Ask question

Ask question

All categories

2 years ago

10

If numerator is 2 less than the denominator of a rational number and when 1 is subtracted from numerator and denominator both, t

he resulting new rational number in its simplest form is 1/2 . Find the original rational number.

1 answer:

xenn [34]2 years ago

6 0

Answer:

$\frac{3}{5}$

Step-by-step explanation:

Let the denominator be x
So, numerator = x - 2
According to the given condition: when 1 is subtracted from numerator and denominator both, the resulting new rational number in its simplest form is $\frac{1}{2}$

$\implies \frac{x-2-1}{x-1}=\frac{1}{2}$

$\implies \frac{x-3}{x-1}=\frac{1}{2}$

$\implies 2(x-3)=x -1$

$\implies 2x-6=x -1$

$\implies 2x-x=6-1$

$\implies x=5$

$\implies x-2=-5-2= 3$

$Required \: rational\: number = \frac{3}{5}$

You might be interested in

What is the factored form of 125a^6-64

SVETLANKA909090 [29]

<span>(5a^2-4)*(25a^4+20a^2+16) is your answer</span>

6 0

3 years ago

Read 2 more answers

The slope f′(x) at each point (x,y) on a curve y=f(x) is given, along with a point (a,b) on the curve. Use this information to f

Montano1993 [528]

$f'(x)=\dfrac{4x}{1+7x^2}$

Integrating gives

$f(x)=\displaystyle\int\frac{4x}{1+7x^2}\,\mathrm dx$

To compute the integral, substitute $u=1+7x^2$ , so that $\frac27\,\mathrm du=4x\,\mathrm dx$ . Then

$f(x)=\displaystyle\frac27\int\frac{\mathrm du}u=\frac27\ln|u|+C$

Since $u=1+7x^2>0$ for all $x$ , we can drop the absolute value, so we end up with

$f(x)=\dfrac27\ln(1+7x^2)+C$

Given that $f(0)=10$ , we have

$10=\dfrac27\ln1+C\implies C=10$

so that

$\boxed{f(x)=\dfrac27\ln(1+7x^2)+10}$

7 0

3 years ago

You eat five slices of bread. Your friend eats two slices fewer than you eat. Write an expression that describes the number of s

olya-2409 [2.1K]

X-2 or 5-2 because 2 fewer you would need to subtract two from the amount you ate

5 0

3 years ago

The mass of an ornament is m grams.

MArishka [77]

Given:

m is directly proportional to the cube of h.

m = 525 when h= 5.

To find:

The equation connecting m and h.

Solution:

m is directly proportional to the cube of h.

$m\propto h$

$m=kh$ ...(i)

Where, k is the constant of proportionality.

Putting m = 525 and h= 5, we get

$525=k(5)$

$\dfrac{525}{5}=k$

$105=k$

Putting k=105 in (i), we get

$m=105h$

Therefore, the required equation is $m=105h$ .

8 0

2 years ago

out of the total 20000 people, it was found that 30% like to listen to hindi flim songs 20% like to listen to english music 15%

alexira [117]

Answer:

Hindi Film: 6,000 people

English: 4,000 people

Classical: 3,000 people

Other: 7,000 people

7 0

2 years ago