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IRINA_888 [86]
3 years ago
10

Sixty-one diminished by ten x. Answer: _______________________ . The product of twice a number k. Answer: ______________________

_ ____________________ _______________ 2 . 3 The quotient of forty-two and six is seven. Answer: _______________________ . Twice the total of nineteen and a number m. Answer: _______________________ __________________________ 4 . Six less than 3 times y. Answer: _______________________ _________________ 5
Mathematics
1 answer:
KengaRu [80]3 years ago
6 0

Answer:

61 - 10x

2k

42 / 6 = 7

38 + 2m

3y - 6

Step-by-step explanation:

A. Sixty-one diminished by ten x

= 61 - 10x

B. The product of twice a number k

= 2 * k

= 2k

C. The quotient of forty-two and six is seven

42 / 6 = 7

D. Twice the total of nineteen and a number m.

= 2(19 + m)

= 38 + 2m

E. Six less than 3 times y

3y - 6

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Answer:

\huge\boxed{\bf\:1}

Step-by-step explanation:

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }

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\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}

Now factorise the next set : \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }.

\frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\=  \frac{x-4}{x-1}

Now, multiply the two simplified results.

\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}

\rule{150pt}{2pt}

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