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Anettt [7]
3 years ago
12

Jan is 2/3 of Karyn's age. Jan's age 8 years ago is 2/5 of Katyn's age 4 yeats from now. Jan is how many younger than Karyn?

Mathematics
1 answer:
Elden [556K]3 years ago
8 0

Answer:

12 years younger.

Step-by-step explanation:

Let Jan's age be J and Karyn's age be K.

J= \frac{2}{3}  K

Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.

J-8 = \frac{2}{5} (K+4)

=> (\frac{2}{3} - \frac{2}{5} ) K = \frac{8}{5} + 8

=> 4K = 48 X 3

=> K= 36.

=> J= 24.

So Jan is 12 years younger.

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Find and simplify each of the following for
WINSTONCH [101]

Answer:

(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

(B) f(x + h) - f(x) = 8xh + 4h² - 6h

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Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

- To find f(x + h) substitute x in the function by (x + h)

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) = 4(x + h)² - 6(x + h) + 6

- Lets simplify 4(x + h)²

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∴ 6(x + h) = 6x + 6h

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- Remember (-)(+) = (-)

∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

- Lets find f(x + h) - f(x)

∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)

- Remember (-)(-) = (+)

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6

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∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)

∴ f(x + h) - f(x) = 8xh + 4h² - 6h

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∴ \frac{f(x+h)-f(x)}{h}=8x+4h-6

* (C) \frac{f(x+h)-f(x)}{h}=8x+4h-6

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