 7 = 21
3 * - 5i = - 15i
2i * 7 = 14i
2i * -5i = - 10i^2 = - 10 * -1 = 10
Putting it all back together.
31 - i
We start with

and wish to write it as

First, pull 2 out from the first two terms:

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have

and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square:

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have

and when we multiply that out it does not give us what we started with. It gives us

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.
We do this as follows:

which gives us the final expression we seek:

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e = -103
We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106
The angle of the roof on Wendy's dollhouse is 56 degrees she built a scale model of the dollhouse with a scale ratio of 1 to 4 what is the measurement of the angle of the roof of the model?
Answer: 14
Answer:
s = 22.5 m
Step-by-step explanation:
the equation for the speed change of a coach moving along a straight section of the road and starting braking at a speed of 20 m / s has the form v (t) = 25-5t. Using integral calculus, determine the coach's braking distance.
v (t) = 25 - 5 t
at t = 0 , v = 20 m/s
Let the distance is s.

Let at t = t, the v = 20
So,
20 = 25 - 5 t
t = 1 s
So, s = 25 x 1 - 2.5 x 1 = 22.5 m
Answer:
Her score in the first game was 173.
Step-by-step explanation:
Sue's total score for the 3 games = 3*162 = 486 points.
Let her score in the first game be x points. Then in the second game she scored (x - 10) and in the third, ( x - 10 - 13) points:
x + (x - 10) + (x - 23) = 486
3x - 33 = 486
3x = 519
x = 173 (answer).