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3 years ago

Given that 3x-y : x+2y = 2 : 5, Determine the ratio x:y

Mathematics

1 answer:

N76 [4]3 years ago

7 0

Answer:

x : y = 9 : 13

Step-by-step explanation:

Given that

3x - y : x + 2y = 2 : 5

Express the ratio in fractional form, that is

$\frac{3x-y}{x+2y}$ = $\frac{2}{5}$ ( cross- multiply )

5(3x - y) = 2(x + 2y) ← distribute parenthesis on both sides )

15x - 5y = 2x + 4y ( subtract 2x from both sides )

13x - 5y = 4y ( add 5y to both sides )

13x = 9y ( divide both sides by 13 )

x = $\frac{9}{13}$ y ( divide both sides by y )

$\frac{x}{y}$ = $\frac{9}{13}$ , that is

x : y = 9 : 13

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3 years ago

How to factor 6n2 - 6n - 12

alexandr402 [8]

We see that in these 3 terms, 6 is a common factor. So, let's factor out a 6:

$6n^2-6n-12 = 6(n^2-n-2)$

We can set this equal to 0 and factor by using the quadratic formula which is:

$x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

So, let's do just that:

$6(n^2-n-2) = 0$

Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:

$\frac{1 \pm \sqrt{(-1)^2-4(1)(-2)} }{2(1)} = \frac{-1 \pm \sqrt{1-(-8)} }{2}$

$\frac{-1 \pm \sqrt{9} }{2} = {1, -2}$

So, we can write this as:

$6n^2 - 6n - 12 = 6(n-1)(n+2)$

Notice that the 6 comes back because it was only temporarily mad. And that the roots have opposite signs in the parentheses because to find the roots, you need to set each parentheses equal to 0 and solve for n. With that in mind, your final answer is 6(n-1)(n+2). Hope I could help you!

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