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2 years ago

Simplify the expression. 16(1/2x)^4 The simplified expression is

Mathematics

1 answer:

SVEN [57.7K]2 years ago

4 0

Answer:

1/x^4

Steps:

(1/2x)^4 = 1/2^4x^4

= 16 * 1/2^4x^4

Multiply fractions: a * b/c = a * b/c

= 1 * 16/2^4x^4

Multiply the numbers: 1 * 16 = 16

16/2^4x^4

Factor 16: 2^4

= 2^4/2^4x^4

Cancel the common factor: 2^4

= 1/x^4

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Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

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This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

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Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

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Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

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$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

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