Find all the complex roots of the equation x4 − 16 = 0.

Answers

Answer 1

Answer:

4+16=0

4=−16=162

2=±4

Case 1  2=+4

=±2√

√=±(12√+12√)

=±2‾√+2‾√

Case 2  2=−4=43

=±23/2=±2()1/2

∵√=±(12√+12√)

=±(2‾√+2‾√)

So in all,

=2‾√+2‾√

=−2‾√+2‾√

=2‾√−2‾√

=−2‾√−2‾√

Let  √=+

Squaring both sides, we have

=(+)2

0+1=2−2+2⟹

2−2=0(1)

2=1

=12

Plugging in  (1)  … ⟹

2−1(2)2=0

4=14

2=12

∴=±12‾√

∴=±12‾√

∴√=+=±(12+12)

This can also be shown as below

√=12+12

Or

√=−12−12 \


Related Questions

Select the correct answer

Answers

Answer:

D.  5 weeks

Step-by-step explanation:

A population of pea aphids double every week beginning with 300 aphids.

Week 1:   300 × 2 = 600

Week 2:  600 × 2 = 1200

Week 3:  1200 × 2 = 2400

Week 4:  2400 × 2 = 4800

Week 5:  4800 × 2 = 9600

It will take 5 weeks

Find the lowest number divisible by 15, 20 & 25.

Answers

Answer:

300.

Step-by-step explanation:

This is the LCM.

15  = 3 * 5

20 = 2 * 2 * 5

25 = 5 * 5

One 5 appears in all 3  factors so we only use this once in the calculation:

LCM = 2 * 2 * 3 * 5* 5 = 300

There are 11 coins in total. Aditi!S piggy bank has $1.85. The coins are either quarters or dimes.How many of each coin are there. Solve with elimination.

Answers

Hey there! I'm happy to help!

Let's represent our number of quarters with q and our dimes with d. We know that each q has a value of 0.25, and each d has a value of 0.1. This means that 0.25q+0.1d=1.85. We also know that q+d=11 as there are 11 total coins.

Here is our system of equations.

0.25q+0.1d=1.85

q+d=11

We are asked to solve with elimination. To do this, we need combine the equations to cancel out a variable to solve for the other. We have 1d on the bottom. Let's multiply the entire top equation by -10 to get a -1d on the top so we can do this.

-2.5q-d=-18.5

q+d=11

We combine the equations.

-1.5q=-7.5

We divide both sides by -1.5

q=5

Since there are 11 coins in total, this means that there are 5 quarters and 6 dimes.

Have a wonderful day!

6|2x+3|=36 need a mini step by step

Answers

Answer:

x=1.5

Step-by-step explanation:

We are trying to get x  by itself to see what it equals.

6(2x+3)=36

So first you want to distribute you proprieties.  You do that by multiplying 6 and 2x.  Then multiplying 6 and 3.

12x+18=36

Now in equations where you need to find the variable, whatever you  do on one side of the equal sign, you have to do on the other side.  So now we want to subtract 18 from both sides.

12x+18=36

     -18  -18

Then we divide 12 from both sides.

12x=18

÷12   ÷12

Now you have your answer!

x=1.5

where to put √3 and √9 on a number line? ​

Answers

[tex]\sqrt{3}\approx1.3[/tex]

[tex]\sqrt{9}=3[/tex].

Put first on about 1 and a third and second on exactly 3.

Hope this helps.

Charle has 10 guests over at his house. If he gives each guest bacon, he will have given
out a total of 30 pieces of bacon. How much bacon did each guest get?

This needs to be converted into and algebraic expression plz help its due soon

Answers

Answer:

Each guest got 3. (if he doesn't have any for himself).

Step-by-step explanation:

if each guest is x

30=10x

divide by 10

x=3

hope this helps and if you want please consider giving me brainliest! :)

adam bought a box of fruit that weighed 6 1/4 pounds. if he bought a second box that weighed 8 1/8 pounds , what is the combined weight of the boxes?

Answers

Answer:

14 3/8 pounds

Step-by-step explanation:

6 pounds plus 8 pounds= 14 pounds. 1/4 + 1/8= 3/8. 1/4 can be turned into 2/8, and 2/8 plus 1/8 equals 3/8. Hope this helps :)

Find the equation of a parabola with a focus at (-4, 7) and a directrix of y=1. ANSWERS ATTACHED, 15 points, due in 2 HOURS!

Answers

Answer:

Solution: y - 4 = 1 / 12(x + 4)² or Option B

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down -

(x - h)² = 4p(y - k)

Remember that the vertex, (h, k) is halfway between the directrix and focus. Therefore we can find the  y  coordinate of the vertex using the formula y = y coordinate of focus + directrix / 2.The  x -coordinate will be the same as the  x  coordinate of the focus.

Vertex: (- 4, 7 + 1 / 2) = (- 4,4)

Now we can find the distance from the focus to the vertex. The distance  from the vertex to the directrix is  represented by | p |. We can subtract the  y  coordinate of the vertex from the  y -coordinate of the focus to find  p.

p = 7 - 4 = 3

Substitute the known values for these variables into the given equation (x - h)² = 4p(y - k) to get our solution.

(x + 4)² = 4(3)(y - 4),

(x + 4)² = 12(y - 4)

1 / 12(x + 4)² = y - 4

y - 4 = 1 / 12(x + 4)² ~ As you can see your solution is option b.

Express in simplest radical form.
Sqrt (27)

Answers

Answer:

3√3

Step-by-step explanation:

√27 =

= √3×9

= √3×3²

= 3√3

Let f(x) = 4x + 8 and g(x) = 2x - 12. Perform the function operation, (f+g)
(x), and then find the domain of the result.??

Answers

you just add these functions:

(f+g)(x)=4x+8+2x-12=6x-4

domain of this function is still all reals (R)

Round to the nearest tenth:
7.0760

Answers

Answer:

the answer is 7.1

Step-by-step explanation:

the tenth is the first number after the decimal point.

answer is approximately 7.1

El Sr negron tiene que redactar una serie de cartas en su oficina. A Lourdes le toma 6 horas pasar todas las cartas. A su compañera rosabel, le toma 9 horas en realizar la misma tarea. Si ambas trabajan juntas para hacer todo el trabajo de la oficina

Answers

El Sr negron tiene que redactar una serie de cartas en su oficina. A Lourdes le toma 6 horas pasar todas las cartas. A su compañera rosabel, le toma 9 horas en realizar la misma tarea. Si ambas trabajan juntas para hacer todo el trabajo d ela oficina,

a. Cuánto tiempo le tomará a ambas realizar el trabajo?

Answer:

3.6 horas

Step-by-step explanation:

Sea el número total de horas que ambos trabajaron = T

Deje que la cantidad total de letras por las que pasaron = 1

De la pregunta, se nos dice:

Lourdes necesitó 6 horas para revisar las cartas.

Esto significa que, cada 1 hora, Lourdes revisaba 1/6 de las letras

Rosabel tardó 9 horas en leer las letras.

Esto significa que, cada 1 hora, Rosabel revisó 1/9 de las letras

Por lo tanto,

(1/6 × 1) T + (1/9 × 1) T = 1

(1/6 + 1/9) T = 1

(3 + 2/18) T = 1

(18/5) T = 1

5T / 18 = 1

Cruz multiplicar

5T = 18

T = 18/5

T = 3.6 horas

Por lo tanto, les tomó a ambas 3.6 horas hacer el trabajo.

What is the slope of the line that passes through (4, 5) and (8, -1)?

Answers

Answer:

m = -3/2

Step-by-step explanation:

The slope of a line is equivalent to the formula:

m = slope = rise/run = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Given the two coordinate pairs, we can label them accordingly.

In math, coordinate pairs are set up in a way that the x-coordinate is given first and the y-coordinate is given second.

Therefore, with this information, we can label the coordinate pairs with this info.

[tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] is the default labeling system for two coordinate pairs.

Then, we can use this information to label our coordinate pairs, place them into the slope formula, and solve for m.

[tex]m=\frac{-1-5}{8-4}\\\\m = \frac{-6}{4}\\\\\boxed{m=-\frac{3}{2}}[/tex]

Persephone is creating a flower garden in her back yard. If she needs 30 pounds of soil per square foot of the flower garden, how much soil will Persephone need to create her garden?

Answers

I might be wrong, but there’s not enough info to solve this. You know she needs 30 pounds per square foot, but how big is the garden in the first place?

Answer:

152

Step-by-step explanation:

Multiply 19 and 8

Find X. Need help ASAP

Answers

Answer:

A

Step-by-step explanation:

Given a tangent and a secant from an external point to the circle, then

the product of the external part and the whole of the secant is equal to the square of the tangent, that is

48(48 + x) = 60² = 3600 ( divide both sides by 48 )

48 + x = 75 ( subtract 48 from both sides )

x = 27 → A

dear friends answer is

x= 27

84 divide by 7 show all work

Answers

Answer:

12

Step-by-step explanation:

84÷7=12

you can check by multiplying 12x7=84

12

×7

84.

Answer:all you do is divide 84 by 7 which is the answer you should get is 12

A savings account rounds the amount of money deposited to the nearest hundredths place. After tax returns on April 15th, Mulan earned
exactly $239.1639 in retums.
How much money was deposited into the savings account?
A. $200
B. $239.16
C. 236.17
D. 239.164
E. I don’t know yet

Answers

Answer:

Step-by-step explanation:

What is 8c + 10b ÷ 7a if c = 10, b = 17, and a = 2. Please give a full and good explanation for a brainliest...​

Answers

Answer:

The answer is 92.14

Step-by-step explanation:

Plugin the variables: 8c + 10b ÷ 7a=> 8(10)+10(17)/7(2)Multiply the variables: 8(10)+10(17)/7(2)=> 80+170/14Divide due to order of operations: 80+170/14=> 80+12.14Add: 80+12.14=>92.14Final answer: 92.14

324 is the same as the sum of 144 and v

Answers

Answer:

v = 180

Step-by-step explanation:

324 = 144 + v

v = 324 - 144

v = 180

Answer:

v = 180

Step-by-step explanation:

The equation is basically 324 = 144 + v

Then you just solve the equation:

324 = 144 + v

-144 = -144

180 = v

Hope this is what you were looking for.

Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 mph, and the rest was along a highway, where his average speed was 60 mph. The drive took 8 hours. What distance, in miles did Minato drive along local roads?

Answers

Answer:

45 miles.

Step-by-step explanation:

Given that the:

Total distance covered = 390 miles

Total time = 8 hours

Let the distance covered along the local way = L

And the distance covered along the highway = H

Along with local way,

Speed = distance/ time

20 = L / T

T = L /20 .... (1)

Along the highway,

Distance covered H = 390 - L

Let the time = t

Speed = distance/time

60 = (390 - L)/t

t = ( 390 - L)/60

But total time = T + t

That is

8 = L/20 + (390 - L)/60

The LCM at right hand side will be 60

8 = ( 3L + 390 - L )/60

Cross multiply

480 = 2L + 390

Collect the like terms

2L = 480 - 390

2L = 90

L = 90/2

L = 45 miles.

Therefore, the distance Minato drive along local roads is 45 miles

(7x+5)/(6) write the fraction as a sum or difference

Answers

Answer: Factor the numerator and denominator and cancel the common factors.

7x/6+5/6

Step-by-step explanation:

hello, if you’re feeling generous today please lend a hand!! thank you

Answers

Answer:

[tex]x \leqslant 2[/tex]

Step-by-step explanation:

The point is shaded which means its is equal to and since the arrow goes to the left it is less than. Therefore x is less than or equal to 2

Df = 9x -39 find EF.
DE =47

Answers

Greetings from Brasil....

Looking at the figure we can say that:

DF = DE + EF

DF = 9X - 39

DE = 47

EF = 3X + 10

inserting these data in the 1st expression....

DF = DE + EF

9X - 39 = 47 + (3X + 10)

9X - 39 = 47 + 3X + 10

9X - 3X = 57 + 39

6X = 96

X = 96/6

X = 16

EF = 3X + 10 anb X = 16, so

EF = 3·16 + 10

EF = 48 + 10

EF = 58

-14 = x - 12 PLS help ASAP and show checked solution

Answers

Answer:

The correct answer is x = -2.

Step-by-step explanation:

To solve this equation, we must remember that it is our end goal to get the variable x alone on one side of the equation.

To do this, our first step should be to add 12 to both sides of the equation to cancel the -12 on the right side.  This is modeled below:

-14 + 12 = x - 12 + 12

If we add together the like terms to simplify, we get:

-2 =x

This is our answer. To check that our answer is correct, we can plug in the value we obtained for x back into the original equation.

-14 = x - 12

-14 = -2 - 12

-14 = -14

Since plugging in our value for x yielded a true statement, we can conclude that our answer is correct.

Hope this helps!

The number 650,000 written in scientific notation would be _____. 6.5 × 10 -5 6.5 × 10 5 65 × 10 4 0.65 × 10 -6

Answers

Answer:

6.5 * 10 ^5

Step-by-step explanation:

650,000

Scientific notation is of the form

a * 10 ^b where a is between 1 and less than 10

Move the decimal 5 places to the left

6.50000

5 becomes the exponent b,  since we moved it to the left, the exponent is positive

6.5 * 10 ^5

Answer:

the answer is:6.5times 10to the power of 5

which two numbers does sqrt 128 lie between

Answers

It’s 10 and 12 because it’s 11 but it’s a decimal that goes on longer than 5 times hope this makes sense

Evaluate 4
M-n if m= -7 and n = 2.

Answers

Answer:

-30

Step-by-step explanation:

I'm assuming the equation is [tex]4m-n[/tex]. If it is not please tell me.

If we know the values of m and n, we can just substitute inside the expression.

[tex]4(-7) - 2\\\\-28 - 2\\\\-30[/tex]

Hope this helped!

Maureen took a train from Chesterton to Riverside by way of Watertown and Salem. The train went 8 kilometers from Chesterton to Watertown. It was 2 kilometers from Watertown to Salem and 3 kilometers from Salem to Riverside. How many kilometers was Maureen's train ride?

Answers

Answer:

hi......

.

........

........

Distribute: -3(x+2)
-3x + 2
-3x + 6
-3x - 6
X-1

Answers

Answer:

it would be -3x-6

Step-by-step explanation:

if you distribute right you will change the two and the positive change into a negative and the last one x is not by itself plus it only change to one

Mia climbs 2/5 of the height of the rock wall. Lee climbs 3/8 of Mia's distance. What fraction of the wall did Lee climb?

Answers

Answer:

you got this

Step-by-step explanation: be a smart person like you are

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