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pychu [463]
3 years ago
13

Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.

Mathematics
2 answers:
Alex777 [14]3 years ago
7 0

9514 1404 393

Answer:

  7 +5i   or   7 -5i

Step-by-step explanation:

If the two numbers are represented by x and y, then ...

  x+y = 14

  xy = 74

Substituting for y, we have ...

  x(14 -x) = 74

  x^2 -14x +49 = -74 +49 . . . . . multiply by -1, complete the square

  (x -7)^2 = -25 . . . . . . . . . . . write as a square

  x -7 = ±√(-25) = ±5i . . . . take the square root

  x = 7 ± 5i . . . . . . . . . . . add 7

One of the numbers is 7 +5i.

IrinaVladis [17]3 years ago
3 0

Answer:

Hello,

Step-by-step explanation:

The 2 numbers are roots of the equation:

U²-14U+74=0

Discriminant=14²-4*74=-100

<u>U=7-5i or U=7+5i</u>

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Write the number below as a fraction in its simplest form 0.˙49˙9 (more clearer picture is attached here)
mars1129 [50]

Answer:

499/999

Step-by-step explanation:

The decimal number written is:

0.499...

Such that these 3 decimals are repeated as:

0.499499499...

Let's define this number as k

k = 0.499...

Let's multiply this number by 1000 (the same number of zeros as important decimals after the decimal point)

we get:

1000*k = (1000)*(0.499...) = 499.499...

Now we can subtract the original number k, so we get:

1000*k - k = 499.499... - 0.499...

In this way, we remove the part after the decimal point:

1000*k - k = 499.499... - 0.499...

(1000 - 1)*k = 499

999*k = 499

Now we can divide both sides by 999

(999*k)/999 = 499/999

k = 499/999

The fraction notation of our number is 499/999 (and this is the simplest form)

5 0
3 years ago
Performance Task A. Directions: Solve the problem and answer the following questions. Renz' family attended a pool party. The po
dezoksy [38]

Answer: 144 meters

Step-by-step explanation: area of circle = r^2

6^2 = 36 = 144 Meters given = 4

radius of pool is 6 meters

diameter of pool is 12 meters

= 4

area of circle = r^2

area of swimming pool is 144 meters

8 0
2 years ago
PLEASE HELP ME! Images below &amp; I give Brainliest
neonofarm [45]

Answer:

Graph C with the green dots.

Step-by-step explanation:

y = 0.5x + 5 is a linear equation, so we can rule out A because it is not straight.

5 represents the y-intercept, so we rule out B because that graph doesn't intercept the y-axis at (0,5).

Graph C represents a straight line that passes through (0, 5) & has a 0.5 slope, so that is our answer.

Hope this helps. :0)

4 0
3 years ago
SOMEONE PLEASE HELP. Please show me how to do it and what the answer would be thank you.
goblinko [34]

Answer:

hiiii

Step-by-step explanation:

welcome back

3 0
3 years ago
Read 2 more answers
I round to 900 I have twice as many hundreds as ones and all my digits are different but their sums are 18 can someone answer th
stellarik [79]

Answer:

The number of once is 9.1  

The number of hundreds is 8.9

Step-by-step explanation:

Given as :

The total of digits having ones and hundreds = 900

The sum of digits = 18

Let The number of ones digit = O

And The number of hundreds digit = H

So, According to question

H + O = 18             .........1

100 × H + 1 × O = 900          ........2

Solving the equation

( 100 × H - H ) + ( O - O ) = 900 - 18

Or, 99 H + 0 = 882

Or , 99 H = 882

∴   H = \frac{882}{99}

I.e H = 8.9

Put the value of H in eq 1

So, O = 18 - H

I.e  O = 18 - 8.9

∴    O = 9.1

So, number of once = 9.1

number of hundreds = 8.9

Hence The number of once is 9.1  and The number of hundreds is 8.9

Answer

4 0
3 years ago
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