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pychu [463]
2 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]2 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]2 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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Answer:

(12,0) and (3, -1) and (0,-4/3)

Step-by-step explanation:

To find if a point makes an equation true, just substitute its x and y values in in the equation and simplify.

1) Let's test the point (12,0). Substitute 12 for x and 0 for y in the equation:

x-9y=12\\(12)-9(0)=12\\12-0=12\\12=12

12 does equal 12, so (12,0) makes the equation true.

2) Let's test the point (0, 12). Substitute 0 for x and 12 for y in the equation:

x-9y=12\\(0)-9(12) = 12\\0-108 = 12\\-108 = 12

However, -108 does not equal 12, so (0,12) does not make the equation true.

3) Let's test the point (3, -1). Substitute 3 for x and -1 for y in the equation:

x-9y=12\\(3)-9(-1) = 12\\3 + 9 = 12\\12 = 12

12 does equal 12, so (3, -1) makes the equation true.

4) Let's test the point (0, -4/3). Substitute 0 for x and -4/3 for y in the equation:

(0) -9(-\frac{4}{3} ) = 12\\0 + \frac{36}{3} = 12\\0 + 12 = 12 \\12 = 12

12 does equal 12, so (0, -4/3) makes the equation true.

8 0
3 years ago
A plumber and his assistant work together to replace the pipes in an old house. The plumber charges $30 an hour for his own labo
Korvikt [17]

Answer:

The plumber worked 50 hours, and his assistant worked 25 hours.

Step-by-step explanation:

Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:

40 x 30 + 20 x 20 = 1200 + 400 = 1600

50 x 30 + 25 x 20 = 1500 + 500 = 2000

Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.

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2 years ago
It costs John $13.50 to take Mary out for the evening. Sixty percent of this total was for theater tickets. What was the cost of
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The slope of the line whose equation is 3x - 2y = 4 is 2/3 3/2 -2
alexandr1967 [171]
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4 0
2 years ago
Which of the following is a quadratic equation?
Aloiza [94]

Answer:

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Step-by-step explanation:

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2) a cubic equation (degree = 3)

3) a quadratic equation

4) a linear equation (degree = 1)

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