Choose the answer that shows what to do in the process step, and what the solution (answer is).

If the same number is added to the numerator and subtracted from the denominator of LaTeX: \frac{23}{12}23 12, the resulting fra

lions [1.4K]

Hence, -45 is the number which when added to the given fraction will give 2/3

Further explanation:

Given fraction is:

$\frac{23}{12}$

Let x be the number which has to be added to numerator and denominator

Then

$\frac{23+x}{12+x}=\frac{2}{3}$

Cross-multiplying

$\frac{23+x}{12+x}=\frac{2}{3} \\3(23+x)=2(12+x)\\69+3x=24+2x\\3x-2x=24-69\\x=-45$

Hence, -45 is the number which when added to the given fraction will give 2/3

Keywords: Linear equation in one variable, Cross-multiplication

Learn more about linear equation at:

#LearnwithBrainly

6 0

3 years ago

In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=60°, and JH = 80 feet. Find the length of IJ to the nearest foot.

atroni [7]

Answer:

46.2

Step-by-step explanation:

46.188= 46.2

3 0

3 years ago

Can someone give me two equations an tell me which of the two would be steeper ?

netineya [11]

Well when you look at equations, they are all built from y=mx+b. Y and x are a point on that line, m is your slope, and b is the y intercept. So when you look at two equations, take the absolute value of m to find which is steeper. Take these two examples.
y=3x+4
y=-7x+4
Take the absolute value of 3 and -7
|3|=3
|-7|=7
7 is the larger number so y=-7x+4 has a steeper slope.

4 0

3 years ago

Pete’s Electric charges $75 plus $30 per hour of work while Greg’s Electric charges $45 plus $45 per hour. How many hours must e

viktelen [127]

H: hours
45h + 45 = 30h + 75
15h + 45 = 75
15h = 30
h = 2 hours

45 ( 2 ) + 45 = 30 ( 2 ) + 75
90 + 45 = 60 + 75
135 = 135

Therefore the awnser is 2 hours.

8 0

3 years ago

What's the intuition behind the equation 1+2+3+⋯=−1121+2+3+⋯=−112 ?

Aleks [24]

The sum clearly diverges. This is indisputable. The point of the claim above, that

$1+2+3+\cdots=-\dfrac1{12}$

is to demonstrate that a sum of infinitely many terms can be manipulated in a variety of ways to end up with a contradictory result. It's an artifact of trying to do computations with an infinite number of terms.

The mathematician Srinivasa Ramanujan famously demonstrated the above as follows: Suppose the series converges to some constant, call it $C$ . Then

$\begin{matrix}C&=&1&+2&+3&+4&+5&+6&+\cdots\\4C&=&&+4&&+8&&+12&+\cdots\\-3C&=&1&-2&+3&-4&+5&-6&+\cdots\end{matrix}$

Now, recall the geometric power series

$\displaystyle\sum_{n\ge0}x^n=1+x+x^2+x^3+\cdots=\dfrac1{1-x}$

which holds for any $|x|$ . It has derivative

$\displaystyle\sum_{n\ge1}nx^{n-1}=1+2x+3x^2+4x^3+\cdots=\dfrac1{(1-x)^2}$

Taking $x=-1$ , we end up with

$1+2(-1)+3(-1)^2+4(-1)^3+\cdots=1-2+3-4+\cdots=\dfrac14$

and so

$-3C=\dfrac14\implies C=-\dfrac1{12}$

But as mentioned above, neither power series converges unless $|x|$ . What Ramanujan did was to consider the sum $1-2+3-4+\cdots$ as a limit of the power series evaluated at $x=-1$ :

$\displaystyle-3C=\lim_{x\to-1^+}\sum_{n\ge1}nx^{n-1}=\lim_{x\to-1^+}\frac1{(1-x)^2}=\frac14$

then arrived at the conclusion that $C=-\dfrac1{12}$ .

But again, let's emphasize that this result is patently wrong, and only serves to demonstrate that one can't manipulate a sum of infinitely many terms like one would a sum of a finite number of terms.

4 0

3 years ago