Find the real roots of
[tex] \frac{18}{ {x}^{4} } + \frac{1}{ {x}^{2} } = 4[/tex]

Answers

Answer 1

see the photos above given

Find The Real Roots Of [tex] \frac{18}{ {x}^{4} } + \frac{1}{ {x}^{2} } = 4[/tex]
Answer 2

Answer:

[tex]$x^2=\frac{9}{4} \implies x=\pm \frac{3}{2} $[/tex]

[tex]$x^2=-2 \implies x=\pm\sqrt{-2} \implies x=\pm\sqrt{2i} $[/tex]

The solutions are

[tex]$\{-\frac{3}{2},\frac{3}{2}, -\sqrt{2i}, \sqrt{2i} \}$[/tex]

The Real roots are

[tex]$\{-\frac{3}{2},\frac{3}{2}\}$[/tex]

Step-by-step explanation:

[tex]$\frac{18}{x^4} +\frac{1}{x^2}=4$[/tex]

Multiply both sides by [tex]x^4[/tex]

[tex]$x^4\frac{18}{x^4} +x^4\frac{1}{x^2}=4\cdot x^4$[/tex]

[tex]$18+x^2=4x^4$[/tex]

[tex]4x^4-x^2-18=0[/tex]

Substitute [tex]x^2=t[/tex]

[tex]4t^2-t-18=0[/tex]

Solving the quadratic equation using the quadratic formula:

[tex]$t=\frac{-(-1)\pm \sqrt{(-1)^2-4\cdot 4(-18)}}{2\cdot 4}$[/tex]

[tex]$t=\frac{1\pm \sqrt{289}}{8}$[/tex]

[tex]$t=\frac{1\pm 17}{8}$[/tex]

[tex]$t_1=\frac{9}{4}$[/tex]

[tex]t_2=-2[/tex]

Now we have to solve for [tex]x^2=t[/tex]

[tex]$x^2=\frac{9}{4} \implies x=\pm \frac{3}{2} $[/tex]

[tex]$x^2=-2 \implies x=\pm\sqrt{-2} \implies x=\pm\sqrt{2i} $[/tex]


Related Questions

Solve to 3 s.f and in scientific notation (5.11×10^-4)+(4.33×10^-3)

Answers

Answer:

0.00484

Step-by-step explanation:

What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14? (5 points)

Answers

Answer:

x= -1

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

3x+2(x-9)=8x+x-14 ;; equation

simplify the equation to the form

3x+2(x-9)=8x+x-14

reorder the terms in parentheses

3x+(+2x-18)=8x+x-14

remove unnecessary parentheses

+3x+2x-18=+8x+x-14

move all terms containing x to the left and all other terms to the right.

+3x+2x-8x-1x=-14+18

simplify left and right side of the equation.

-4x=+4

divide both sides of the equation by -4 to get x.

x=-1

the residents of the state of texas pay an 8.25% sales tax on most purchases.which decimal represents the texas state sales tax?
A) 0.825
B)0.00825
C)0.0825
D)8.250

Answers

0.0825 because you move 2 to the left
C is correct answer

A student studied the sleeping habits of senior at his high school as 34 randomly selected seniors how many hours of sleep they got the previous night

Answers

Are there any more variables or options?


For f(x) = -3x - 5, find f(-11). Explain what f(11) really means for the problem ?? Need this in like the next 4 hours please!!!!

Answers

Answer:

for -11, 28. for 11, -38

Step-by-step explanation:

Typos in your question. can't tell if you need -11 or pos 11

-3(-11)-5 = 33-5= 28

-3(11)-5 = -33-5 = -38

Solve the equation. Chec)
5m - l = 4m + 5

Answers

Answer:

m=6

Step-by-step explanation:

M=6

5m-4mv5+1

M=5+1

M=6

Brainliest?

through: (-2,-2), slope = 1/2

Write the slope-intercept form of the equation of the line through the given point with the given slope.​

Answers

Answer:

The answer is

[tex]y = \frac{1}{2} x - 1[/tex]

Step-by-step explanation:

To find an equation of a line given a point and slope we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question the point is (-2,-2) and slope = 1/2

The equation of the line is

[tex]y + 2 = \frac{1}{2} (x + 2) \\ y + 2 = \frac{1}{2} x + 1 \\ y = \frac{1}{2} x + 1 - 2[/tex]

We have the final answer as

[tex]y = \frac{1}{2} x - 1[/tex]

Hope this helps you

What is 88.2 rounded to the nearest whole number?​

Answers

Answer:

88

Step-by-step explanation:

if the decimal is below 5 then round down

Answer:

88

Step-by-step explanation:

2 is less than 5, therefor it would be rounded to 88. If a number higher than five or five was in two's place it would be rounded to 89.

how do i solve this? 12x÷100+35000minus 14x ÷100​

Answers

Answer:

-2x/100 + 35

Step-by-step explanation:

Step 1:

12x ÷ 100 + 35,000 - 14x ÷ 100

Step 2:

- 2x ÷ 100 + 35,000 ÷ 100

Step 3:

- 2x ÷ 100 + 35

Answer:

- 2x/100 + 35

Hope This Helps :)

The graph below represents the solution set of which inequality? x2 – 2x – 8 0 x2 + 2x – 8 > 0

Answers

Answer: x^2+2x-8<0

Step-by-step explanation:

A. x^2 - 2x - 8 < 0

(x - 4)(x + 2) < 0

B. x^2 + 2x - 8 < 0

(x + 4)(x - 2) < 0

C. x^2 - 2x - 8 > 0

(x - 4)(x - 2) > 0

D. x^2 + 2x - 8 > 0

(x + 4)(x - 2) > 0

When you test a point in the interval between -4 and 2, for example 0, it is negative.

[tex]x^2+2x-8 < 0[/tex] represents the given solution set.

What is known as inequality?

A mathematical expression in which left hand side is not equal to right hand side is known as inequality.

The given solution set is x>-4 and x<2

Option A: [tex]x^2-2x-8 < 0[/tex]

(x+2)(x-4)<0

x<-2 and x<4

Option B: [tex]x^2+2x-8 < 0[/tex]

(x-2)(x+4)<0

x<-4 and x<2

Option C: [tex]x^2-2x-8 > 0[/tex]

(x+2)(x-4)>0

x>4 and x>-2

Option D: [tex]x^2+2x-8 > 0[/tex]

(x-2)(x+4)>0

x>-4 and x>2

Hence, [tex]x^2+2x-8 < 0[/tex] represents the given solution set.

Learn more about inequality here:

https://brainly.com/question/16792145

#SPJ2

Two vertices of an equilateral triangle are located at (2, 0) and (–2, –3). What is the triangle’s perimeter?​

Answers

Answer:

15

Step-by-step explanation:

one side is equal to 5. So 5 ×3

A piece of charcoal was unearthed at an archeological site and found to contain 10% of its original carbon-14. The half-life of carbon-14 is 5,730 years. Which equation can be solved to determine the age of the charcoal?

0.10Ao = Aoe0.000121t
Ao = 0.10Aoe0.000121
0.10Ao = Aoe –0.000121t
Ao = 0.10Aoe –0.000121t

Answers

Answer:

It is C

Step-by-step explanation:

Got it right in edg

Answer:

A piece of charcoal was unearthed at an archeological site and found to contain 10% of its original carbon-14. The half-life of carbon-14 is 5,730 years. This means that after 5,730 years, only half of the original amount of carbon-14 will remain.  Which equation can be solved to determine the age of the charcoal?

C on edg

Step-by-step explanation:

What type of angles are ECH and FCG?

Answers

ECH is an acute angle.

FCG is also an acute angle.

Answer:

Vertical angles

Step-by-step explanation:

Vertical angles are angles formed by two intersecting lines, which the angles are facing the opposite direction. Also the angles are on the same vertice (point).

y=1/4x + 8 what would be the slope and the y-intercept

Answers

Answer:

y= 1/4x + 8

comparing with

y= mx + c

slope = 1/4

for y intercept x=0

y=8

Step-by-step explanation:

The slope of the line is 1/4, The y-intercept is 8.

In the equation y = (1/4)x + 8, the coefficient of x is 1/4. This coefficient represents the slope of the line.

Therefore, the slope of the line is 1/4.

The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this equation, the y-intercept is the value of y when x is 0. By substituting x = 0 into the equation, find the y-intercept.

y = (1/4)(0) + 8

= 0 + 8

= 8

Hence, the y-intercept is 8.

To know more about line here

https://brainly.com/question/30003330

#SPJ6

The height of a tree is 38 inches. After 4 years, the height is 9 feet 10 inches. How many inches did the tree grow each year?

Answers

The tree grows linearly, then the tree grows each year will be 20 inches.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The height of a tree is 38 inches.

After 4 years, the height is 9 feet 10 inches.

1 ft = 12 inches

9 ft = 180 inches

Then 9 ft and 10 inches will be

→ 108 + 10

→ 118 inches

The tree grows in 4 years and will be

→ 118 - 38

→ 80 inches

Let the tree grows linearly, then the tree grows each year will be

→ 80 / 4

→ 20 inches

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

m∠1 = 65°, what is m∠2?

Answers

Answer:

m∠2=65

Step-by-step explanation:

They are corresponding angels which means they are congruent.

11. Solve by completing the square.
- 10x = 5x^2-1

Answers

Answer:

x = (√6/√5) - 1

Step-by-step explanation:

- 10 x = 5x^2 -1

can be written as

5x² + 10x - 1 = 0

completing the square method :

for quadratic equation of the format ax² + bx + c = 0 ,

step 1, divide equation by a

therefore. dividing the equation by 5

=> x² + 2x - (1/5) = 0

=> x² + 2x = 1/5

c - 2b/4 = -1/5 - (2(2)/4) = -(6/5)

b/2 = 1

=> x² + 2x +1 = 6/5

=> (x + 1)² = 6/5

=> x = (√6/√5) - 1

If a given area of a square is 24cm2, estimate the length of one side of the square?

Answers

Answer:

2√6cm

Step-by-step explanation:

Area = L×L

A=L2

24 =L2

√24 =√L2

2√6= L

:.L =2√6.cm.

What's the greatest common factor of 26 and 104 (gcf)

Answers

I’m not completely sure if this is right but I think it is 26

Write algebraic expressions for this word phrase.
The sum of ¾ of a number and 7.

Answers

Answer:

¾x + 7

Step-by-step explanation:

"The sum of": Addition expression

"¾ of a number": ¾x

"and 7": + 7

Combine them all and you get ¾x + 7

NEED HELP ASAP!!! find the measure of the angle BXE

Answers

Answer:

110 Degrees

Step-by-step explanation:

Subtract 150 from 40

Find the midpoint of the line segment joining the points (-1,-2) and (-3,13)

Answers

The answer is (-2,5.5)

Step-by-step explanation:

Hope this helps

Using a spinner, conduct an experiment to compare experimental probability with theoretical probability.

Answers

The probability of an event is a number from 0 to 1 that measures the chance that an event will occur. In this lesson, we will look into experimental probability and theoretical probability.

The following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions.

he following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions.

Experimental vs Theoretical Probability

How to find the Experimental Probability of an event?

Step 1: Conduct an experiment and record the number of times the event occurs and the number of times the activity is performed.

Step 2: Divide the two numbers to obtain the Experimental Probability

How to find the Theoretical Probability of an event?

The Theoretical Probability of an event is the number of ways the event can occur (favorable outcomes) divided by the number of total outcomes.

The perimeter of a rectangle is 22 inches. Find the dimensions if its length is 3 inches greater than its width.

Answers

Answer:

Length: 7

Width: 4

Step-by-step explanation:

We can create a system of equations for this problem, where [tex]w[/tex] is the width and [tex]l[/tex] is the length.

The perimeter of a rectangle is twice its length added to twice its width.

[tex]2l+2w=22[/tex]

The length is 3 more than the width:

[tex]l = w+3[/tex]

We can now substitute in [tex]w+3[/tex] as [tex]l[/tex] in the equation [tex]2l+2w=22[/tex].

[tex]2(w+3) + 2w = 22[/tex]

Distribute the first terms:

[tex]2w+6+2w=22[/tex]

Combine like terms:

[tex]4w+6=22[/tex]

Subtract 6 from both sides:

[tex]4w=16[/tex]

Divide both sides by 4:

[tex]w = 4[/tex]

Now we know that w = 4. We can now substitute this inside an equation to find [tex]l[/tex].

[tex]l = w+3\\\\l = 4+3\\\\l=7[/tex]

Hope this helped!

Answer:

What the other guy said XDDDDDDDDDD

Step-by-step explanation:

I'm awesome =D

A map has a scale of 1 inches : 10 miles. Use the given map distance to find the actual distance.





15 miles


12 miles


30 miles


39 miles

A map has a scale of 1 inch : 5 kilometers. Use the given actual distance to find the map distance.







14.4 inches


9.25 inches


68 inches


20.3 inches

Answers

Answer:

  A) inches: 1.5, 1.2, 3.0, 3.9

  B) km 72, 46.25, 340, 101.5

Step-by-step explanation:

A) To find the distance in inches, divide by 10 miles:

  15 miles ⇒ 1.5 inches

  12 miles ⇒ 1.2 inches

  30 miles ⇒ 3.0 inches

  39 miles ⇒ 3.9 inches

__

B) To find the distance in km, multiply the map distance by 5.

  14.4 in ⇒ 72 km

  9.25 in ⇒ 46.25 km

  68 in ⇒ 340 km

  20.3 in ⇒ 101.5 km

Help quick !! Will give brainliest

Answers

1. 5/6

2. 7/8

3. 1/2

4. 5/4

5. 4/5

6. 5/4

7. 11/12

8. 5/4

9. 11/12

10. 2/3

11. 13/20

12. 1/12

13. 7/22

14. 7/18

15. 2/3

16. 5/12

17. 5/12

18. 3/8

What x value makes this equation true -12x - 2(x+9) = 5(x+4)

A. -2
B. 13/19
C. 5
D. -1/3

Answers

Answer:

A. -2, x= -2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

- 12x - 2(x + 9) = 5(x + 4) ← distribute parenthesis on both sides )

- 12x - 2x - 18 = 5x + 20 , that is

- 14x - 18 = 5x + 20 ( subtract 5x from both sides )

- 19x - 18 = 20 ( add 18 to both sides )

- 19x = 38 ( divide both sides by - 19 )

x = - 2 → A

what is good for your health

Answers

Answer:

Exercise, 8 hrs of sleep, healthy diet with lots of fruits and vegetables are all good for your health

Step-by-step explanation:

1. Find the slope of the line containing the points (9,6) (11,9).

Answers

Answer:

[tex]y=\frac{3}{2}x-\frac{15}{2}[/tex]

Step-by-step explanation:

Use the point-slope formula [tex]y-y_{1}=m(x-x_{1})[/tex]

First you have to find m with the formula [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

[tex]m = \frac{9 - 6}{11 - 9} = \frac{3}{2}[/tex]

Choose whichever point you want as [tex](x_{1}, y_{1})[/tex], in this case I'll choose [tex](9, 6)[/tex]

[tex]y - y_{1} = m(x - x_{1})\\y - 6 = \frac{3}{2} (x - 9)\\y - 6 = \frac{3}{2}x - \frac{27}{2} \\y = \frac{3}{2}x - \frac{27}{2} + 6\\y = \frac{3}{2}x - \frac{15}{2}[/tex]

Divide.

-4 4/5 divided by 4

Answers

Answer:

-1 1/5

Step-by-step explanation:

-1.2 or -1 1/5 is ur answer!!
Other Questions
At which stage of development does the embryo implant in the uterus? use the word magnanimity in a complex sentence. Both Navajo and Apaches were known for _____________a.skill in using weapons.b.taking scalps, horses, and food.c.raiding pueblos, Spaniards, and Mexican inhabitants.d.all of the above. 2(y + 5) = 18 - 122y + 10 = 18 - 122y + 10 = 6- 10 -10222y = -2 What is the name of this method ? The elements are the words; the principles are the syntax. Explain this qoutation. what resources did Margaret Hutchinson Rousseau use ? An 8ft length of 4 inch wide crown molding costs $14. How much will it cost to buy 56 ft of crown molding? 1Select the correct text in the passage.Which two words are domain-specific words?In the 1860s, a fossil of an avian or flying dinosaur known as Archaeopteryx was found. Scientists identified it as a combination of bird and reptile. This discovery led to the theory that birds have evolved from carnivorous avian dinosaurs. Archaeopteryx lived in the southern region of Germany during the Late Jurassic period when Germany had a tropical climate.Reset Next Three sixth-grade students competed in the 100-meter dash. The table shows their times.Which list shows the times in order from least to greatest?StudentTime (seconds)13.1TianaJames13.2Dakota12.9A. 13.2, 13.1, 12.9B. 12.9, 13.2, 13.1OC. 12.9, 13.1, 13.2OD. 13.1, 13.2, 12.9 what did the author find in a junk shop? why Newtown made the laws of motion The length of the line? What is Marxism? I need help writing a paragraph about what it is. Is fish cheeks the article on commitlit, positive, neutral, or negative? (Tone) Please Help!! 10 Points! Brainliest Answer Which of the following is equivalent to the given equation 7x2 = 98x - 343a(x+4)(x-3)(x-7)b(x-6)(x+7)d What is Upton Sinclair known for doing?exposing poor conditions in the meat packing industryforming alliances that helped farmers with their credit problemsfounding progressive organizations in the late 1800sserving as mayor of Chicago Write in Spanish what do we have in the classroom, in a complete sentences, more than 50 words The correlation coefficient r between an employees age, x, and yearly salary, y, is 0.633. What percent of the variation in yearly salaries can be explained by differences in the employees ages? 31.7% 63.3% 15.8% 40.1% What did the US Constitution do to the goals that were set in the Declaration ofIndependent