HELPP PLEASEEE ASAP!!!

Step-by-step explanation:

Formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

……………………………………………………………

if c, d, e, and f are positive real numbers

then

c f + d e  is a positive number.

then

The product of the two complex numbers

lies in Quadrant 1 or Quadrant 2.

Since , c, d, e, and f are positive real numbers

Then

The two complex numbers c + d i  and  e + f i  lie in Quadrant 1

We want to find an example of two complex numbers

That lie in Quadrant 1 ,such that ,their product lies in the other possible

Quadrant, which is Quadrant 2.

EXAMPLE:

Let c + d i = 1 + i

      e + f i = 2 + 3i

By applying the formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

We get :

(1 + i)(2 + 3i) = -1 + 5i

[tex]\\ \rm\Rrightarrow \left(x+\dfrac{1}{x}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x}\right)^2\dots(1)[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{1}{\sqrt{2}+\sqrt{5}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{2+2\sqrt{10}+5}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{2\sqrt{10}+7}[/tex]

Now put in eq(1)

[tex]\\ \rm\Rrightarrow \left(\dfrac{\dfrac{1}{2\sqrt{10}+7}+1}{\dfrac{1}{2\sqrt{10}+7}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{1+2\sqrt{10}+7}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{2\sqrt{10}+8}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{(2\sqrt{10}+8)\cancel{(2\sqrt{10}+7)}}{\cancel{2\sqrt{10}+7}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow (2\sqrt{10}+8)^2[/tex]

[tex]\\ \rm\Rrightarrow 40+32\sqrt{10}+64[/tex]

[tex]\\ \rm\Rrightarrow 32\sqrt{10}+94[/tex]

More simplification (If required)

[tex]\\ \rm\Rrightarrow 2^52^{\frac{1}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow 2^{5+\frac{1}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow 2^{\frac{11}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{2^{11}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{2048(5)}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{10240}+94[/tex]

Most accurate

[tex]\\ \rm\Rrightarrow 101.19+94[/tex]

[tex]\\ \rm\Rrightarrow 195.19[/tex]

Answer:

Step-by-step explanation:

Answer:

B. sammy can use the distance formula to show that all sides are equal

Step-by-step explanation:

Short explanation: I took the test

Actaul explantion:

- Hi! ive been having trouble submitting my answer recently (and for what reason, i have no clue) but attached is the full explantion with step by step help on why the answer is the answer!

- i hope you take the time to read it!

- I hope this helped!! thank you so much for reading my answer :))                 ~addison~

Answer:

Step-by-step explanation:

Sammy can use the distance to show opposite sides have equal slopes

Work Shown:

8 x 22

8 x (20 + 2)

8 x 20 + 8 x 2

160 + 16

176

Answer: ok so the answer is 15/23 , as a fraction .

Step-by-step explanation: there are 6 blue tokens , 9 green tokens and 8 red tokens . We have to know how many tokens in total so we add them and the answer is 23 so 23 tokens in total . He asked about the probability of green or blue tokens . So add how many green or blue tokens are there so the answer is 15 . So the probability of finding green or blue tokens is 15 over 23 . HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST .THANKS .

Answer:

A. 1,998,723

Step-by-step explanation:

1.182(1.34)^49

Answer:

[tex]\frac{12g^{5} }{h}[/tex]

Step-by-step explanation:

[tex]\frac{12g^{8}h^{4} }{g^{3}h^{5} } =12g^{(8-3)} h^{4-5} =12g^{5} h^{-1} =\frac{12g^{5} }{h}[/tex]

Hope this helps

Answer:

all but 15 over three

Step-by-step explanation:

because 1/6 x2 =2/12, 1.5=9 since 1=6 and half would be 3, and 4x1/6=4/24

Answer:

x=3

Step-by-step explanation:

(x+10)+(2x-10)=90

3x (10-10)=90

3x=90

90/3

x=30

(30+10) and (30-10)

=40 and 20

Answer:

( [tex]\frac{1}{4}[/tex], 8 )

Step-by-step explanation:

y = 8x + 6 → (1)

y = 32x → (2)

substitute y = 32x into (1)

32x = 8x + 6 ( subtract 8x from both sides )

24x = 6 ( divide both sides by 24 )

x = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]

substitute this value into either of the 2 equations and solve for y

substituting into (2)

y = 32 × [tex]\frac{1}{4}[/tex] = 8

solution is ( [tex]\frac{1}{4}[/tex], 8 )

[tex]~~~~~~6(2+x) = -18\\\\\implies 2+x = -\dfrac{18}6\\\\\implies 2+x = -3\\\\\implies x = -3-2\\\\\implies x =-5[/tex]

Given equation:

Step-by step solution;

Simplifying the distributive property;

⇒ -18 = (6 × 2) + (6 × x)  

Further simplifying the distributive property;

⇒ -18 = (12) + (6x)

Subtracting 12 to both sides of the equation;

⇒ -18 - 12 = (12) + (6x) - 12

Simplifying both sides of the equation;

⇒ -30 = (6x)

Dividing 6 to both sides of the equation;

⇒ -30/6 = (6x)/6

⇒ -5 = x

Therefore, the value of "x" is -5.

Learn more about this topic: https://brainly.com/question/851533

Answer:

[tex]r = 7\ km[/tex]

Step-by-step explanation:

The formula for the area of a circle is:

[tex]A = \pi r^2[/tex]

Since we know that a semicircle is half of a circle, we can say the area is:

[tex]A = \frac{1}{2}\pi r^2[/tex]

From here solve for r:

[tex]76.97 = \frac{1}{2}\pi r^2\\153.94 = \pi r^2\\\frac{153.94}{\pi} = r^2\\r = \sqrt{\frac{153.94}{\pi}}\\r = 7[/tex]

The exact dimension of the prism is as follows;

volume of rectangular prism = Bh

where

Therefore,

volume  = 100 cm³

Hence, the base of the prism is a square. The whole side of the base is equal.

Therefore,

length = width = x

x² = h

Therefore,

x² × x × x = 100cm³

x⁴ = 100

volume = x = [tex]\sqrt[4]{100}[/tex]

learn more on rectangular prism here : https://brainly.com/question/21308574

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Answer:

(-2.5, -2) (-2, -1.5) (1.5, 2) (2, 2.5)

Step-by-step explanation:

In these intervals, the y value is decreasing.

Answer:

81

Step-by-step explanation:

that is the solution above

A Pentagon

A Dodecagon

A Decagon

Sure hope this helps you

The equation of the translated function is:

g(x) = (x + 3)^2 - 2

We can see that the blue graph is a translation of the red one, where the equation for the red graph is:

f(x) = x^2

Remember that the translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.

If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:

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

So the correct option is A.

If you want to learn more about translations, you can read:

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Answer:

Its 12

Step-by-step explanation:

It says what is MORE than 39 so you count every "I" and you get 12.

Using a system of equations, it is found that Debbie worked 45 hours during the week.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Juan and Debbie each earn 9 per hour at their "jobs", and earned a total of 765 for the week, hence:

9x + 9y = 765

Simplifying the expression by 9:

x + y = 85 -> x = 85 - y.

Debbie worked five hours more than juan during the week, hence:

y = x + 5.

Since x = 85 - y, we replace in the expression:

y = 85 - y + 5.

2y = 90.

y = 45.

Debbie worked 45 hours during the week.

More can be learned about a system of equations at https://brainly.com/question/24342899

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Answer:

there are 83 percent of books

Answer:

20

Step-by-step explanation:

First, the rectangle is 10 by 5, so an easy 50. Then we have the triangle. The base is 5, and since the whole height is 18 and the rectangle's is 10, 18-10=8. The formula for a triangle is 1/2(b)h, so:

1/2*5=2.5

2.5*8=20 cm

Hope this helps!

Answer:

18 feet³

Step-by-step explanation:

3 · 3 · 2 =

9 · 2 =

18 feet³

Answer:

x=2

Step-by-step explanation:

Answer:

3. True, wall clouds are good indicators that a tornado could form

Step-by-step explanation:

The correct answer is option A

Answer: 7

Step-by-step explanation:

[tex]Mean = \frac{Sum of terms}{Number of terms}[/tex]

          = [tex]\frac{7+6+6+7+6+9+7+8}{8}[/tex]

          = [tex]\frac{56}{8}[/tex]

          = 7

Hope it helps and please mark as brainiest!

C.8 is the answer.

Step-by-step explanation:

Mode: The number that occurs the highest number of times.

Answer:

The Answer is C). 8

Step-by-step explanation:

bcause there are more 8's then all the other number if that makes sense

Hope this helps!!!

Answer:

175

Step-by-step explanation:

its easy just multiply 7 and 25