1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mars1129 [50]
3 years ago
8

(-1)(-6 +3i) + (81)(-8+ 4i)

Mathematics
1 answer:
Tanya [424]3 years ago
4 0

Answer: here is the simplify version −642+321i

Step-by-step explanation:

You might be interested in
1. Cash is
Drupady [299]

Answer:

Untraceable

Step-by-step explanation:

3 0
4 years ago
Help with geometry hw
tiny-mole [99]

QUESTION 1

Let the third side of the right angle triangle with sides x,6 be l.

Then, from the Pythagoras Theorem;

l^2=x^2+6^2

l^2=x^2+36

Let the hypotenuse of  the right angle triangle with sides 2,6 be m.

Then;

m^2=6^2+2^2

m^2=36+4

m^2=40

Using the bigger right angle triangle,

(x+2)^2=m^2+l^2

\Rightarrow (x+2)^2=40+x^2+36

\Rightarrow x^2+2x+4=40+x^2+36

Group similar terms;

x^2-x^2+2x=40+36-4

\Rightarrow 2x=72

\Rightarrow x=36

QUESTION 2

Let the hypotenuse of the triangle with sides (x+2),4 be k.

Then, k^2=(x+2)^2+4^2

\Rightarrow k^2=(x+2)^2+16

Let the hypotenuse of the right triangle with sides 2,4 be t.

Then; we have t^2=2^2+4^2

t^2=4+16

t^2=20

We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;

[(x+2)+2]^2=k^2+t^2

(x+4)^2=(x+2)^2+16+20

x^2+8x+16=x^2+4x+4+16+20

x^2-x^2+8x-4x=4+16+20-16

4x=24

x=6

QUESTION 3

Let the hypotenuse of the triangle with sides (x+8),10 be p.

Then, p^2=(x+8)^2+10^2

\Rightarrow p^2=(x+8)^2+100

Let the hypotenuse of the right triangle with sides 5,10 be q.

Then; we have q^2=5^2+10^2

q^2=25+100

q^2=125

We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;

[(x+8)+5]^2=p^2+q^2

(x+13)^2=(x+8)^2+100+125

x^2+26x+169=x^2+16x+64+225

x^2-x^2+26x-16x=64+225-169

10x=120

x=12

QUESTION 4

Let the height of the triangle be H;

Then H^2+4^2=8^2

H^2=8^2-4^2

H^2=64-16

H^2=48

Let the hypotenuse of the triangle with sides H,x be r.

Then;

r^2=H^2+x^2

This implies that;

r^2=48+x^2

We apply Pythagoras Theorem to the bigger triangle to get;

(4+x)^2=8^2+r^2

This implies that;

(4+x)^2=8^2+x^2+48

x^2+8x+16=64+x^2+48

x^2-x^2+8x=64+48-16

8x=96

x=12

QUESTION 5

Let the height of this triangle be c.

Then; c^2+9^2=12^2

c^2+81=144

c^2=144-81

c^2=63

Let the hypotenuse of the right triangle with sides x,c be j.

Then;

j^2=c^2+x^2

j^2=63+x^2

We apply Pythagoras Theorem to the bigger right triangle to obtain;

(x+9)^2=j^2+12^2

(x+9)^2=63+x^2+12^2

x^2+18x+81=63+x^2+144

x^2-x^2+18x=63+144-81

18x=126

x=7

QUESTION 6

Let the height be g.

Then;

g^2+3^2=x^2

g^2=x^2-9

Let the hypotenuse of the triangle with sides g,24, be b.

Then

b^2=24^2+g^2

b^2=24^2+x^2-9

b^2=576+x^2-9

b^2=x^2+567

We apply Pythagaoras Theorem to the bigger right triangle to get;

x^2+b^2=27^2

This implies that;

x^2+x^2+567=27^2

x^2+x^2+567=729

x^2+x^2=729-567

2x^2=162

x^2=81

Take the positive square root of both sides.

x=\sqrt{81}

x=9

QUESTION 7

Let the hypotenuse of the smaller right triangle be; n.

Then;

n^2=x^2+2^2

n^2=x^2+4

Let f be the hypotenuse of the right triangle with sides 2,(x+3), be f.

Then;

f^2=2^2+(x+3)^2

f^2=4+(x+3)^2

We apply Pythagoras Theorem to the bigger right triangle to get;

(2x+3)^2=f^2+n^2

(2x+3)^2=4+(x+3)^2+x^2+4

4x^2+12x+9=4+x^2+6x+9+x^2+4

4x^2-2x^2+12x-6x=4+9+4-9

2x^2+6x-8=0

x^2+3x-4=0

(x-1)(x+4)=0

x=1,x=-4

 We are dealing with length.

\therefore x=1

QUESTION 8.

We apply the leg theorem to obtain;

x(x+5)=6^2

x^2+5x=36

x^2+5x-36=0

(x+9)(x-4)=0

x=-9,x=4

We discard the negative value;

\therefore x=4

QUESTION 9;

We apply the leg theorem again;

10^2=x(x+15)

100=x^2+15x

x^2+15x-100=0

Factor;

(x-5)(x+20)=0

x=5,x=-20

Discard the negative value;

x=5

QUESTION 10

According to the leg theorem;

The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the portion of the hypotenuse adjacent to that leg.

We apply the leg theorem to get;

8^2=16x

64=16x

x=4 units.

QUESTION 11

See attachment

Question 12

See attachment

6 0
3 years ago
Each number in pascal's triangle is the ___ of the two numbers directly above it in the previous row.
mrs_skeptik [129]
Sum. To build the triangle, start with 1 at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together.
5 0
3 years ago
The perimeter of a rectangle is 34 m. The base is two times more than two times the height. What is the length of the base?​
mafiozo [28]

Answer:

sdgfgfdggdfgfsdfdgdsd

Step-by-step explanation:

8 0
4 years ago
You select a card at random from the cards that make up the word replacement. On each card, there is one letter. Without replaci
Murrr4er [49]
In the word replacement, there are 11 letters.

4 of them are vowels : e, a, e, e

7 of them are not vowels : r, p, l, c, m, n, t

The probability of getting a vowel the first try is 4/11.

The probability of getting something that is not a vowel is 7/10. The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.

Multiply.
4/11*7/10
=28/110
=14/55

The probability is 14/55.

Hope this helps!
5 0
3 years ago
Other questions:
  • List four real-world objects that rotate.
    6·2 answers
  • Please help will mark brainleist
    9·1 answer
  • Janie receives an allowance of \$3$3dollar sign, 3 per week. In addition, she can earn \$2$2dollar sign, 2 for each chore she do
    15·2 answers
  • Help me please, and thank u
    11·1 answer
  • -5 2/3 + 3 1/4 + (-7 1/3)
    15·1 answer
  • Eight of your friends came to your house to watch a movie. Three-fourths of your friends stayed overnight. How many friends stay
    10·1 answer
  • What is the missing statement in the proof below ?
    7·1 answer
  • If you're having a party for 27 people and 1 out of 9 wants a cupcake how many cup cakes was ordered???
    7·2 answers
  • The rapper NFL Oldgeezer has released some details about one of his upcoming albums. He states that the album is 39 minutes long
    14·1 answer
  • kristy had two brothers and 2 sister the little sister name kylie was 8 years old the big sister name kaylie is 12 years old the
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!