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sasho [114]
3 years ago
9

Prove that 27 to the 10th-9 to the 14th is divisible by 24

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
3 0

Answer:

27^{10}-9^{14}\\\\=(3^3)^{10}-(3^2)^{14}\\\\=3^{30}-3^{28}\\\\=3^{(27+3)}-3^{(27+1)}\\\\=3^{27} \cdot3^3-3^{27}\cdot3^1\\\\=3^{27}(3^3-3^1)\\\\=3^{27}(27-3)\\\\=3^{27}\cdot24

3^{27}\cdot24 is divisible by 24, hence proving that 27^{10}-9^{14} is divisibe by 24

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Step2247 [10]
  • h(x) = f(x) + g(x) = h(x) = 18.5x-16
  • h(x) = g(x) – f(x) = h(x) = 23.5x-40
  • h(x) = 4g(x) = h(x) = (84x-112)

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

Here we have , f(x) = -2.5x + 12; g(x) = 21x - 28 or f(x) = -2.5x + 12, g(x) = 21x - 28 .

10. Find h(x) = f(x) + g(x).

⇒ h(x) = f(x) +g(x)

⇒ h(x) = ( -2.5x + 12)+( 21x - 28)

⇒ h(x) = ( 21x-2.5x )+( 12 - 28)

⇒ h(x) = 18.5x-16

11. Find h(x) = g(x) – f(x).

⇒ h(x) = g(x)-f(x)

⇒ h(x) = ( 21x - 28)-( -2.5x + 12 )

⇒ h(x) = ( 21x+2.5x )+( -12 - 28)

⇒ h(x) = 23.5x-40

12. Find h(x) = 4g(x).

⇒ h(x) = 4g(x)

⇒ h(x) = 4( 21x - 28)

⇒ h(x) = (84x-112)

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