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3 years ago

If y is directly proportional to x and y = 6 when x = 2, what is the proportion equation?

Mathematics

2 answers:

lorasvet [3.4K]3 years ago

8 0

Formula for direct proportion: y = kx

Solution:

6 = 2k

~Divide 2 to both sides

3 = k

Best of Luck!

Ivan3 years ago

7 0

Answer:

y = 3x

Step-by-step explanation:

Direct proportion equation is

y = kx

6 = k*2

Divide each side by 2

6/2 = 2k/2

3 =k

The equation is y = 3x

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3 years ago

Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resultin

Vesna [10]

The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

According to the given question.

We have an equation

$\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}$

So, to find the resulting equation of the above equation we need to simplify.

First we will take LCD

$\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}$

Multiply both the sides by x.

$\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}$

Again multiply both the sides by x

$2x^{2} -2x-12 = 5x^{2} +18x$

$\implies 5x^{2} -2x^{2} +18x +2x +12 = 0$

$\implies 3x^{2} + 18x+2x + 12 = 0$

Factorize the above equation

⇒3x(x+6)+2(x+6) = 0

⇒(3x + 2)(x+6) = 0

⇒ x = -2/3 or x = -6

Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

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