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The expression is in the form of a+bi where a,b ∈R. where, a = [tex]\frac{29}{5}[/tex]and b = [tex]\frac{-41}{5}[/tex] therefore, The complex number is [tex]\frac{29}{5}[/tex] [tex]-\frac{41i}{5}[/tex].

Given expression is:[tex]\frac{(i+2)(i-3)((1+2i)(3+i))}{(-2+i)}[/tex]

To simplify the above expression, first, we need to expand all the terms in the brackets which are given above.

We get,= [tex]\frac{(i^{2} - i*3 + 2i - 6) * (3 + i + 2i + 2i^{2} )}{(-2+i)}[/tex]

We know that i² = -1 and i²² = 1 and i*3 = 3i.

Therefore, the above expression becomes=[tex]\frac{(-1 -3i + 2i - 6) * (3 + i + 2i - 2)}{(-2+i)} =\frac{(-7 - i) * (5 + 3i)}{(-2 + i)}[/tex]

Now, we need to simplify the above expression by multiplying the numerator and denominator by the conjugate of the denominator.

Conjugate of -2 + i = -2 - i

Therefore, the expression becomes=[tex]\frac{(-7 - i) * (5 + 3i)*(-2 - i)}{((-2 + i)*(-2 - i))} = \frac{(-7 - i) * (5 + 3i)*(-2 - i)}{(4 + 1)} = \frac{(29 - 41i)}{5}[/tex]

The expression is in the form of a+bi where a,b ∈R. where, a = [tex]\frac{29}{5}[/tex]and b = [tex]\frac{-41}{5}[/tex]

Therefore, The complex number is [tex]\frac{29}{5}[/tex] [tex]-\frac{41i}{5}[/tex].

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Answer:

∠2=67°

Step-by-step explanation:

Angles along a straight line add up to 180. Therefore:

∠1+∠2=180

113+∠2=180

∠2=180-113

∠2=67°

Answer:

52

Step-by-step explanation:

Answer:

1 2/3 or 1.67

Step-by-step explanation:

(2x+1)+(x-6)=0

Remove parenthesis.

2x+1+x-6=0

Rearrange to make life temporarily easier.

2x+x+1-6=0

Now combine like terms.

3x-5=0

Add 5 to cancel it out.

3x-5=0

   +5 +5

3x=5

Divide 3 from both sides to cancel that out.

3x=5

/3  /3

x=5/3 or 1 2/3

So the answer is 1 2/3 or 1.67

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hope it helps

Answer:

50

Step-by-step explanation:

30 + 100 = 130

130 + 50 = 180

all triangles are 180 degrees, so add it up and subtract.

Answer:

50 degrees will be your answer

Step-by-step explanation:

180-(30+100)=50

180 degrees is the whole angle of a triangle. so we subtract the two sides.

Answer:

77or more

Step-by-step explanation:

Answer:

Yuri made 947 more copies than Nathan.

Step-by-step explanation:

Since we are finding the difference from the amount Yuri and Nathan made, the operation is subtraction. Since Yuri made more copies, his number will go first: 1272-325. Then, we solve by subtracting the two numbers, and you should get 947.

Thus, Yuri made 947 more copies than Nathan.  

Answer:

4.5

Step-by-step explanation:

The median we know is the middle number of a set of numbers. Putting the set in least to great order, we have (1, 3, 3, 6, 8, 9). The middle number here is 3 and 6. We take the mean of 3 and 6, (3+6)/2 which gives us 4.5 and that is our answer.

Answer:

4.5

Step-by-step explanation:

i took the test

Answer:

(-1/4, 1 3/4)

Step-by-step explanation:

The first thing to look at is the scale of the grid. To do that, look at the x-axis (horizontal). The space between 0 and 1 has been divided into 4 equal parts, so each part (square) is worth 1/4 in the horizontal directio.

The scale on the y-axis (vertical) is similar. Again, the space between 0 and 1 is divided into 4 equal parts, so each square represents 1/4 in the vertical direction.

To get to point A, begin at the origin, then go left one space. The x-coordinate of point A is -1/4. Now go up to point A, moving up through 7 spaces. The y-coordinate of point A is 7/4 = 1 3/4.

Answer:

7.44 × 10⁹

Step-by-step explanation:

You would take a decimal point from the last zero to in-between 7 and 4 and see how many places you moved it then write the scientific formula.

9 spaces so it would be 7.44 × 10⁹

The scientific notation of the current population of the Earth will be;

⇒ 7.44 × 10⁹

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The current population of the Earth is estimated to be about 7,440,000,000 people.

Now,

Since, The current population of the Earth = 7,440,000,000 people

Hence, The scientific notation of the current population of the Earth is written as;

⇒ 7,440,000,000

⇒ 7.44 × 10⁹

Thus, scientific notation of the current population of the Earth is,

⇒ 7.44 × 10⁹

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Amount of deduction

Net pay check

Answer:

$171.92

Step-by-step explanation:

Given information:

Gross pay is the pay received before any deductions are taken.

Therefore, if 25% of deductions are taken from the given gross pay, the net pay will be 75%, since 100% - 25% = 75%.

Therefore, to calculate the expected weekly paycheck, find 75% of the gross weekly pay:

  75% of $229.22

= 0.75 × 229.22

= 171.915

= $171.92

Answer:

No triangle possible since the lines need to attach, hope this helps :)

Step-by-step explanation:

Answer:

12 km/hr

Step-by-step explanation:

The average speed is 12 km/hr.

It is to find the average speed in km /h.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Given that :

Distance covered by Niamh = 6 km

Time =30minutes=30/60hour

=1/2hour

∴ The average speed=Total distance/Total time

The average speed=6*2/1

The average speed=12 km/hr.

So, the average speed is 12 km/hr.

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Answer:9

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= πr squared

D=r*2

r=24

π=3.14

A= π(24 * 24) = 576

A= π576

A=10808.64

A=10808.6

Step-by-step explanation:

[tex]\tt{}3 \frac{7}{8} - 2 \frac{5}{8} [/tex]

[tex]\tt{}(3 -2) + ( \frac{7}{8} - \frac{5}{8} )[/tex]

[tex]\tt{}1 + \frac{1}{4} [/tex]

[tex]\tt{}1 \frac{1}{4} [/tex]

[tex]\tt{} \frac{5}{4} [/tex]

[tex]\tt{}1.25[/tex]

Answer:

R

Step-by-step explanation:

Answer:

=> P(X <= 62500) = P((X-mean)/sd < (62500-65000)/3000)

= P(Z < -0.8333)

= 1 - P(Z < 0.8333)

= 1 - 0.7967

= 0.2033

=> P(X > 68500) = P(Z > (68500-65000)/3000)

= P(Z > 1.1667)

= 0.1210

=> P(60500 < X < 69500) = P((60500-65000)/3000 < Z < (69500-65000)/3000 )

= P(-1.5 < Z < 1.5)

= 0.8664

=> for P(X < x) = 0.03, for Z = -1.88

X = mean + Z*Sd = 65000 - (1.88*3000) = 59360

Step-by-step explanation:

I'm not sure if that correct , I really try my best to help

The required percent of tires last at least 60,000 kilometers is about 91%.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation,

To solve this problem, we need to use the standard normal distribution. This is a special type of normal distribution where the mean is 0 and the standard deviation is 1. We can use this to standardize the tire life spans by subtracting the mean (65,000 km) and dividing by the standard deviation (5,200 km).

This gives us a standard normal distribution with a mean of 0 and a standard deviation of 1, and we can use a table or calculator to find the probability of a tire lasting at least 60,000 kilometers.

To do this, we need to find the probability that a tire lasts less than 60,000 kilometers and subtract this from 1. This probability is:

P(tire life < 60,000 km) = P(z < (60,000 - 65,000) / 5,200)

Where z is the standardized tire life span, and the probability is calculated using the standard normal distribution.

Calculating this, we find that P(tire life < 60,000 km) = P(z < -1.346) = 0.0913

Therefore, the probability that a tire lasts at least 60,000 kilometers is 1 - 0.0913 = 0.9087 or about 91%.

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Answer:

62.16

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Given

f(x) = 13x - 9 , then

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

= [tex]\frac{13(x+h)-9-(13x-9)}{h}[/tex]

= [tex]\frac{13x+13h-9-13x+9}{h}[/tex]

= [tex]\frac{13h}{h}[/tex]

= 13

Answer:

[tex] \sqrt{18 } is \: a \: \: answer \: pls \: follow \: me[/tex]

Answer:

Step-by-step explanation:

-3i Square root of 2

Answer:

Step-by-step explanation:

║( - 5, 3 )║ = √34

Answer:

(2/3,10/3)

(.667,3.333)

Step-by-step explanation:

y=5x,x+y=4

Answer:

Your answer is 8 dogs

Step-by-step explanation:÷

42 ÷ 5 = 8.4 = 8

I hope this helps

have a nice day/night

mark brainliest please :)

Step-by-step explanation:

What exactly are you looking for?

Answer:

0.75 .................