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Svetlanka [38]
3 years ago
6

8

ula1" title=" \frac{x}{12} = \frac{x}{13} - 9" alt=" \frac{x}{12} = \frac{x}{13} - 9" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Lostsunrise [7]3 years ago
8 0
So this is a rational equation. So to find the value of x you must do the act of cancelling or isolating.
The equation is like this am I right?
8 \times \frac{x}{12} = \frac{x}{13} - 9
In the left side of the equation, times sign or no times sign, it is still the same.
8 \times \frac{x}{12} = 8 \frac{x}{12}
Lets continue on to the equation:
First lets focus on the left side:
Turn the number 8 into a fraction, that would be 8/1.
\frac{8}{1} \times \frac{x}{12} = \frac{x}{13} - 9
Then, we need to factor the numbers:
What are the factors of 8?
8=2*2*2*2
What about factors of 1?
1=1
What about the factors of 12?
2*2*3
Factors of x?
x=x
Now let us cancel the same factors on the numerators to the factors of the denominators:
\frac{2 \times 2 \times 2}{1} \times \frac{x}{2 \times 2 \times 3}

Cancel the two 2 pairs:
\frac{2}{1} \times \frac{x}{3}
Now multiply the numerators and denominators:
\frac{2 \times x}{1 \times 3} = \frac{2x}{3}
Now we are done solving for the left side, now its turn for us to solve for the right side:
Again, make the whole number (9) into a fraction, that would be 9/1
\frac{x}{13} - \frac{9}{1}
Now its time for us to subtract these fractions:
(For me, the butterfly shortcut method is easier)
So the answer would be:
\frac{x}{13} - \frac{9}{1} = \frac{x - 117}{13}
Now we are done with the both sides of the equation. This is the result:
\frac{2x}{3} = \frac{x - 117}{13}
But we're not done yet
Now we need to cross-multiply (the easiest method for me) meaning we need to multiply the numerator on the left side to the denominator on the right side and vice versa.
2x \times 13 = 3 \times (x - 117)
26x = 3x - 351

We're getting really close, one step and we are done! (End my typing suffering, PLEASEEE!!!)

Now its isolating time!
Here is a fill-in-the-blanks question:
3x-__=0
The answer would be 3x right? (Because 3x-3x=0)
Wait I accidentally pressed save please be patient for the answer
Ill just say the answer for you: the answer is: x=-351/23 (yes its a fraction)
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Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form
mr Goodwill [35]

Answer:

f(x) = (x - (-5))^2 + (-18)

Step-by-step explanation:

Given:

f(x) = x^2 + 10x + 7

Rewrite f(x) in vertex form

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f(x) = ax^2 + bx + c is a quadratic function.

The vertex form of f(x) is a(x - h)^2 + k, where (h, k) is the vertex.

=> f(x) = x^2 + 10x + 7

          = x^2 + 10x + 25 - 18

          = (x + 5)^ - 18

          = (x - (-5))^2 + (-18)

=> f(x) can be rewritten in form of a(x - h)^2 + k, where (h, k) is the vertex, with a = 1, h = -5, k = -18

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3 years ago
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