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slavikrds [6]
3 years ago
10

What is the name of a number that can be written in the form a + bi where a and b are nonzero real

Mathematics
1 answer:
san4es73 [151]3 years ago
8 0

Answer:

Complex numbers

Step-by-step explanation:

Given

a + bi

Required

Determine the type of number in that form

Numbers written in a + bi are referred to as complex numbers

Where a \neq 0; b\neq 0 and i = \sqrt{-1}

<em>Note that a and b can either integers or non integers and a and be can also be positive or negative</em>

<em />

The following are valid examples of complex numbers

2 + 3i

2.4 - 5i

-3 - i

<em>and lots more..</em>

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Step-by-step explanation:

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3 0
3 years ago
In a 3-digit number, the hundreds digit is one more than the ones digit and the tens digit is twice the hundreds digit. If the s
MaRussiya [10]

Answer:

The mentioned number in the exercise is:

  • <u>362</u>

Step-by-step explanation:

To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.

If:

  • x = hundredths digit
  • y = tens digit
  • z = ones digit

We can write:

  1. x = z + 1 (the hundreds digit is one more than the ones digit).
  2. y = 2x (the tens digit is twice the hundreds digit).
  3. x + y + z = 11 (the sum of the digits is 11).

Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:

  • x + y + z = 11
  • (z + 1) + y + z = 11 (remember x = z + 1)
  • z + 1 + y + z = 11
  • z + z +y + 1 = 11 (we just ordered the equation)
  • 2z + y + 1 = 11 (z + z = 2z)
  • 2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
  • 2z + y = 10
  • 2z + (2x) = 10 (remember y = 2x)
  • 2z + 2x = 10
  • 2z + 2(z + 1) = 10 (x = z + 1 again)
  • 2z + 2z + 2 = 10
  • 4z + 2 = 10
  • 4z = 10 - 2
  • 4z = 8
  • z = 8/4
  • <u>z = 2</u>

Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:

  • x = z + 1
  • x = 2 + 1
  • <u>x = 3</u>

And we'll use the second equation to obtain the value of y (the tens digit):

  • y = 2x
  • y = 2(3)
  • <u>y = 6</u>

Organizing the digits, we obtain the number:

  • Number = xyz
  • <u>Number = 362</u>

As you can see, <em><u>the obtained number is 362</u></em>.

8 0
3 years ago
A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is
anzhelika [568]

A number cube is rolled 120 times. The number 4 comes up 47 times.

We have to determine the experimental probability of rolling a 4.

The formula to evaluate probability of an event is given by:

Probability  = \frac{Favourable outcomes}{Total outcomes}

So, Probability of rolling a 4 = \frac{ Total number of times when 4 appears}{Total number of times number cube rolled}

= \frac{47}{120}

Now, we have to find the theoretical probability of rolling a 4.

Total number of outcomes of number cube = {1,2,3,4,5,6}

Probability of rolling a 4 = \frac{1}{6}

So, Option B is the correct answer.

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A car travels a distance on a road of 12.42 miles at a slope of 6.4%. The car has a maximum speed of 203 mph. Assume the car wil
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Answer:

4 mins 31 seconds

Step-by-step explanation:

Maximum speed is 203 mph equivalent to

203*\frac {5280}{3600}=297.73 ft/s

Time taken to attain maximum speed, t=\frac {v}{a} where v is velocity and a is acceleration hence

t=\frac {297.73}{2.93}=101.6155 s

The distance traveled when at top speed

d=\frac {v^{2}}{2a}=\frac {(297.73)^{2}}{2*2.93}=15127.16 \approx 15127.2 ft

Total distance is provided as 12.42 miles converted to ft is 12.42*5280=65577.6 ft

Total distance-distance moved to attain maximum speed will be

65577.6 ft-15127.2 ft=50450.44 ft

Time taken during maximum speed

t=\frac {50450.44}{297.73}=169.45 s

Total time=101.6155 s+169.45 s=271.06 s

271.06/60=4 mins 31 seconds

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3 years ago
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A 96 ounce container of orange juice cost $4.80 at what price should a 128 ounce container be sold in order for the unit rate fo
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It is $0.05 per ounce, so at that rate, a 128 oz container would cost $6.40.
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