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sergij07 [2.7K]
4 years ago
10

Plz help me with this

Mathematics
2 answers:
seropon [69]4 years ago
8 0
HEY mate here is your answer

I think the correct option is equivalent...

I am from India..

hope it helps you.

be brainly
SSSSS [86.1K]4 years ago
5 0

Answer: Inconsistent

<u>Step-by-step explanation:</u>

When given a system of equations, the definitions of the solution are:

  • Consistent & Independent: exactly ONE solution (lines intersect)
  • Consistent & Dependent: INFINITE solutions (same line)
  • Inconsistent: NO solutions (parallel lines)

In the given graph, the lines are parallel, which means they have NO solutions --> The system is Inconsistent.

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

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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}

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

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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}

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