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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

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Identify the variation as direct, inverse, joint or combined. y = cx²
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Answer:

combined variation          

Step-by-step explanation:

we have

y=cx^{2}

we know that

a)<u> in the interval </u>----> (0,∞)

If the value of x increase the value of y increase

so

Is a direct variation

b) <u>in the interval -</u>---> (-∞,0)

If the value of x increase the value of y decrease

so

Is a inverse variation

therefore

Is a combined variation


4 0
3 years ago
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Len has 3 strips of construction paper. Each strip is the same size and a different color-red, yellow, and pink. He tapes the st
Helen [10]

Answer:

2/6

Step-by-step explanation:

Each of the rectangle strips are taped together to form a rectangle. Therefore 1 of the third of the rectangle would be red, this means that 1/3 of the rectangle would be red color. The rectangle is then divide into sixths, this can be achieved by dividing each of the taped strip into 2.

Therefore 2 of the sixths rectangle would be red in color, Hence the fraction of the rectangle that would be red is given as 2/6

7 0
2 years ago
Can you PLEASE write a paragraph of how tragicomic functions work PLEASE!!!
iogann1982 [59]
They are used for making the sides of a triangle into a ratio. Sine is opposite of the angle divide by the hypotenuse, cosine is adjacent divided by the hypotenuse, and tangent is the opposite divided by the adjacent. Sine is the y-component, cosine is the x-component, and tangent is the ratio of sine/cosine or can also be considered the slope.
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2 years ago
PLZ HELP!!! I don't understand.
lilavasa [31]

Answer:

Step-by-step explanation:

14.)

lets first find x:

2x+x+90=189

3x=90

x=30

lets find y:

2y=x

2y=30

y=15

lets find z:

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The H.C.F and the LCM of two numbers are 36 and 720 respectively. If one of the numbers is 180, which is the other number. *
lutik1710 [3]

Answer:

let p(x)=180

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WE HAVE TO FIND q(x)=?

as we know that

p(x)×q(x)=LCM×HCF

NOW WE HAVE TO FIND q(x)

q(x)=LCM×HCF/p(x)

q(x)=720×36/180

q(x)=25920/180

q(x)=144

i hope this will help you

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