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Find the product of (x + 9i)^2 Find the product of (x+(3+5i))^2

Ket [755]

Remember that
$i = \sqrt{1}$
so
${i}^{2} = - 1 \: \: and \: \: {i}^{3} = - i \: \: \: and \: \: {i}^{4} = 1$
(a+ b)^2 = a^2 + 2ab + b^2

1. x^2 + 2x*9i + (9i)^2 = x^2 + 18xi - 81

2. x^2 + 2x*(3+5i)+ (3+5i)^2 = x^2 + 6x + 10xi+ 9+30i-25 = x^2 - 16 + 30i + 6x + 10xi

3 0

3 years ago

The startup division made 80% of 1/2 of the established division. The startup division’s growth was 1/3 greater than the establi

Gnesinka [82]

Answer:

Step-by-step explanation:

First, let's create variables:

s = startup division

e = established divisioN

The startup division made 80% of 1/2 of the established division.

Let's take a look at what the above statement means: Making 80% of 1/2 means...

0.8 of 1/2 = 0.8*0.5 = 0.4 --> s = 0.4e.

Next: The startup division’s growth was 1/3 greater than the established division’s.

Seems like this is additional information is not needed.

If the divisions made 280,000 combined, how much did the startup division make?

s + e = 280,000 --> s = 280,000 - e, then we can substitude s = 0.4e for s -->

280,000 - e = 0.4e --> 1.4e = 280,000 --> e = 200,000.

This means that s = 80,000.

MARK AS BRAINLEST PLZZZZZ

5 0

3 years ago

We are drawing two cards without replacement from a standard 52-card deck. find the probability that we draw at least one red c

alina1380 [7]

The probability of drawing only one red card in two draws without replacement is given by:
$P(1\ red)=\frac{26C1\times26C1}{52C2}=0.51$
The probability of drawing two red cards in two draws without replacement isgiven by:
$P(2\ red)=\frac{26C2\times26C0}{52C2}=0.245$
The events 'draw one red card' and 'draw two red cards' are mutually exclusive. Therefore the probability of drawing at least one red card is 0.51 + 0.245 = 0.755.

8 0

3 years ago

A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If i

11111nata11111 [884]

Answer:

the proportion of days that are Sunny is 0.2

Step-by-step explanation:

Given the data in the question;

Using markov chain;

3 states; Sunny(1), Cloudy(2) and Rainy(3)

Now, based on given conditions, the transition matrix can be obtained in the following way;

$\left[\begin{array}{ccc}0&0.5&0.5\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]$

so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.

such that, from column 1

S = 0.25C + 0.25R -------------let this be equation 1

from column 2

0.5C = 0.5S + 0.25R

divided through by 0.5

C = S + 0.5R ---------------------- let this be equation 2

now putting equation 2 into equation;

S = 0.25(S + 0.5R) + 0.25R

S = 0.25S + 0.125R + 0.25R

S - 0.25S = 0.375R

0.75S = 0.375R

S = 0.375R / 0.75

S = 0.5R

Therefore,

from equation 2; C = S + 0.5R

input S = 0.5R

C = 0.5R + 0.5R

C = R

Now, we know that, the sum of the three proportion should be equal to one;

so

S + C + R = 1

since C = R and S = 0.5R

we substitute

0.5R + R + R = 1

2.5R = 1

R = 1/2.5

R = 0.4

Hence, the proportion of days that are Rainy is 0.4

C = R

C = 0.4

Hence, the proportion of days that are Cloudy is 0.4

S = 0.5R

S = 0.5(0.4)

S = 0.2

Hence, the proportion of days that are Sunny is 0.2

8 0

3 years ago

HELP!!! ASAP!!!!!!!! WILL GIVE LOTS OF POINTS PLUS BRAINLIEST

olya-2409 [2.1K]

Answer:

x = 3.27837238

Step-by-step explanation:

1. The value of a variable that makes an equation true.

2. In chemistry, a solution is a homogeneous mixture composed of only one phase.

3 0

3 years ago