Find the real roots of
[tex] \frac{18}{ {x}^{4} } + \frac{1}{ {x}^{2} } = 4[/tex]
Answers
see the photos above given
![Find The Real Roots Of [tex] \frac{18}{ {x}^{4} } + \frac{1}{ {x}^{2} } = 4[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/NsNFF5aVXjmdsqi828qQGUgh1sQxczRO.jpeg)
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
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
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.
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:
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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:
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
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
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
NEED HELP ASAP!!! find the measure of the angle BXE
Answers
Answer:
110 Degrees
Step-by-step explanation:
Subtract 150 from 40
Divide.
-4 4/5 divided by 4
Answers
Answer:
-1 1/5
Step-by-step explanation:
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.
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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
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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
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).
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
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
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.
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:
Solve the equation. Chec)
5m - l = 4m + 5
Answers
Answer:
m=6
Step-by-step explanation:
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
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]
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
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
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
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
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 :)
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.
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
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.
What's the greatest common factor of 26 and 104 (gcf)