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
alina1380 [7]
2 years ago
11

Solve the equation: k^2+5k+13=0

Mathematics
1 answer:
mr_godi [17]2 years ago
8 0

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}  \\

From the question

a = 1 , b = 5 , c = 13

So we have

k =  \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)}  \\  =  \frac{ - 5 \pm \sqrt{25 - 52} }{2}  \\  =  \frac{ - 5 \pm \sqrt{ - 27} }{2}  \:  \:  \:  \:  \:  \:  \\  =  \frac{ - 5  \pm3 \sqrt{3}  \: i}{2}  \:  \:  \:  \:  \:  \:

<u>Separate the solutions</u>

k_1 =  \frac{ - 5 + 3 \sqrt{3} \: i }{2}  \:  \:  \:  \: or \\ k_2 =  \frac{ - 5 - 3 \sqrt{3}  \: i}{2}

The equation has complex roots

<u>Separate the real and imaginary parts</u>

We have the final answer as

k_1 =  -  \frac{5}{2}  +  \frac{3 \sqrt{3} }{2}  \: i \:  \:  \:  \: or \\ k_2 =  -  \frac{5}{2}  -  \frac{3 \sqrt{3} }{2}  \: i

Hope this helps you

You might be interested in
Help ASAP please ..<br> Explain answer ..
Luba_88 [7]

Answer:

C

Step-by-step explanation:

Becuase it is the number of caleders purchesed times how many calenders

8 0
3 years ago
Read 2 more answers
Patrick and Shelby are playing a game. They toss a fair six-sided number cube, numbered 1 through 6, and they spin a spinner whi
zhuklara [117]

Answer:

(Red, 1) (Red, 2) (Red, 3) (Red, 4) (Red, 5) (Red, 6)

(Blue, 1) (Blue, 2) (Blue, 3) (Blue, 4) (Blue, 5) (Blue, 6)

Step-by-step explanation:

8 0
2 years ago
Si un empresario paga diariamente 50 a cada trabajador le faltaria 110 pero si les pagara 45 le sobraria 60 cuantos trabajadores
N76 [4]

Answer:

34 trabajadores.

Step-by-step explanation:

Supongamos que el empresario tiene N trabajadores, y tiene la cantidad de dinero D para pagarles cada día.

Si el empresario decide pagarle 50 a cada trabajador le faltan 110.

Esto se puede reescribir como:

50*N = D + 110

(50 por número de empleados es igual que el dinero que tiene más lo que le falta para pagar)

También sabemos que si pagara 45 a cada empleado, le sobraría 60.

Esto se puede reescribir como:

45*N = D - 60

Entonces tenemos dos ecuaciones:

50*N = D + 110

45*N = D - 60

Para resolver esto, el primer paso es aislar una de las variables en una de las ecuaciones, en este caso aislaré D en la segunda ecuación.

45*N + 60 = D

Ahora podemos reemplazar esto en la primer ecuación y resolver para N

50*N = (45*N + 60) + 110

50*N = 45*N + 170

50*N - 45*N = 170

5*N = 170

N = 170/5 = 34

El empresario tiene 34 trabajadores.

7 0
2 years ago
Which of the following best describes a regular tessellation?A. A tessellation that uses only one type of regular polygonB. A te
Naya [18.7K]

Answer: A. A tessellation that uses only one type of regular polygon

Step-by-step explanation:

When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.

A regular tessellation is tessellation made up by using nly one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex

Hence, A is the correct option.

8 0
2 years ago
6​(7x-4​y)-5 it says to use distributive property to answer
Alexeev081 [22]

Answer:

42x-24y-5

Step-by-step explanation:

We can start by using the distributive property.

This will help us rewrite the expression, since the terms in the parentheses can't be combined.

I'll attach an image to better explain this.

When using it, we'll get:

6*7x+6*-4y-5

Simplify.

42x-24y-5

This is our final answer since there are no like terms that can be combined.

3 0
3 years ago
Other questions:
  • A histogram can only display what data?
    5·2 answers
  • Please help me!!! :(
    13·2 answers
  • The fastest speed a table tennis ball has been hit about 13.07 times as fast as the speed for the fastest swimming. What is the
    5·1 answer
  • 8x = -6 please answer!!​
    13·2 answers
  • PLEASE HELP ASAP MUCH APPRECIATED.
    5·2 answers
  • Which tables could be used to verify that the functions they represent are inverses of each other? Select two
    14·1 answer
  • Lionheart Ranch has bought a new herd of race horses. If there is one stable for every four horses, which equation shows the cor
    13·1 answer
  • A pack of snack bars includes 2 blueberry bars, 3 chocolate bars, and 5 cherry bars. What is the ratio of the number of blueberr
    15·2 answers
  • Please help!! I'll give brainliest!!!
    9·1 answer
  • Please assist me in the geometry please !!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!