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asambeis [7]
3 years ago
12

G(g(x)) g=(x+14)/(x+2)

Mathematics
1 answer:
GalinKa [24]3 years ago
6 0

\bf g(x)=\cfrac{x+14}{x+2}~\hspace{8em}g(~~g(x)~~)=\cfrac{g(x)+14}{g(x)+2}\\\\\\(~~g(x)~~)=\cfrac{~~\frac{x+14}{x+2}+14~~}{\frac{x+14}{x+2}+2}\implies (~~g(x)~~)=\cfrac{~~\frac{x+14~~+14x+28}{x+2}~~}{\frac{x+14~~+2x+4}{x+2}}\\\\\\(~~g(x)~~)=\cfrac{~~\frac{15x+42}{x+2}~~}{\frac{3x+18}{x+2}}\implies (~~g(x)~~)=\cfrac{15x+42}{\underline{x+2}}\cdot \cfrac{\underline{x+2}}{3x+18}\\\\\\(~~g(x)~~)=\cfrac{15x+42}{3x+18}\implies (~~g(x)~~)=\cfrac{3(5x+14)}{3(x+6)}\implies (~~g(x)~~)=\cfrac{5x+14}{x+6}

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Answer:

  • Seat 1: Peter
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  • Seat 3: Kenny
  • Seat 4: Jennie
  • Seat 5: Harvey
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  • Seat 8: Mark

Step-by-step explanation:

From Rule 6: Jennie is at Seat 4 and next to Harvey; and by rule 1 (Harvey has a higher seat number than Jennie)

  • Seat 4: Jennie
  • Seat 5: Harvey

From Rule 2:  Peter is across from Harvey.

Since Seat 5 is across from Seat 1

  • Seat 1: Peter

From Rule 7: Peter is next to Lia.

Therefore, Lia can either be in Seat 2 or Seat 8, but by Rule 3 (Neither Joyce nor Lia is in seat 8), therefore, Lia is in Seat 2.

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By Rule 5: Lia is next to Kenny, therefore:

  • Seat 3: Kenny

From Rule 4: Rick is across from Kenny, and Rick is also next to Joyce.

Seat 7 is across from Seat 3, therefore:

  • Seat 7: Rick

Since Rick is also next to Joyce (and by Rule 3, Joyce cannot be on Seat 8)

  • Seat 6: Joyce

Therefore, we have:

Seat 1: Peter

Seat 2: Lia

Seat 3: Kenny

Seat 4: Jennie

Seat 5: Harvey

Seat 6: Joyce

Seat 7: Rick

Since Mark has the remaining seat, Mark is on Seat 8.

4 0
3 years ago
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