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REY [17]
2 years ago
8

5. What is the value of x?

Mathematics
1 answer:
balu736 [363]2 years ago
4 0

Answer:

5\sqrt{3}

Step-by-step explanation:

in a 30-60-90 triangle the ratio of sides, respectively, is 1 : \sqrt{3} : 2

you can set up a proportion like this to solve for 'x':

\sqrt{3} / 1 = 15 / x

cross-multiply:

\sqrt{3}x = 15

x = 15/\sqrt{3}

rationalize the denominator by multiply top and bottom by \sqrt{3}

you get 15\sqrt{3} ÷ 3 which is 5\sqrt{3}

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What does the fundamental theorem of algebra illustrate?
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Answer:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

Step-by-step explanation:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

We have to find the roots of this given equation.

If a quadratic equation is of the form ax^{2}+bx +c=0

Its roots are \frac{-b+\sqrt{b^{2}-4ac } }{2a} and \frac{-b-\sqrt{b^{2}-4ac } }{2a}

Here the given equation is 2x^{2}-4x-1 = 0

a = 2

b = -4

c = -1

If the roots are x_{1} and x_{2}, then

x_{1} = \frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}

                       = \frac{4 +\sqrt{24}}{4}

                       = \frac{2+\sqrt{6} }{2}

x_{2} = \frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}

                        = \frac{4 +\sqrt{8}}{4}

                        = \frac{2-\sqrt{6} }{2}

These are the two roots of the equation.

6 0
2 years ago
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