this is for 8th grade pls answer .​

This Is For 8th Grade Pls Answer .

Answers

Answer 1

Step-by-step explanation:

We have that

[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]

We are trying to find the number value so that we can apply in the later equation.

Qe first simplify.

Remeber that

[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]

Also remeber that

[tex] \frac{1}{x} = {x}^{ - 1} [/tex]

so

[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]

We then simply remeber that x^0=1 so

[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]

Multiply both sides by x^2.

[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]

Subtract both sides by 3x^2

[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]

Notice that x^4= (x^2)^2.

So our reformed equation is

[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]

Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.

[tex]w {}^{2} - w + 1 = 0[/tex]

Now we use the quadratic formula

[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

and

[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Let a=1 b=-1 and c=1.

[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]

[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]

Now, we get

[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]

Now since we set both of these to the x^2 we solve for x.

and

[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]

We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is

[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]

and

[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]

Next we take the sqr root of 1 which is 1, and divide the degree by two.

[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]

and

[tex]x = 1( \cos(150) + i \: sin(150)[/tex]

We are asked for the 2nd root so just add 180 degrees to this and we have

[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]

and

[tex]x = 1( \cos(330) + i \: sin(330)[/tex]

which both simplified to

[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

and

[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

Now we must find

x^18+x^12+x^6+1.

We just use demovire Theorem. Which is a complex number raised to the nth root is

[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]

So let plug in our first root.

[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]

To save time we multiply the angle and use rules of terminals angle and we get

[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]

And we get

[tex] - 1 + 1 + - 1 + 1 = 0[/tex]

So one of the answer is x=0

And the other, let see

[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]

[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]

We get

[tex] - 1 + 1 + 1 + 1 = 2[/tex]

So our answer are 2.

So the answer to the second part is

0 and 2.


Related Questions

Here is a free 100 points annnnd brainliest

This question is about strategy
Skill
Precision


Alr here it is:
Problem one: Molly bought and infinite amount of bottles of dish soap. She had an infinite amount of money. When she bought the dish soap, she lost all of it.

How is this possible?

Problem one (part two): Molly then called her friend Blitzo over. Blitzo then gave Molly and infinite amount of money without losing all of his money.

How is this possible

If you have questions or want hints, ask in comments below this question

Answers

1. She bought the infinite dish soap with her money

2. you can't lose anything infinite

3. remeber our deal? brainliest pls.

The nth term of the sequence 27,37,47

Answers

Answer: The 9th term of the sequence 27,37,47 is 107.

Which expression has a sum of 1 2/21

A. 3/7 + 2/3
B. 4/7 + 1/3
C. 5/7 + 2/3
D. 6/7 + 1/3

Answers

Answer:

A. is the answer

Step-by-step explanation:

the LCM of 7 and 3 is 21.

When added it would be 9+14 =23

23/21= 1 2/21

what is the value of x? 48°(3x + 6)

Answers

Answer:

No clue

Step-by-step explanation:

BRAINLIEST 87x89 PLEASE

Answers

Answer:

7743 caught you again lolllll

=7743

Hope you find this helpful!
Brainliest and a like is much appreciated!

does anyone have an answer to this question?

Answers

Answer:

8.9 cm to 1 dec. place.

Step-by-step explanation:

First, use Pythagoras to find the length of BD.

BD^2 = 6^2 + 7^2 = 85

BD = √85.

BM = √85 / 2.

Consider the triangle TBM, by Pythagoras:

TB^2 = BM^2 + MT^2

MT^2 = 10^2 - (√85 / 2  )^2

= 100 - 21.25

= 78.75.

MT = 8.874

(-x + 3) + (4x - 10)

Answers

the correct answer is 3x-7
this is so simple, 3x-7

Cynthia gave 1/5 of her toys to her little sister. If she had 25 toys, how many did she give away?

Answers

Answer:

25*1/5(or 0.2)=

5

she gives a way 5 toys

Hope This Helps!!!

The number of toys that she gives away will be 5.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Cynthia gave 1/5 of her toys to her little sister.

If she had 25 toys.

Then the number of toys that she gives away will be given by the product of 25 and 1/5.

⇒ 25 x 1 / 5

⇒ 5

The number of toys that she gives away will be 5.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

the two triangles below are similar.

Answers

Answer:

Step-by-step explanation:

yes they are just a rotated triangle

Someone please help

Answers

i would guess the answer is 1 since that’s where b is on the other side

evaluate the expression 16.78-12.237​

Answers

Answer: The answer to the expression is 4.543.

Answer : 4.543

Step-by-step explanation :

First step, subtract . . . what is 16.78 minus 12.237​ ? 4.543

Eric scored 95% on his math test. He got 19 problems correct. How many questions were on the test?

Answers

i'm pretty sure it's 20.

A motor-boat takes the same time to travel 80 miles downstream as it takes to travel 60 miles upstream. If the speed of the stream is 5 miles/hr, find the speed of the motor-boat in still water.

Answers

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the motor boat in still water and t represent the time. Hence for downstream:

a + 5 = 80/t

t = 80/(a + 5)

For upstream:

a - 5 = 60/t

a - 5 = 60 / (80/(a + 5))

a - 5 = 0.75a + 3.75

0.25a = 8.75

a = 35 miles per hour

The speed of the motor-boat in still water is 35 miles per hour.

Find out more on speed at: https://brainly.com/question/751218

If tanx = 0.75, what is the value of cosx + sinx ?

Answers

cosine (x) = 4 over 5
cos
(
x
)
=
4
5
Explanation:
First you must apply sohcahtoa
it means
sine = opposite side over hypotenuse
sine = opposite/hypotenuse
cosine = adjacent side over hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite side over adjacent side
tangent = opposite/adjacent
then
solve the unknown by applying the Right Triangle Theorem.
draw a right triangle.
label the parts where
a
is the opposite side
b
is the adjacent side
c is the hypotenuse
Solve the unknown. The hypotenuse using
a
2
+
b
2
=
c
2

since the given
tan
x
=
3
4

it means
tan = opposite/adjacent
a
= opposite side =
3

b
= adjacent side =
4

c
= hypotenuse = ??
a
2
+
b
2
=
c
2

substitute the value
(
3
)
2
+
(
4
)
2
=
c
2

9
+
16
=
c
2

25
=
c
2

get the square root of
25

it is equal to
5

therefore
c
=
5

c
= hypotenuse =
5

cos
= adjacent/hypotenuse
cos
(
x
)
=
4
over
5

cos
(
x
)
=
4
5

Answer:

theta is eq to 36.86 value is. 0.5998+0.8=1.399

how do you think I'm NOW

Answers

Answer:

u are u and u and u and u and u

Write 110% as a mixed number in simplest form.

110% = $$

Answers

Answer:

50

Step-by-step explanation:

What is this expression in simplest form?

Answers

Answer:

A. 1÷(X+1) (x-2)

some steps are directly

tag me in brainlist if you like it

solve (2x + 5)= (2x + 3)(2x - 1)

Answers

[tex](2x + 5)= (2x + 3)(2x - 1)\\<=>2x+5=4x^2-2x+6x-3\\<=>4x^2-2x+6x-3-2x-5=0\\<=>4x^2+2x-8=0\\<=>(4x+1-\sqrt{33})( 4x+1+\sqrt{33})=0 \\<=> x=\frac{-1+\sqrt{33} }{4} /or/x=\frac{-1-\sqrt{33} }{4}[/tex]

Answer:

x = -1± sqrt( 33)

    ----------------------------

             4

Step-by-step explanation:

(2x + 5)= (2x + 3)(2x - 1)

Distribute

2x+5 = 4x^2 +6x-2x-3

Combine like terms

2x+5 = 4x^2 +4x -3

Subtract 2x +5 from each side

0 = 4x^2 +4x-3-2x-5

Combine like terms

0 =4x^2 +2x -8

Using the quadratic formula

a=4  b=2  c=-8

x = -b± sqrt( b^2-4ac)

    ----------------------------

             2a

x = -2± sqrt( 2^2-4(4)(-8))

    ----------------------------

             2(4)

x = -2± sqrt( 4+128)

    ----------------------------

             8

x = -2± sqrt( 132)

    ----------------------------

             8

x = -2± 2sqrt( 33)

    ----------------------------

             8

x = -1± sqrt( 33)

    ----------------------------

             4

HELP ME OUT REAL QUICK!

Answers

Answer:

Step-by-step explanation:

ab abahha

PLEASE HELP!!! Can someone help me figure this out

Answers

Answer:

Step-by-step explanation:

x^2 = 5x + 24                                Transfer (subtract) 5x + 24 to the left.

x^2 - 5x - 24 = 5x-5x+24  -24

x^2 - 5x - 24 = 0                            This does factor. -8 and 3  are your factors.

(x - 8)*(x + 3) = 0

So if x - 8 = 0

then x - 8 + 8 = 0 + 8

x = 8

If x + 3 = 0

then x = - 3

Are these both correct?

x^2 = 5x + 24

x = 8

8^2 = 5*8 + 24

64 = 40 + 24

64 = 64

and x - 8 is a factor

x^2 = 5x + 24

x = - 3

(-3)^2 = 5 * -3 + 24

9 = -15 + 24

9 = 9

And x + 3 is a correct factor

GIVING BRAINLIEST. please help.


Answers

OK ILL HELP

Its the first option

Help me plz plz plz plz plz plz plz plz plz plz plz

Answers

It’s a ok sir so please put the answer

please help me with this

Answers

Answer: 3Z

Step-by-step explanation:

-2a
0b
-2
× -5b
4
× -b

Answers

Answer:

Step-by-step explanation:

Army DA administrative publications and forms by the Army Publishing Directorate APD. The latest technologies high quality electronic pubs and forms view ...

x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

Answers

Answer:

(x+1)^2*(x+2)*(x+3)

Step-by-step explanation:

(x+1)(x+2)(x+3)x.(x+1)

(x+1)^2*(x+2)*(x+3)

(x+3)

 (((x•(x+1))•(x+2))•—————)•(x+1)

                      x  

(x + 1) • (x + 2) • (x + 3) • (x + 1)

Multiply  (x+1)  by  (x+1)

PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT

Answers

Answer:

sin =5/3

tan = sin/cos= 3/5/5/3=1

Step-by-step explanation:

you haven't game me much to work with but sin= opp/adj and cos= adj/opp so there you go

10 A seal pup gains 28% of its birth weight each
day for the first 10 days of its life.
A one-day-old pup weighs 17.92 kg.
How much did it weigh at birth?

Answers

Answer:

WEIGHT

550 to 880 pounds

LIFESPAN

25 to 35 years

LENGTH

7.5 to 10 feet

THREATS

Entanglement, harassment, chemical contaminants, oil spills and energy exploration, vessel and vehicle interactions

REGION

New England/Mid-Atlantic

Step-by-step explanation:

Step-by-step explanation:

Hmm so a pup gains 28% weight every day for the next 10 days.. But a day old puppy weight 17.92kg sooo

28%+10every day=10.28

17.92-28%=12.9

17.92x10=179.2

Hmmmm

Well a seal pup weights 8-12kg on birth so ye I was right anweser is 12

What do the following two equations represent?
9-3 = 2(x – 3)
y+5 2(+ 1)
Choose 1 answer:
The same line
ons
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines
HELP

Answers

Answer:

Intersecting but not perpendicular

Step-by-step explanation:

Assuming you forgot to add the = between y+5 and 2(1)

Since there is a opposite single variable in either equation the lines will intersect but not be perpendicular

Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?

Answers

Answer:

B.

Step-by-step explanation:

Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?

She bought a total of 17 apples and lemons combined.

So the equation that would represent this is,

l + a = 17.

Each apple costs 35¢ and each lemon costs 15¢. All the lemons and apples cost $3.95 togther.

So the equation that would represent this is,

0.15l + 0.35a = $3.95

Find the factors of f(x) given that x = 5 is a zero.
f(x) = x3 − 6x2 − x + 30.

(x − 5)(x + 3)(x − 2)
(x − 5)(x − 3)(x + 2)
(x + 5)(x − 3)(x + 2)
(x + 5)(x + 3)(x − 2)

Answers

If x = 5 is a zero of the given polynomial, then,(x - 5) is a factor of the polynomial. [Since, x = 5 or, x - 5 = 0]Now, divide the polynomial with (x - 5) using long division method. (See the picture)We get (x^2 - x - 6) as the quotient.Now, factorise the above polynomial:(x^2 - x - 6) = (x^2 - 3x + 2x - 6) = x(x - 3) + 2(x - 3)= (x - 3)(x + 2)Therefore, x^3 − 6x^2 − x + 30 = (x − 5)(x − 3)(x + 2)

Answer:

B.(x − 5)(x − 3)(x + 2)

Hope you could get an idea from here.

Doubt clarification - use comment section.

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