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solmaris [256]
3 years ago
13

- 3 - 4i" alt=" - 3 + 5i \div - 3 - 4i" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Likurg_2 [28]3 years ago
6 0

Answer:

\frac{-11}{25}+\frac{-27}{25}i given you are asked to simplify

\frac{-3+5i}{-3-4i}

Step-by-step explanation:

You have to multiply the numerator and denominator by the denominator's conjugate.

The conjugate of a+bi is a-bi.

When you multiply conjugates, you just have to multiply first and last.

(a+bi)(a-bi)

a^2-abi+abi-b^2i^2

a^2+0         -b^2(-1)

a^2+-b^2(-1)

a^2+b^2

See no need to use the whole foil method; the middle terms cancel.

So we are multiplying top and bottom of your fraction by (-3+4i):

\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}

So you will have to use the complete foil method for the numerator. Let's do that:

(-3+5i)(-3+4i)

First: (-3)(-3)=9

Outer::  (-3)(4i)=-12i

Inner: (5i)(-3)=-15i

Last: (5i)(4i)=20i^2=20(-1)=-20

--------------------------------------------Combine like terms:

9-20-12i-15i

Simplify:

-11-27i

Now the bottom (-3-4i)(-3+4i):

F(OI)L (we are skipping OI)

First:-3(-3)=9

Last: -4i(4i)=-16i^2=-16(-1)=16

---------------------------------------------Combine like terms:

9+16=25

So our answer is \frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:[tex]\frac{-11}{25}+\frac{-27}{25}i

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Factor the expression. 9b2 – 25
rewona [7]

Answer: (3b + 5)(3b - 5)

Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.

The square root of 9b² is 3b (3b × 3b = 9b²).

The square root of 25 is 5 (5 × 5 = 25).

9b² - 25 has a negative, so the factored expression would be

(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the  expression, 9b² - 25, has no middle term.

You can check your work by using FOIL. See the attachment below.

F irst

O utside

I nside

L ast

5 0
3 years ago
Read 2 more answers
The perimeter of the triangle is 34 cm. Solve for x.
Musya8 [376]
5x-2+x-3+x-3 = 34
7x-8 = 34
7x/7 = 42/7
x = 6
3 0
3 years ago
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Your plan was to be on the road by 9 A.M. but you did not leave the garage until 10 A.M. You then drove with the cruise control
Wittaler [7]

Answer:

The average speed over the time interval from 9 A.M. to noon was of 33.33 mph.

Step-by-step explanation:

The average speed is given by the following equation:

v = \frac{d}{t}

From 10A.M. to noon.

You traveled at 50mph during 2 hours. So how long you traveled?

50 = \frac{d}{2}

d = 50*2

d = 100

You traveled 100 miles.

What was your average speed over the time interval from 9 A.M. to noon

From 9 A.M. to 10 A.M, you did not travel.

From 10 P.M. to noon, 100 miles.

So 100 miles during 3 hours.

v = \frac{d}{t} = \frac{100}{3} = 33.33

The average speed over the time interval from 9 A.M. to noon was of 33.33 mph.

8 0
3 years ago
It's nothing new: Let's recap rounding to the nearest 100.
Nuetrik [128]

Answer:

7000

61700

70300

Not sure tho.....

6 0
2 years ago
A length of 9 and<br> a perimeter of 22
Bad White [126]

Answer:

Width is 2 if that's what you were looking for.

Step-by-step explanation:

I'm guessing it's a rectangle and you want the width?

22-9-9=2w

2w=4

The width is 2

4 0
3 years ago
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