Mathematics College

20 points Easy question
what is 5/20 simplify

Answers

Answer 1
1/4 or.25 or 0.25 is the answer
Answer 2
Hi there!

To simplify this question, we can just divide both sides of the fraction by 5. 

5 / 5 = 1
20 / 5 = 4

So, the fully simplified fraction would be 1/4. 

Hope this helps!

Related Questions

Please help me!!!! Help me find the dimensions. :(

Answers

The volume, surface area and the ratios of the SA to volume will be as follows:
Volume=πr²h
Area=2πr²+πdh
Ratio of SA to volume=Area/volume
π=3.14
Thus using the above formula:

1.
a]
Radius: 3 inches
Height: 2 inches
Volume=πr²h
volume=π×3²×2=56.52 in³

b]
Area=2πr²+πdh
2×π×3²+π×2×3×2
=56.55+37.68
=94.23 in²

c]
Ratio=area/volume
=94.23/56.52
=1.6672


1. 
Radius: 2 inches
Height: 9 inches

a]
V=πr²h
V=3.14*2^2*9
V=113.04 in³

b] 
Area=2πr²+πdh
=2*3.14*2^2+3.14*2*2*9
=25.12+113.04
=138.16 in²

c]
Ratio=area/volume
=138.16/113.04
=11/9

3.
Diameter=4 inches
Height= 9 inches

a]
V=πr²h
V=3.14×2²×9
V=113.04

b]
Area=2πr²+πdh
=2*3.14*2^2+3.14*4*9
=25.12+113.04
=138.16 in²

c]
Ratio=area/volume
=138.16/113.04
=11/9

4]
Diameter: 6 inches
Height: 4 inches

a]
Volume=πr²h
=3.14×3²×4
=113.04 in³

b]
Area=2πr²+πdh
=2×3.14×3²+3.14×6×4
=56.52+75.36
=131.88 in²

c] Ratio
131.88/113.04
=7/6

1. For the surface area to volume to be small it means that the area is smaller than the volume, for surface area to volume  be larger it means that the surface area is larger than the volume. It is more economical for the surface area to volume to be small because it will mean that small amount of materials make cans with large volume. This means cost of production is cheaper.

2. To evaluate this process let's use one of the dimensions:
Radius: 3 inches
Height: 2 inches:

i. add radius and height:
3+2=5 inches
ii. Multiply radius and height:
3×2=6
iii. Dividing the result from step 1 by the result in step 2:
5/6

iv. Multiply the result from step 3 by 2:
5/6×6
=5
This result does not seem to add up to the result in our earlier ratio. Thus we conclude that Khianna was wrong. This method can't work with 3-D figures.


Hey can you please help me posted picture of question

Answers

Answer: 32

Explanation:

The number of leaves in a tree diagram for probabilities is equal to the number of possible outcomes.

Tossing a coin 5 times leads to these results:

First,second, third and fourth tossing are the nodes; and fifth tossing has the leaves.

Root → 2 nodes → 2² nodes → 2³ nodes → 2⁴ → 2⁵ leaves = 32

Those 32 leaves is this sample space:

head-head-head-head-head              
head-head-head-head-tail

head-head-head-tail-head
head-head-head-tail-tail

head-head-tail-head-head
head-head-tail-head-tail

head-head-tail-tail-head
head-head-tail-tail-tail

head-tail-head-head-head
head-tail-head-head-tail

head-tail-head-tail-head
head-tail-head-tail-tail

.......... (continue)

And so on until you have included all the possibilities, ending with tail-tail-tail-tail-tail. Those will be 32 outcomes.

The ball game begins at 2pm. It takes ying 30 minutes to get to the ballpark. At what time should ying leave home to get to the the game 30 minutes before it starts

Answers

She should leave a 1 PM, 
the answer is fairly simple 1:30

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. What is the probability that a battery you buy lasts at most 100 hours? Standardize the variable.

Answers

Answer:

x = 100 is equivalent to z = -1.75

Step-by-step explanation:

Answer:

1-P(z<1.75) D in EDG

Step-by-step explanation:

For the second part !!

In a class of 40, 28 passed their maths test. What fraction of the class passed?

Answers

Final answer:

Out of a class of 40 students, 28 passed their maths test. The fraction of the class that passed the test is 28/40, which simplifies to 7/10.

Explanation:

The class consists of 40 students. The problem mentions that 28 of these students passed their maths test. To find the fraction of the class that passed, we have to compare the number of students who passed with the total number of students in the class. This is done by dividing the number of students who passed the test by the total class size. So, the fraction of the students who passed is 28/40. However, this fraction can be simplified by dividing both the numerator (28) and the denominator (40) by their greatest common divisor, which is 4. The result is 7/10. Therefore, the fraction of the class that passed the maths test is 7/10.

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Q # 8 Solve the graph please

Answers

Answer: Second option
CD congruent with XY, DA congruent with YZ, AC congruent with ZX

A ball is thrown upward and outward from a height of 77 feet. the height of the​ ball, f(x), in​ feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.2 x squared plus 1.4 x plus 7f(x)=−0.2x2+1.4x+7 where x is the​ ball's horizontal​ distance, in​ feet, from where it was thrown. use this model to solve parts​ (a) through​ (c).

Answers

From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x), 
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft

b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.


 c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.

Let f = (ax + by + 4z) i + (x + cz) j + (9y + mx) k where a, b,c, and m are constants.
a.suppose that the flux of f through any closed surface is 0. which of the constants can be determined?

Answers

Let [tex]\mathcal R[/tex] be an arbitrary closed region with boundary the surface [tex]\mathcal S[/tex]. By the divergence theorem,

[tex]\displaysytle\iint_{\mathcal S}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]

We have

[tex]\nabla\cdot\mathbf f(x,y,z)=\dfrac{\partial(ax+by+4z)}{\partial x}+\dfrac{\partial(x+cz)}{\partial y}+\dfrac{\partial(9y+mx)}{\partial z}=a[/tex]

so that the flux satisfies

[tex]\displaystyle a\iiint_{\mathcal R}\mathrm dV=0[/tex]

We're assuming [tex]\mathcal R[/tex] is a closed region, and the integral above is its volume, which must be positive. This means we must have [tex]a=0[/tex].
Final answer:

If the flux of a vector field through a closed surface is zero, this implies that the divergence of the field is zero everywhere. This condition can be used to determine some constants of the vector. In the provided equation, we can determine one of the constants a, c or m if we know the other two.

Explanation:

The subject matter of this question is within vector calculus, a field of mathematics used in physics and engineering. The question talks about the flux of a vector field f through a closed surface which is given to be zero.

When the flux through any closed surface is zero, it implies that the divergence of the vector field f is zero everywhere. This condition allows us to determine some of the coefficients of the components of f. In this case, we have: f = (ax + by + 4z) i + (x + cz) j + (9y + mx) k

The operation that gives the divergence of a vector field in three-dimensional Cartesian coordinates is given by the dot product of the del operator with the vector field. This means:

div f = ∂/∂x(ax+by+4z) + ∂/∂y(x+cz) + ∂/∂z(9y+mx) = a + c + m

For the flux of f through the surface to be zero, the divergence of f needs to equal zero, that is a + c + m =0. Therefore, for a given set of a, c, and m, we can determine one of them knowing the others.

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hey can you please help me posted picture of question

Answers

For this case we can have the following function:
 r = f (t)
 Where,
 Independent variable is t.
 Dependent variable is r.
 To find the inverse we solve for the independent variable, that is, the data entry variable.
 Answer:
 FALSE
 option B

What is the volume of a cube with an edge length of 4.5 cm?
Enter your answer, as a decimal, in the box.

___ cm 3

Answers

91.13 cm 3.

hope this helps...
volume of a cube is determined by multiplying the side length by itself three times, in this case 4.5^3 or 4.5x4.5x4.5. Doing this quickly on a calculator you find your answer is 91.125 cm^3

Brainliest would be fantastic, have a nice day!!

please help me with math
i need it soon

Answers

Lets get started :)

We are told that Mrs. Thymes is buying mulch for her gardens.

Let us check the price for each option:

[tex]\boxed {Option \ A}[/tex]
3 yd³ for $165
Divide 165 by 3, to find the price per cubic yard:
[tex] \frac{165}{3} [/tex] = $55 per cubic yard

[tex]\boxed {Option \ B }[/tex]
4 yd³ for $240
Do the same:
[tex] \frac{240}{4} [/tex] = $60 per cubic yard

[tex]\boxed {Option \ C }[/tex]
6 yd³ for $300
[tex] \frac{300}{6} [/tex] = $50 per cubic yard

[tex]\boxed {Option \ D }[/tex]
8 yd³ for $360
[tex] \frac{360}{8} [/tex] = $45 per cubic yard

Therefore, we can see that 8 yd³ for $360 is the best price

[tex]\boxed {Your \ Answer \ will \ be \ Option \ D }[/tex]
Divide each price by the number of cubic yards it buys to find the cost per cubic yard.

A. $165/(3 yd³) = $55/yd³

B. $240/(4 yd³) = $60/yd³

C. $300/(6 yd³) = $50/yd³

D. $360/(8 yd³) = $45/yd³ . . . . . . . this is the best price per cubic yard.

Hey can you please help me posted picture of question

Answers

The correct answer for the problem shown in the picture attached is the option A:

 A. G(x)=(x+3)^2-2

 The explanation is shown below:

 1. As you can see in the graph shown in the picture attached, there is two parabolas. The red parabola has the patern function F(x)=x^2, which means that is the most basic function of the quadratic functions. The blue parabola is shifted 3 units on the -x axis and 2 units on the -y axis, therefore, the correct option is the Option A.

4.63 ​clark's country pet resort is fencing a new play area for dogs. the manager has purchased 130 yd of fence to enclose a rectangular pen. the area of the pen must be 1050 ydsquared. what are the dimensions of the​ pen?

Answers

Let W and L be width and length of the rectangular pen respectively.

Therefore,
Circumference, C = 2W+2L= 130 yd
Area, A = LW = 1050 yd^2=> L = 1050/W

Using the circumference expression and substituting for L;
130 = 2W + 2(1050/W) = 2W+2100/W
130*W = 2W*W + 2100
130W = 2W^2 +2100
2W^2-130W+2100 = 0

Solving for W;
W= [-(-130)+/- Sqrt ((-130)^2-4(2)(2100)]/2*2 = 32.5+/- 2.5
W = 30 or 35 yd

When W = 30, L = 1050/30 = 35
When W = 35, L = 1050/35 = 30

Therefore, W = 30 yd and L = 35 yd.

The problem involves determining the dimensions of a rectangular pen using given fencing length and area. Two possible solutions were found: the dimensions of the pen could be 30 yards by 35 yards, or 100 yards by 15 yards.

The manager at Clark's Country Pet Resort is trying to construct a rectangular pen for dogs with a fixed amount of fencing and a desired area.

Given that the length of the fencing is 130 yards and the area must be 1050 square yards, we can solve this problem by applying algebra and the principles of rectangle properties.

Consider 'l' to be the length of the rectangle and 'w' to be the width of the rectangle. We know that the perimeter of a rectangle is 2l + 2w. Given the total length of fencing available is 130 yards, it can be formulated as 2l + 2w = 130.

The area of a rectangle is given by l*w. As we know the area is 1050 square yards, it can be written as l*w = 1050.

We now have a pair of equations which we can solve simultaneously to find the values of 'l' and 'w'.

From the first equation, we can express 'w' as (130 - 2l) / 2. Putting this into the area equation gives us l * (130 - 2l) / 2 = 1050. Solving for 'l' we get two possible solutions: l = 30 yd or l = 100 yd. By substituting these values back into the first equation, we get the corresponding values of 'w' which are 35 yd and 15 yd respectively.

Thus, the dimensions of the pen could be either 30 yd by 35 yd or 100 yd by 15 yd.

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Hey can you please help me posted picture of question

Answers

Two events are occurring:

1) Rolling a die
Sample Space = {1,2,3,4,5,6}
Total number of outcomes in sample space = 6
Favorable outcomes = Odd number
Number of Favorable outcomes = 3

Probability of getting an odd number = 3/6 

2) Tossing a coin
Sample Space = {H, T}
Probability of getting a head= 1/2

The probability of getting odd number and head will be the product of two probabilities, which will be = 3/6 x 1/2 = 3/12 

Thus there is 3/12 = 1/4 (0.25 or 25%) probability of getting an odd number and a head in given scenario. 

So correct answer is option C

Three of the six numbers on the die are odd, so the probability of rolling an odd number is 3/6.

One of the two sides of the coin is a head, so the probability of tossing a head is 1/2.

These are considered to be independent events, so the joint probability is the product of these probabilities.

The probability of getting an odd number and a head is
  (3/6)*(1/2) = 3/12

The appropriate choice is ...
  C. 3/12

On a certain day, $1 is worth 30.23 Russian rubles.Omar has $75.How many rubles will he get in exchange?

Answers

242.25 rupies. 75 x 30.23 = 242.25 rupies.

Hope this helps!
Omar would get 2,267.25 Russian Rubles.

To find this you multiply his amount of money ($75) by how many Russian Rubles $1 equals (30.23). This will give you an answer of 2,267.25.

I hope this helps!

Given the parent function f(x)=x^2 describe the graph of g(x)=(3x-6)^2+3


a.
expanded vertically by a factor of 3, horizontal shift left 6, vertical shift up 3
c.
compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3
b.
expanded horizontally by a factor of 3, horizontal shift left 6, vertical shift up 3
d.
compressed vertically by a factor of 1/3, horizontal shift right 2, vertical shift up 3

Answers

For this case we have the following functions transformation:
 Vertical expansions:
 To graph y = a * f (x)
 If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
 f1 (x) = (3x) ^ 2
 Horizontal translations
 Suppose that h> 0
 To graph y = f (x-h), move the graph of h units to the right.
 f2 (x) = (3x-6) ^ 2
 Vertical translations
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 g (x) = (3x-6) ^ 2 + 3
 Answer:
 expanded horizontally by a factor of 3, horizontal shift rith 6, vertical shift up 3

Answer:

C. Compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3

Step-by-step explanation:

If a function f(x) is transformed and make f(kx),

f(x) is compressed horizontally by the factor 1/k if k > 1

f(x) is stretched horizontally by the factor 1/k if 0 < k < 1

Also, if f(x) is transformed and make f(x+a),

f(x) is shifted right if a < 0

f(x) is shifted left if a > 0,

Now, if f(x) gives f(x) + k after transformation,

f(x) is shifted vertically k unit up if k > 0,

f(x) is shifted vertically k unit down if k < 0,

Here, the parent function,

[tex]f(x) = x^2[/tex]

transformed function,

[tex]g(x)=(3x-6)^2+3=(3(x-2))^2+3[/tex]

Thus, by the above explanation,

f(x) is compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3.

Option C is correct.

For a certain manufacturer, only ⅘ of the items produced are not defective.If 2,000 items are manufactured in a month, how many are not defective?

Answers

To find the number of non-defective chips, we simply use this equation:
2,000 * 4/5
8000/5
Now you simply divide:
1600
1600 chips aren't defective

what is 6.4 ÷ 4.6272

Answers

6.4/4.6272=1.3831258645 or 1.4.
convert to fraction-32/5 divided by 4.6272
multiply by reciprocal of that fraction-32/2 times 625/2892
reduce the numbers wit 5 -32 times 125/2892
calculate-1000/723

A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game. Their high scores are all between 180 and 220, except for Adam, whose high score is 250. Adam then bowls a great game and has a new high score of 290. How will increasing Adam's high score affect the mean and median?

A
Both the mean and median will increase.
(Choice B)
B
The median will increase, and the mean will stay the same.
(Choice C)
C
The mean will increase, and the median will stay the same.
(Choice D)
D
The mean will increase, and the median will decrease.

Answers

Answer:

Option: C is the correct answer.

    C     The mean will increase, and the median will stay the same.

Step-by-step explanation:

We know that the mean of scores is the average value of the scores of  the score obtained by 4 friends.

i.e. it is the ratio of sum of scores of 4 friends to the total number of person i.e. 4.

Hence, if the score of any of the person will increase then the mean will also increase

( Since, the denominator remains the same and the numerator is increasing so , the resultant value will increase )

Also, we know that the median of the score lie between the data set, i.e. the change in the score of the last score won't affect the median :

Since, here we have  4 data points and the median lie between the 2nd and 3rd data point so change in the 4th data point won't affect the median.

Hence, increasing Adam's high score affect the mean and median as:

Mean will increase and Median remains the same.

The mean and median will increase as Adam's high score rises, while the median will remain unchanged. Then the correct option is C.

What is Mean?

Mean is simply defined as the average of the given set of numbers. The mean is considered one of the measures of central tendencies in statistics.

What is a median?

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

A group of 4 friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game.

Their high scores are all between 180 and 220, except for Adam, whose high score is 250.

Adam then bowls a great game and has a new high score of 290.

If any of the individuals' scores improve, the mean will improve as well.

We also observe that the median of the scoring lies inside the data set, implying that a change in the last score will have no effect on the median.

Because we have four data sets and the median is between the second and third, a change in the fourth data point will have no effect on the median.

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what is the median of this data set 17,42,53,97,102,82

Answers

67.5 ... Hope I helped! :D brainliest? 
Answer = 67.5

To solve this you put the number in order so (17 42 53 82 97 102) then you count them off by removing them left to right, first 17, then 102, then 42, then 97, then you are left with 2 numbers in the middle so you average them by adding them together and then dividing them by 2 to get 67.5. If you are left with one in the middle then that is your answer.

HI, PLEASE HELP ASAP~(no one is helping me ;-;) + BRAINLIST!!

Janelle is at the movie theater and has $20 to spend. She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99 . How many snacks, x , can Janelle buy? Inequality that represents this situation: 20≥8+4.99x Drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution

Answers

Answer:

Part A : 2 snacks

Part B : Solution to both the inequality and the problem situation ⇒ 1 , 2

             Solution to the inequality only ⇒ -4 , 3/4 , 2.3

             Not a solution ⇒ 2.5

=================================================================

Step-by-step explanation:

Part A :

Janelle  has $20 to spend

She spends $8 on a ticket, so , the remaining = 20 - 8 = $12

Each snack costs $4.99

So, the number of snacks =

the integer of ( 12 / 4.99 ) = integer of (2.4) = 2 snacks

Part B:

Inequality that represents this situation: 20 ≥ 8 + 4.99x

Solve for x

∴ 20 - 8 ≥ 4.99 x

12 ≥ 4.99 x

divide both sides by 4.99

∴ (12/4.99) ≥ x

∴ x ≤ 2.4048

The given options are : -4 , 3/4 , 2.3 , 2.5 , 1 , 2

So,

Solution to both the inequality and the problem situation ⇒ 1 , 2

solution to the inequality only ⇒ -4 , 3/4 , 2.3

Not a solution ⇒ 2.5

Answer:

Solutions to Both:

1

2

Solutions to the Inequality Only;

3/4

-4

2.3

Not a Solution:

2.5

Step-by-step explanation:

15t+30+5t=-4t+6 please show step by step

Answers

15t+4t+5t=6-30
24t=-24
t=-1

a jogger runs around a 220 yard track in 125 seconds. what is the average speed in yards per second? Explain.

Answers

I am probably very, very wrong because i forgot how to do this but 1.76??????

Hello there, and thank you for asking your question here on brainly.

Answer: You can find how much yps (yards per second) by dividing 220 by 125. Divided, 220 / 125 ==> 1.76 He runs 1.76 yps. To check, you can multiply 1.76 by 125. Multiplied, 1.76 x 125 ==> 220. This is true.

Hope this helped you! ♥

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)

Answers

Answer:

c

Step-by-step explanation:

edge 2020

Answer:

The correct answer is C.

Step-by-step explanation:

Four of a sample of 150 computers will be selected and tested. How many ways are there to make this selection? Type a numerical answer in the space provided. Do not type any commas or spaces in your answer.

Answers

This is a question of combinations.
The number of ways of selecting 4 computers from 150 computers = 150C4= 20260275

There are 20260275 ways of selecting 4 computers from 150 sample of computers.

The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot

Answers

the correct question is
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot. The base of the rectangular prism is not a square and the width is greater than 2 feet. What is the length and width of the rectangular prism?

let
x-------> the length of the base of the rectangular prism
y-------> the width of the base of the rectangular prism

we know that
volume of the prism=area of the base*height 
volume=48 ft³
height of the prism=3/4 ft

area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft²

area of the base=64 ft²
area of the base=x*y
64=x*y--------> equation 1

y=x+2--------> equation 2

substitute equation 2 in equation 1
64=x*[x+2]-----> 64=x²+2x------> x²+2x-64=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=7.062 ft
y=x+2-----> y=7.062+2-----> y=9.062 ft

the answer is
the length of the base of the rectangular prism is 7.062 ft
the width of the base of the rectangular prism is 9.062 ft

please help I need a good grade

Answers

The answer would be 1.85, because .85 is 85% so it is 85% out of 100% which means it is .85 out of 1.00, which makes 1.00 c so you add 1.00 and .80 and get 1.85

Which of the following equations is the result of completing the square on x 2 - 6x - 9 = 0?

Answers

If you want to complete the square on that, you do this:

x² - 6x - 9 = 0
x² - 6x = 9
x² - 6x + 9 = 9 + 9

x² - 6x + 9 = 18 is your equation. 

If you want, I can keep going:

(x - 3)² = 18

x - 3 = +/- √18
x - 3 = +/- 3√2

x = 3 +/- 3√2


Which of the following uses estimation to check 267 - 154 = 113

A. 300 - 150 = 150

B. 300 - 200 = 100

C. 270 - 150 = 267

D. 113 + 154 = 267

Answers

Answer: it is the third but there is a typo. It is C. 267 - 150 = 117

Explanation:

You can do that estimation searching to make a quick verification, because adding rounding 154 to the tens leads to 150 and it is very easy to subtract 267 - 150 instead of 267 - 154, driving to a quick approximate check of the subtraction.


Solve the rational equation 8/x+1/5=3/x

Answers

Final answer:

To solve the equation 8/x + 1/5 = 3/x, we multiply the entire equation by 5x to get rid of the fractions to get 40 + x = 15. Solving for x we get x = -25.

Explanation:

To solve the given rational equation 8/x + 1/5 = 3/x, we first need to find a common denominator to combine the fractions. Hence, we multiply the entire equation by 5x to get rid of the denominators:

5 * 8 + x = 15

which simplifies to

40 + x = 15.

Then by subtracting 40 from both sides to solve for x, we get:

x = -25.

That is the solution to the rational equation.

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Final answer:

The rational equation 8/x + 1/5 = 3/x is solved by finding a common denominator, simplifying the equation and then factoring the resulting polynomial to find the roots.

Explanation:

To solve the given rational equation 8/x + 1/5 = 3/x, we first find a common denominator for the fractions. Seeing x and 5, we can take the common denominator as 5x.

Next, we rewrite each term with the common denominator: (40/5x) + (x/5x) = (15/5x). This simplifies to 40/5x + x/5x - 15/5x = 0. Simplifying further we have 8/x - 3/x + 1/5 = 0.

After setting the equation to zero, one may notice that this equation can be solved by bringing the terms together and then trying to factorize the resulting polynomial. The solution of the equation are the roots of the factored polynomial.

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