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3 years ago

Find the quadratic equation whose roots are 3+- i / 2

1 answer:

4 0

(x - root#1) times (x - root#2) = 0 . . . . . This is how to BUILD the quadratic equation.

All the rest is just multiplying out that first line:

(x- (3+i/2)) times (x - (3-i/2)) = 0

x² -x(3-i/2) -x(3+i/2) + (3+i/2)(3-i/2) = 0

x² -3x + ix/2 -3x - ix/2 + 9 -3i/2 + 3i/2 = 0

<u>x² -6x +9 = 0</u> There it is. That's your quadratic equation.

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Rearrange the equation so a is the independent variable. -3a+6b=a+4b, b=

leva [86]

Answer:

Step-by-step explanation:

Given that

-3a+6b=a+4b

We want to make b subject of formula

First to remove the 4b in the Right hand side of the equation

Subtract 4b from both side of the equation

-3a+6b-4b=a+4b-4b

Then we have,

-3a+2b=a

Now to remove the -3a from the left hand side of the equation add 3a to both side

Then,

-3a+2b+3a=a+3a

2b-3a+3a=4a

Then, 2b=4a

Divide both side by 2

2b/2=4a/2

b=2a.

6 0

3 years ago

Read 2 more answers

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounc

Ludmilka [50]

Answer:

$\mu = 12.1\\\sigma = 0.3$

a) Find the probability that the drink is less than 11.9 fluid ounces

We are supposed to find P(x<11.9)

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

Refer the z table

So, P(z<-0.67) = 0.2514

Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514

b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces

x= 11.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.6-12.1}{0.3}$

$z=-1.67$

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

We are supposed to find P(11.6<x<11.9)

So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

Refer the z table

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

P(-1.67<z<-0.67)= 0.2514-0.0475

P(-1.67<z<-0.67)= 0.2039

So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.

c)Find the probability that the drink is more than 12.6 fluid ounces

We are supposed to find P(x>12.6)

x= 12.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{12.6-12.1}{0.3}$

$z=1.67$

Refer the z table

P(x>12.6)=1-P(x<12.6)

P(z>1.67)=1-P(z<1.67)

P(z>1.67)=1-0.9525

P(z>1.67)=0.0475

Hence the probability that the drink is more than 12.6 fluid ounces is 0.0475

d) Is the drink containing more than 12.6 fluid ounces an unusual event?

Since p value is less than alpha (0.05)

Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.

3 0

3 years ago

Consider the sequence 3, -9, 27, -81, .. Find the 14th term of the sequence.

bagirrra123 [75]

Answer:

let 'a' be the first term, 'd' be the common difference between all the terms of the sequence

Step-by-step explanation:

therefore, a = 3,

and, d = -9 -3

= -12

hence the 14th term would be,

=> a + 13d

=> 3 + 13( -12 )

=> 3 - 156

=> - 153

5 0

3 years ago

Read 2 more answers

My favorite songstress gives away 25% of the cells of her signature fragrance collection to her charity. last month her cells we

Pachacha [2.7K]

Answer:

$300

Step-by-step explanation:

Multiply 1,200 by .25 and that is your answer

3 0

2 years ago

Farah harvests 20 pounds of tomatoes from her garden. She needs 4 4/5 pounds to make a batch of soup. Additionally, if she uses

Romashka [77]

Answer:

1 batch

Step-by-step explanation:

Farah needs 4 and 4/5 pounds of tomatoes & and additional 5 and 3/5 pounds of tomatoes to make soup.

4.8 + 5.6 = 10.5 pounds per soup

10.5*2 = 21 > 20 pounds

Farah would need one more pound of tomatoes in order to make 2 batches of soup. Therefore she can only make 1 batch.

6 0

3 years ago