Answer:
Step-by-step explanation:
Given is a rational algebraic expression in x as
[tex]\frac{5x+2}{x^4-4x^2}[/tex]
First let us factorize the denominator.
[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]
Let the given term be
[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]
Equate the numerator to get
[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]
Substitute x =-2
[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]
Now substitute x =2
We get
[tex]16C=12\\C=\frac{3}{4}[/tex]
Put x=0
[tex]-4B=2\\B=\frac{-1}{2}[/tex]
Next equate X cube terms to 0 on right side
[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]
Hence partial fraction is
[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]
To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Explanation:To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.
To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.
Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
The size of a television is given by the length ofthe diagonal of the screen. the ratio of the height to the width of wide flat-screen tv is 8:15. find expressions for the width and height of a wide-screen tv in terms of the length of its diagonal.\
A technician is launching fireworks near the event of a show. Of the remaining 11 fireworks, 4 are blue and 7 are red. If she launches 6 of them what’s the probability that 2 of them will be blue
[tex] \displaystyle
|\Omega|=\binom{11}{6}=\dfrac{11!}{6!5!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\
|A|=\binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6\\\\
P(A)=\dfrac{6}{462}=\dfrac{1}{77}\approx1\% [/tex]
An organization will give a prize to a local artist. The artist will be randomly chosen from among 10 painters, 3 sculptors, and 5 photographers. What is the probability that the artist chosen will be a sculptor or a photographer?
The probability is 8/18 or 44%.
Since there are 3 sculptors and 5 photographers, and the question is asking for either a sculptor or photographer, you add them together. There are a total of 18 artists, and the probability is the chance of a certain thing happening over the total amount of things that can happen (i.e. a coin landing on heads is 50%).
The answer would be 8/18.
Use Euler’s Formula to find the number of edges in a polyhedron with seven faces: two pentagons and five rectangles.
To determine the number of edges in a polyhedron with seven faces, two being pentagons and five being rectangles, you apply Euler's formula, resulting in a total of 15 edges.
To find the number of edges in a polyhedron with seven faces using Euler's formula, which is V - E + F = 2, we first need to determine the number of vertices (V) and faces (F) of the polyhedron.
Given that the polyhedron has two pentagons and five rectangles, we can calculate the total number of vertices. Each pentagon has 5 vertices and each rectangle has 4, but since rectangles share sides, some vertices will be counted twice.
Therefore, for the rectangles, we should calculate the vertices as if there were four distinct ones and then subtract the overlaps. Assuming all rectangles share exactly one side with its adjacent, we would have 4 vertices for each rectangle minus 2 for each shared side, resulting in 2 vertices per rectangle.
With five rectangles, that's 10 vertices, plus the 10 from the two pentagons, we get 20 vertices in total. Now, we apply Euler's formula: V - E + F = 2, substituting the values:
E = V - F + 2
E = 20 - 7 + 2
E = 15
Therefore, the polyhedron has 15 edges. .
The area of the sector formed by the 110 degree central angle is 40 units squared what is the radius
Which solid has a volume that is 3 times the volume of a cone with the same base and height?
a.cylinder
b.prism
c.pyramid eliminate
d.sphere?
What percent of data set is represented in Q1
Fórmula para sacar el área de un circulo
What is y+7/7y÷3y^2+21y/14y−5 simplified?
PLS HELP ME ASAP WITH THESE! THANKS!!
(Brainliest will be given hopefully)
(Random answers gets moderated.)
You and your friend Sam are going to paint your 300 square feet room together.
Sam takes 10 minutes to paint 25 square feet.
You take 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take us 15 minutes to paint 50 square feet!''
Write a EXCEPTIONAL explanation to convince Sam that he is wrong. Thank You.
On Monday, there was no snow on the ground in Buffalo, New York. On Tuesday, three inches of snow fell.On Wensday a half an inch of snow melted. On Thursday two and a half more inches fell. On Friday another inch and a half melted. How much snow was left on the ground Friday night.
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. Another flower is then chosen at random and given to a different woman. What is the probability that both flowers are pink roses?
100 points! Evaluate the equation. Look at the picture. Do #7.
The ratio of men to women working for a company is 4 to 5. if there are 52 men working for the company, what is the total number of employees?
Prove that x²+6x+18 is always greater than
[tex]2 - \frac{1}{x} [/tex]
For any value of x.
1. What is the value of x in the equation –6 + x = –2?
A. 4
B. –8
C. 8
D. –4
2.
How many solutions does the equation –3a + 3a + 6 = 7 have?
A. Infinitely many
B. Two
C. One
D. None
3.
What is the solution to the equation 1.2m – 0.8 = –2.0m?
A. m = 0.25
B. m = 4
C. m = 1
D. m = 0.4
4.
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have?
A. Two
B. Infinitely many
C. None
D. One
5.
What is the value of y in the equation 2(2y – 12) = 0?
A. 4
B. 8
C. 7
D. 6
6.
What is the value of z in the equation 2(4z – 9 – 7) = 166 – 46?
A. 19
B. 34
C. 26
D. 21
7.
Which of these is a simplified form of the equation 7y + 7 = 9 + 2y + 2y?
a vertical pole 10 meters high, casts a shadow 8 meters long. at the same time, a nearby tree casts a shadow 40 meters long. find the height of the tree in meters
Jesse made a model of a mountain range for class. to do this, he bought a cylinder of cardboard and cut it into three cones. each cone is 5 inches tall and has a diameter of 4 inches. what was the volume of the original cylinder jesse bought in terms of \piπ?
The volume of the original cylinder that Jesse bought is 20π cubic inches.
To find the volume of the original cylinder Jesse bought, we need to use the volume formula for a cylinder:
V = πr²h
First, we need to find the volume of each cone using the formula:
Volume of a cone = (1/3)πr²h
Given:
Height(h) of each cone = 5 inchesDiameter of each cone = 4 inches, so the radius(r) = 4/2 = 2 inchesVolume of one cone:
V_cone = (1/3)π(2)²(5) = (1/3)π(4)(5) = (20/3)π cubic inches
Total volume of three cones:
V_total_cones = 3 × (20/3)π = 20π cubic inches
Since the volume of the cylinder equals the total volume of the cones:
V_cylinder = 20π cubic inches
In which quadrant of the coordinate plane is (-2a - 3, -3b - 5), if a = -3 and b = 3?
After substituting a = -3 and b = 3 into the point (-2a - 3, -3b - 5), we get the point (3, -14), which lies in the fourth quadrant of the coordinate plane.
To determine in which quadrant of the coordinate plane the point (-2a - 3, -3b - 5) is located, we substitute the values a = -3 and b = 3 into the coordinates. First, for the x-coordinate we have:
-2(-3) - 3 = 6 - 3 = 3
And for the y-coordinate:
-3(3) - 5 = -9 - 5 = -14
The resulting point is (3, -14), which is located in the fourth quadrant because the x-value is positive and the y-value is negative.
hELPP
A total of 300 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adults tickets sold. How many adult tickets were sold?
By setting up and solving an equation, it was determined that 75 adult tickets were sold for the school play.
To solve the problem of determining how many adult tickets were sold for the school play, we can set up an equation. Let's represent the number of adult tickets sold as A, and since the number of student tickets sold was three times that of adult tickets, we can express the student tickets sold as 3A. We know the total tickets sold were 300, so the equation to represent this scenario is:
A + 3A = 300
Combining like terms, we get:
4A = 300
Dividing both sides of the equation by 4 to solve for A gives us:
A = 300 / 4
A = 75
Therefore, 75 adult tickets were sold.
write an inequality for the following situation
No more than 8 books are in your bag
A. x ≤ 8 B. x < 8 C. x ≥ 8 D. x > 8
A pizza shop offers 12 different topping choices. if you order a large pizza with two toppings, how many possibilities would you have?
Write the first 6 terms of an arithmetc sequence if the first number is 9 and the common diffrence is 5
The probability that the Cubs win their first game is 1/3. The probability that the Cubs win their second game is 3/7. What is the probability that the Cubs win games?
The correct answer is:
1/7.
Explanation:
The two events, the Cubs winning their first game and the Cubs winning their second game, are independent. This is because the Cubs winning their first game does not affect the probability of the Cubs winning their second game.
Since the events are independent, to find the probability that both events occur, multiply the probabilities:
1/3(3/7) = (1*3)/(3*7) = 3/21 = 1/7
If the exchange rate changes from $1.45 = 1 euro to $1.37 = 1 euro, then
Find the possible values of the included angle of a triangle with: A) sides of length 5 cm and 8 cm, and area of 15 cm^2
B) sides of length 45 km and 53 km, and area 800 km^2.
Ok My last 2 questions please!!!
What is compound interest?
A - the interest earned on the principal of an investment
B - the interest earned on both the principal and interest of an investment or savings account
C - the interest earned on a mutual fund
D - the interest earned on a loan
The correct answer is
The interest is earned on the principal and interest earned previously
:)
Factor this trinomial.
x2 – 8x + 15
A. (x – 1)(x – 15)
B. (x – 3)(x + 5)
C. (x – 3)(x – 5)
D. (x – 1)(x + 15)
To factor x^2 -8x + 15, we find two numbers that multiply to get 15 and add to get -8. These two numbers can be -5 and -3. Therefore, this factors as
x^2 - 8x + 15 = (x-5)(x-3)