1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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>

You might be interested in
Complete the table of ordered pairs for the linear y=2x-8
ExtremeBDS [4]

Given:

Consider the below figure attached with this question.

The linear equation is:

y=2x-8

To find:

The values to complete the table of ordered pairs for the given linear equation.

Solution:

We have,

y=2x-8

Substituting x=0 in the given equation, we get

y=2(0)-8

y=0-8

y=-8

So, the value for first blank is -8.

Substituting y=-2 in the given equation, we get

-2=2x-8

-2+8=2x

\dfrac{6}{2}=x

3=x

So, the value for second blank is 3.

Substituting x=2 in the given equation, we get

y=2(2)-8

y=4-8

y=-4

So, the value for third blank is -4.

Therefore, the required complete table is:

     x           y

     0         -8

    3         -2

     2          -4

8 0
2 years ago
What's 9 + 10-4 + 78 ​
Zarrin [17]

Answer:

93

Step-by-step explanation:

78+9+(10-4)=

78+9+6=

93

3 0
3 years ago
Read 2 more answers
A toy that originally sold for 12 dollars went of sale for 8 dollars what was the percent discount? Remember to show your work!
harkovskaia [24]
12———-100%
8 ———— x
X=(8*100)/12=800/12=66.66%
Then discount percent is 100-66.66=33.33%
3 0
3 years ago
Find all the zeros of <br><img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7B6x%7D%5E%7B4%7D%20%20%20-%20%20%7B7x%7D%5E%7B
Svetradugi [14.3K]

Answer:

  {-1, 1/2, 2/3, 1}

Step-by-step explanation:

I find a graphing calculator to be a most useful tool for problems like this. (See attached.)

_____

First of all, observe that the constant is -2, so 0 is not a zero.

It is often useful to look at the sum of coefficients. Here, that is 0, indicating 1 is a zero.

You can divide that out, or simply continue by looking at the sum of coefficients with odd-degree terms negated. Then you have 6 +7 -4 -7 -2 = 0, indicating -1 is also a zero.

__

At this point, it can be useful to divide out the factors you know. The synthetic division tableaus attached show that work. First is division by (x+1), then by (x -1).

The result of doing that is the quadratic ...

  6x^2 -7x +2 = 0

This can be factored ...

  (6x^2 -3x) -(4x -2) = 0 . . . . . . rewrite -7x and group term pairs

  3x(2x -1) -2(2x -1) = 0 . . . . . . . factor each pair

  (3x -2)(2x -1) = 0 . . . . . . the factorization of the remaining quadratic

The zeros of this are the values of x that make the factors zero: 2/3 and 1/2.

The zeros of the given function f(x) are x ∈ {-1, 1/2, 2/3, 1}.

5 0
3 years ago
System of equations by substitution<br> how do this?<br> y= x+2<br> y= -4x+7
jekas [21]
Equations are given,
y= x+2
<span>
y= -4x+7

As you can see both the expressions, x+2 and -4x+7 are equal to "y". That means they are equal to each other too.

So let's equal them and solve it.

</span>x+2=-4x+7\\ \\ x+2+4x=7\\ \\ x+4x+2=7\\ \\ 5x+2=7\\ \\ 5x=7-2\\ \\ 5x=5\\ \\ x=\frac { 5 }{ 5 } \\ \\ x=1
<span>
Now we have x's value we will plug it in the first equation to find "y".

</span>x=1\\ \\ y=x+2\\ \\ y=1+2\\ \\ y=3
<span>
(1,3)</span>
8 0
3 years ago
Other questions:
  • The louvre museum is a metal and glass structure that serves as the main entrance to the louvre museum paris, france. The pyrami
    10·1 answer
  • State whether the given measurements determine zero, one, or two triangles.
    6·2 answers
  • Write the interval (5, 100] as an inequality and using set notation
    15·1 answer
  • 4 1/4 divided by 2/7<br><br> (x+8)-(3x- 5)<br><br> Explain how you got the answer!!!!!
    10·1 answer
  • Help plz ASAP !!!!!!!!!
    14·1 answer
  • Oliver is 33 years older than his son. Eight years ago, Oliver's age is five more than thrice his son's present age. How old is
    12·1 answer
  • • Since January 1980, the population, P, of the city of Brownville has increased closely modeling the
    13·1 answer
  • Write the equation of the line passing through the points (0,-1) And (3,7)
    14·1 answer
  • Written as a simplified polynomial in standard form, what is the result when
    11·1 answer
  • Daniel has 12 cups of orange juice.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!