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vichka [17]
2 years ago
12

What is the following quotient? StartFraction 1 Over 1 + StartRoot 3 EndRoot EndFraction StartFraction StartRoot 3 EndRoot Over

4 EndFraction StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction
Mathematics
2 answers:
bazaltina [42]2 years ago
7 0

Answer:

D

Step-by-step explanation:

edge2020

Tems11 [23]2 years ago
6 0

Answer:

  D.  StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

Step-by-step explanation:

Multiply numerator and denominator by the conjugate of the denominator. Then the denominator is the difference of squares, which will be rational. This simplification is called "rationalizing the denominator."

  \dfrac{1}{1+\sqrt{3}}=\dfrac{1}{1+\sqrt{3}}\cdot\dfrac{1-\sqrt{3}}{1-\sqrt{3}}=\dfrac{1-\sqrt{3}}{1^2-(\sqrt{3})^2}\\\\=\dfrac{1-\sqrt{3}}{-2}=\boxed{\dfrac{-1+\sqrt{3}}{2}}

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2 years ago
Which of the following exponential functions represents the graph below?
mario62 [17]

Answer:

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Step-by-step explanation:

Since the graph shown corresponds to an exponential "decay" (the function decreases as we move from left to right), the base of the exponent has to be a number smaller than 1 (one). So we examine the only two options that give such (options C and D which have fractions as the base - 1/3 and 1/5 respectively)

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