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3 years ago

How to simplify the complex number (9 - 2i) - (-2 + 6i) ?

Mathematics

1 answer:

matrenka [14]3 years ago

3 0

$(9 - 2i) - (-2 + 6i) \\ \\ 9 - 2i + 2 - 6i \\ \\ (9+2) + (-2i - 6i) \\ \\ 11 - 8i \\ \\ Answer: \fbox {11 - 8i}$

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At 8:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 80870 ft and is decreasing at the rate of 4

wel

Let's begin by listing out the information given to us:

8 am

airplane #1: x = 80870 ft, v = -450 ft/ min

airplane #2: x = 5000 ft, v = 900ft/min

We must note that the airplanes are moving at a constant speed. The equation for the airplanes is given by:

$\begin{gathered} E=x_1+vt----1 \\ E=x_2+vt----2 \\ where\colon E=elevation,ft;x=InitialElevation,ft; \\ v=velocity,ft\text{/}min;t=time,min \\ x_1=80,870ft,v=-450ft\text{/}min \\ E=80870-450t----1 \\ x_2=5,000ft,v=900ft\text{/}min \\ E=5000+900t----2 \end{gathered}$

We equate equations 1 & 2 to get the time both airlanes will be at the same elevation. We have:

$\begin{gathered} 5000+900t=80870-450t \\ \text{Add 450t to both sides, we have:} \\ 900t+450t+5000=80870-450t+450t \\ 1350t+5000=80870 \\ \text{Subtract 5000 from both sides, we have:} \\ 1350t+5000-5000=80870-5000 \\ 1350t=75870 \\ \text{Divide both sides by 1350, we have:} \\ \frac{1350t}{1350}=\frac{75870}{1350} \\ t=56.2min \\ \\ \text{After }56.2\text{ minutes, both airplanes will be at the same elevation} \end{gathered}$

The elevation at that time (when the elevations of the two airplanes are the same) is given by substituting the value of time into equations 1 & 2. We have:

$\begin{gathered} E_1=80870-450t \\ E_1=80870-450(56.2) \\ E_1=80870-25290 \\ E_1=55580ft \\ \\ E_2=5000+900t \\ E_2=5000+900(56.2) \\ E_2=5000+50580 \\ E_2=55580ft \\ \\ \therefore E_1\equiv E_2=55580ft \end{gathered}$

6 0

1 year ago

You and a friend are playing a game of chance. Every time you roll a 1 or 2 you are successful, and your friend will pay you $1.

LUCKY_DIMON [66]

At the end of the game you owned 13 cents if 71% of your rolls are successful and 29% of your rolls are unsuccessful option first is correct.

<h3>What is probability?</h3>

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Every time you roll a 1 or 2 you are successful, and your friend will pay you $1. Every time you roll a 3, 4, 5 or 6, you must pay your friend $2.

71% of your rolls are successful:

= 1×0.71

= $0.71 (won)

29% of your rolls are unsuccessful

= 2×2.9

= $0.58 (lose)

The amount owned = 0.71 - 0.58 = $0.13 = 13 cents

Thus, at the end of the game you owned 13 cents if 71% of your rolls are successful and 29% of your rolls are unsuccessful option first is correct.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

6 0

2 years ago

A box contains red marbles and green marbles. Sampling at random from the box five times with replacement, you have drawn a red

olasank [31]

Answer: The probability of drawing a red marble the sixth time is 1/2

Step-by-step explanation:

Here is the complete question:

A box contains 10 red marbles and 10 green marbles. Sampling at random from the box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time?

Explanation:

Since the sampling at random from the box containing the marbles is with replacement, that is, after picking a marble, it is replaced before picking another one, the probability of picking a red marble is the same for each sampling. Probability, P(A) is given by the ratio of the number of favourable outcome to the total number of favourable outcome.

From the question,

Number of favourable outcome = number of red marbles =10

Total number of favourable outcome = total number of marbles = 10+10= 20

Hence, probability of drawing a red marble P(R) = 10 ÷ 20

P(R) = 1/2

Since the probability of picking a red marble is the same for each sampling, the probability of picking a red marble the sixth time is 1/2

3 0

3 years ago

2x^2+3x=(2x-1)(x+1) Pls do explain

Serggg [28]

<h3>Answer:</h3>

$x=-\frac{1}{2}$

<h3>Step-by-step explanation:</h3>

You could solve this problem by either: Factoring or by using the Quadratic Formula.

SOLVING BY FACTORING STEPS

STEP 1: Move (2x−1)(x+1) to the left side of the equation by subtracting it from both sides.

$2x^2+3x-(2x-1)(x+1)=0$

STEP 2: Simplify 2x^2+3x−(2x−1)(x+1).

$2x+1=0$

STEP 3: Simplify each term.

$2x^2+3x-2x^2-x+1=0$

STEP 4: Simplify by adding terms.

$2x+1=0$

STEP 5: Subtract 1 from both sides of the equation.

$2x=-1$

STEP 6: Divide each term by 2 and simplify.

$x=-\frac{1}{2}$

SOLVE BY USING THE QUADRATIC FORMULA STEPS

STEP 1: Move all terms to the left side of the equation and simplify.

$2x+1=0$

STEP 2: Subtract 1 from both sides of the equation.

$2x=-1$

STEP 3: Divide each term by 2 and simplify.

$x=-\frac{1}{2}$

5 0

3 years ago

Read 2 more answers

Math 015 How do you complete this algebric expression. simplify 2/15x2-3/4x+6-3/10x2+2x-15/2

ankoles [38]

Answer:

its x+4 over x+6

Step-by-step explanation:

4 0

3 years ago