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gayaneshka [121]
3 years ago
15

Solve the rational function of (check image) and check for extraneous solutions

Mathematics
1 answer:
Oxana [17]3 years ago
5 0

Answer:

Option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

Step-by-step explanation:

Given the expression

\frac{5}{x}=\frac{4x+1}{x^2}

Solving the rational function

\frac{5}{x}=\frac{4x+1}{x^2}

Apply fraction across multiply: if \frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c

5x^2=x\left(4x+1\right)

Subtract x(4x+1) from both sides

5x^2-x\left(4x+1\right)=x\left(4x+1\right)-x\left(4x+1\right)

Simplify

5x^2-x\left(4x+1\right)=0

5x² - 4x² - x = 0

x² - x = 0

Factor x² - x = x(x-1)

so

x(x-1) = 0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

x=0\quad \mathrm{or}\quad \:x-1=0

Thus, the solution to the equation is:

x=0,\:x=1

But, it is clear that if we substitute x = 0, the equation becomes undefined because we can not have the denominator to be 0.

In other words, the equation is undefined for x = 0

Thus, x = 0 is an extraneous solutions.

Therefore, option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

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Which of these is least likely to be the average salary of another of the groups?
Finger [1]

Answer:

$104,000

The probability that the average salary between two groups is the same, is actually low. It could be close, but it's quite difficult to get the same exact amount.

3 0
3 years ago
How do you complete a tree map withe the following words estimation,benchmark,hundredth ,place value,round,tenth, thousandth
Mashcka [7]
I think  you can put bench mark place valie round tenth thousnadth
3 0
3 years ago
Can someone pls help need it ASAP and can you pls explain in full detail how to do it
GenaCL600 [577]

Answer:

x= 1 , y=4

Step-by-step explanation:

x-y= -3 => Equation 1

x+5y= 21 => Equation 2

<u>Substitut</u><u>ion</u><u> </u><u>Method</u><u>:</u>

<u>Substitu</u><u>te</u><u> </u><u>Equation</u><u> </u><u>1</u>=>

x=y-3 <= Equation 3

Put x=y-3 in Equation 2:

x+5y=21

( y-3)+5y=21

y-3+5y=21

6y-3=21

6y=21+3

6y=24

y=24÷6

y=4

Put y=4 in Equation 1:

x-y= -3

x-4=-3

x=4-3

x=1

Hope this helps :)

8 0
2 years ago
Read 2 more answers
Can someone help me with this and show the step to solving it
anyanavicka [17]

Answer:x = 9/16

Step-by-step explanation:

2x + 3 = 6x - 4

/3

First you gotta get rid of the divided by 3

2x / 3 = 2/3x and 3 / 3 = 1

Now you have

2/3x + 1 = 6x - 4

Second you have to get rid of the 2/3x on the left side

2/3x + 1 = 6x - 4

-2/3x          -2/3x

1 = 5 1/3x - 4

Third you have to get rid of the -4

1 = 5 1/3x - 4

-4             -4

-3 = 5 1/3x

Fourth you have to divide by 5 1/3

-3 = 5 1/3x

/ 5 1/3    / 5 1/3

x = 9/16

3 0
3 years ago
Hodel just got her driver's license. Her parents offer her two options. 1. They'll buy her a used car that will cost her $0.50 p
Romashka-Z-Leto [24]

Answer:

The second option will cost her less than the first one.

Step-by-step explanation:

In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.

For the first option we have:

cost_1(x) = 0.5*x

For the second option we have:

cost_2(x) = 5000 + 0.1*x

Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:

cost_1(60000) = 0.5*60000 = 30000

cost_2(60000) = 5000 + 60000*0.1 = 11000

The second option will cost her less than the first one.

7 0
3 years ago
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