2 years ago

Which of the following best describes the slope of the line below?

Mathematics

1 answer:

kati45 [8]2 years ago

7 0

Answer is- D- (Zero)

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What is the following quotient? 5/√11-√3

kati45 [8]

ANSWER

$\frac{5( \sqrt{11} + \sqrt{3} )} {8}$

EXPLANATION

The given rational function is

$\frac{5}{ \sqrt{11} - \sqrt{3}}$

We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

$\sqrt{11} - \sqrt{3}$

which is

$\sqrt{11} + \sqrt{3}$

When we rationalize we obtain:

$\frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )}$

The denominator is now a difference of two squares:

$(a - b)(a + b) = {a}^{2} - {b}^{2}$

We apply this property to get

$\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )}$

$\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3}$

This simplifies to

$\frac{5( \sqrt{11} + \sqrt{3} )} {8}$

$\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3}$

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Step-by-step explanation:

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