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2 years ago

Which ratio is equivalent to 8:3? 12:32 12:3 40:15 64:9

Mathematics

2 answers:

dexar [7]2 years ago

7 0

It’s 40:15 because 8*5=40 and 3*5=15

OleMash [197]2 years ago

5 0

Answer: 40:15

Step-by-step explanation: 8 x 5 = 40 / 3 x 5 = 15

Both of them are multiple and equivalent hope this helps

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The simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

<h3>Simplifying an expression </h3>

From the question, we are to simplify the expression

From the given information,

$f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}$

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$g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}$

Also,

$R(x) = f(x) \div g(x)$

∴ $R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}$

$R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}$

Factoring each of the quadratics

$R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}$

$R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}$

$R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}$

Simplifying

$R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}$

$R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}$

$R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}$

$R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Hence, the simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Learn more on Simplifying an expression here: brainly.com/question/1280754

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