Simplify Complex numbers 30 points

Answer: 2

Step by step: I start with a long-division set-up

Looking only at the leading terms, I divide 3x3 by 3x to get x2. This is what I put on top:

x^2 up on top

I multiply this x2 by the 3x + 1 to get 3x3 + 1x2, which I put underneath:

3x^3 + 3x put down underneath the dividend

Then I change the signs, add down, and remember to carry down the "+10x – 3" from the original dividend, giving me a new bottom line of –6x2 + 10x – 3:

(3x^3 – 5x^2 + 10x – 3) – (3x^3 + 1x^2) = –6x^2 + 10x – 3

Dividing the new leading term, –6x2, by the divisor's leading term, 3x, I get –2x, so I put this on top:

(–6x^2) ÷ (3x) = –2x, which goes on top

Then I multiply –2x by 3x + 1 to get –6x2 – 2x, which I put underneath. I change signs, add down, and remember to carry down the "–3 from the dividend:

(–6x^2 + 10x –3) – (–6x^2 – 2x) = 12x – 3, which is my new last line

My new last line is "12x – 3. Dividing the new leading term of 12x by the divisor's leading term of 3x, I get +4, which I put on top. I multiply 4 by 3x + 1 to get 12x + 4. I switch signs and add down. I end up with a remainder of –7:

(12x)/(3x) = 4, 4(3x + 1) = 12x + 4, (12x – 3) – (12x + 4) = –7

This division did not come out even. What am I supposed to do with the remainder?

Think back to when you did long division with plain numbers. Sometimes there would be a remainder; for instance, if you divide 132 by 5:

132 ÷ 5: 2 × 5 = 10; put 2 on top and 10 underneath; 13 – 10 = 3; new divisor is 32; 6 × 5 = 30; put 6 on top and 30 underneath; 32 – 30 = 2; answer is 26 with remainder 2

...there is a remainder of 2. Remember how you handled that? You made a fraction, putting the remainder on top of the divisor, and wrote the answer as "twenty-six and two-fifths":

\dfrac{132}{5} = 26\,\dfrac{2}{5} = 26 + \dfrac{2}{5}

5

132

​

=26

5

2

​

=26+

5

2

​

The first form, without the "plus" in the middle, is how "mixed numbers" are written, but the meaning of the mixed number is actually the form with the addition.

We do the same thing with polynomial division. Since the remainder in this case is –7 and since the divisor is 3x + 1, then I'll turn the remainder into a fraction (the remainder divided by the original divisor), and add this fraction to the polynomial across the top of the division symbol. Then my answer is this:

\mathbf{\color{purple}{\mathit{x}^2 - 2\mathit{x} + 4 + \dfrac{-7}{3\mathit{x} + 1}}}x

2

−2x+4+

3x+1

−7

​

Answer:

the second one, $63, i think

Step-by-step explanation:

Answer:

Part 1: 4.5

Part 2: 20%, 0.2

Step-by-step explanation:

1. 1.8 = 80% We need to understand this.

So we can do this then:

2. 1.8/8 = 80%/8

3. 0.225 = 1%

4. 0.225 * 20

5. 4.5

(this is part 1 btw)

Part 2!

20% since 100-80 is 20.

20% -> 0.2

Answer:

Surprisingly the answer is 5,005.

Basically this is asking "in how many ways can you choose 9 things from a set of 15 things".

You will need to use the formula found at the top of this page:

https://www.1728.org/combinat.htm

Filling in the formula in which 'r' = 9 and n = '15'

combinations = n! / (r! * (n-r))!

combinations = 15*14*13*12*11*10 * 9! / (9! * 6!)

combinations = 15*14*13*12*11*10 / 6*5*4*3*2*1

combinations = 14 * 13 * 11 * 10 / 4  

= 14 * 13 * 11 * 2.5

= 5,005

answer is "d"

Step-by-step explanation:

Answer:

Distance = -7.6

Step-by-step explanation:

Using Distance Formula, √((x2-x1)^2 + (y2-y1)^2)

√((-7 - 0))^2 + (-3 - 0)^2) = 7.6

Answer:

y= 43

x= 37

Step-by-step explanation:

Legs: (43 x 4) + (37 x 2) = 248

Heads: 43 + 37 = 80

Answer:

420 calories is your answer.

Step-by-step explanation:

If half of it is 140 we know that the other half is 140, so the full thing of ice cream is 380. So 1 cup is 380, and half is 140. 380+140 = 420. So 1 1/2 = 420 calories. Could i get brainliest :D

Answer:

Diagram not visible!

Step-by-step explanation:

You must ask question again; then, the rightful person may help you.

Good day to you!

Answer:

40

Step-by-step explanation:

the mean is 40 because you add all the numbers then divide them by however many numbers there are.

Answer:

[tex]\sqrt{49}[/tex]

Step-by-step explanation:

[tex]\sqrt{49} =7[/tex]

The square root of 49, which is the greatest perfect square that is less than 55.

A perfect square that is the nearest, greater perfect square to [tex]\sqrt{49}[/tex] is [tex]\sqrt{64}[/tex].

There are no other perfect squares in between [tex]\sqrt{49}[/tex] and [tex]\sqrt{64}[/tex] there are only decimals.

Therefore, [tex]\sqrt{49}[/tex] is your answer.

Proof:

[tex]7^{2} =49[/tex]

[tex]8^{2}=64[/tex]

Answer:

6

Step-by-step explanation:

each tomato=4

7-4=3 so each avocado is 3

5-3=2 so each lime is two

so 4+2=6

Answer:

6

Step-by-step explanation:

Tomato + tomato = 8  ⇒  tomato = 4

Avocado + tomato = 7 ⇒  Avocado = 7 - 4 = 3

Avocado + Lemon = 5  ⇒  Lemon = 5 - 3 = 2

Therefore, Lemon + tomato = 2 + 4 = 6

Answer:

A. {x,y}={-2,-3}

// Solve equation [2] for the variable  x

 [2]    x = 2y + 4

// Plug this in for variable  x  in equation [1]

  [1]    (2y+4) - y = 1

  [1]    y = -3

// Solve equation [1] for the variable  y

  [1]    y = - 3

// By now we know this much :

   x = 2y+4

   y = -3

// Use the  y  value to solve for  x

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

B.   [1]           3x=3y-6

 [2]           y=x+2

Equations Simplified or Rearranged :

  [1]    3x - 3y = -6

  [2]    -x + y = 2

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = x + 2

// Plug this in for variable  y  in equation [1]

  [1]    3x - 3•(x +2) = -6

  [1]    0 = 0 =>  Infinitely many solutions

C.Step by Step Solution

More Icon

System of Linear Equations entered :

  [1]    4x - y = 2

  [2]    8x - 2y = 4

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = 4x - 2

// Plug this in for variable  y  in equation [2]

  [2]    8x - 2•(4x-2) = 4

  [2]    0 = 0 =>  Infinitely many solutions

Answer:

Step-by-step explanation:

a) y = -1/4x    --------------(I)

x + 2y = 4 -----------------(II)

Substitute y = (-1/4)x in equation (I)

[tex]x + 2*\dfrac{-1}{4}x=4\\\\\\x -\dfrac{1}{2}x=4\\\\Multiply \ the \ entire \ equation \ by \ 2 \\\\2x -x = 8\\\\x=8[/tex]

[tex]Substitute \ x = 8 \ in \ equation \ (I)\\\\y=\dfrac{-1}{4}*8\\\\\\y = -2[/tex]

Answer: x = 8  ; y = -2

b) y = -x - 2 --------------(i)

   3x + 3y = 6   -----------(ii)

Divide equation (ii) by m

x + y = 2

  y = -x + 2  ----(iii)

From (i) and (iii), it shows that these lines have same slope. So, they are parallel lines

Answer: No solution

3) -8x + 2y =4

            2y = 8x + 4

Divide the entire equation by 2

             y = 4x + 2 -------------(i)

            y = 4x + 2 ----------------(ii)

From (i) and (ii), we come to know that these lines coincide.So, they have infinite solutions.

Answer:

1. s-110=-124

+110

s=-14

2. 4 gallons

3. 96 oz

Hope This Helps!!!

Answer:

under root 10 will be possible

( 3y )²

Step-by-step explanation:

1. 3(x-2)=4

2. 3x-6=4

3x=10

4.x=10/3

Answer:

Solving for X: x = 8

Step-by-step explanation:

Set up as proportion and cross multiply to solve:

12/15 = x/10

x = 8

y = x + 10

y = 8 + 10

y = 18

Answer:

2

f(x)= -x + 1

2

g(x) = -x + 6x +5

2

h(x)= +ax + bx -c ( its form should be like that )

Seventy percent of fifty (50) is 35

The percent or percentage of a number is the division of the number with 100.

From the given information, we are being told that 70% of a number is 35.

It means that:

70% of x = 35

[tex]\mathbf{(\dfrac{70}{100})x = 35}[/tex]

0.7x = 35

Divide both sides by 0.7

x = 35/0.7

x = 50

Learn more about percentage here:

https://brainly.com/question/24304697

Answer:

p = 0, p= 1/4

Step-by-step explanation:

factor out the common term p

p(4p - 1) = 0

Answer:

b = 35

Step-by-step explanation:

Use the butterfly method (Cross multiply):

b × 13 = 13b

65 × 7 = 455

So you would have:

13b = 455

Divide both sides by 13.

You will get b = 35

Hope this helps!

Answer: b=35

Step-by-step explanation:

[tex]\frac{b}{65}=\frac{7}{13}[/tex]

Multiply both sides by 65:

[tex]\frac{65b}{65}=\frac{7\cdot \:65}{13}[/tex]

[tex]b=35[/tex]

Answer:

150 ft²

Step-by-step explanation:

If you take that triangle and place it on the other side you get a normal rectangle and can just multiply 15 By 10

Answer:

18 sales

Step-by-step explanation:

1020-300=720

720/40

=18 sales in that particular  week

Answer:

Step-by-step explanation:

Answer:

Not sure of the actual quest but

y=-3x+7

slope -3

y=7

x= 7/3

y=6x-2

slope 6

y= -2

x= 1/3

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

please rate 5 stars and thank it and make brainliest

hope this helps have a good day

Answer:

x ≤ 4

Step-by-step explanation:

x ≤ 4

A closed circle means ≤ or ≥

An open circle means < or >

As the shaded area is to the left of 4,   x ≤ 4

Answer:

» 4 → Coefficient of x [slope of a line]

» x → Term of 4

» ⅓ → Coefficient of y

» y → term of ⅓

-2.3 → Constant [y-intercept]

Step-by-step explanation:

Consider equation below:

[tex]{ \bf{ax + by + c}}[/tex]

• a is a coefficient of x-term

• b is a coefficient of y-term

• c is a constant

The indicated part of the algebraic expression 4x + y/3 - 2.3 are

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations.

Given an algebraic expression 4x + y/3 - 2.3

The algebraic equation usually consists of a variable, coefficients, and constants.

Learn  more about algebraic expression here:

https://brainly.com/question/28884894

#SPJ2

Potential is what an individual is capable of doing or becoming

Answer:

Having or showing the capacity to develop into something in the future is called potential