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3 years ago

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=7-5i or U=7+5i

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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:

Step-by-step explanation:

78+9+(10-4)=

78+9+6=

3 0

3 years ago

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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 <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 how do this? y= x+2 y= -4x+7

jekas [21]

Equations are given,
y= x+2

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.

 $x+2=-4x+7\\ \\ x+2+4x=7\\ \\ x+4x+2=7\\ \\ 5x+2=7\\ \\ 5x=7-2\\ \\ 5x=5\\ \\ x=\frac { 5 }{ 5 } \\ \\ x=1$

Now we have x's value we will plug it in the first equation to find "y".

 $x=1\\ \\ y=x+2\\ \\ y=1+2\\ \\ y=3$

(1,3)

8 0

3 years ago