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Alex73 [517]
3 years ago
11

A number is three less than six times another numbers. The sum is 53. Find the numbers

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
3 0
X = 6y - 3
x + y = 53

6y - 3 + y = 53
7y - 3 = 53
7y = 53 + 3
7y = 56
y = 56/7
y = 8

x = 6y - 3
x = 6(8) - 3
x = 48 - 3
x = 45

ur numbers are : 8 and 45
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Answer:

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Step-by-step explanation:

A quadratic expresion is of the form

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The give options are:

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From the given options, the only expression which is quadratic is

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Tan2x =\frac{-24}{7}

<u>Step-by-step explanation:</u>

Here we have , cos x = -4/5 ( corrected as given -45 which is not possible ) ,

180° < x < 270° i.e. in third quadrant  . We need to find tan⁡(2x) . Let's find out:

⇒ Tan\alpha  = \frac{sin\alpha }{cos\alpha }

⇒ Tan\alpha  = \frac{\sqrt{1-(cos\alpha)^2} }{cos\alpha }

⇒ Tan\alpha  = \frac{\sqrt{1-(\frac{-4}{5})^2} }{\frac{-4}{5} }

⇒ Tan\alpha  = \frac{-5}{4}\sqrt{1-(\frac{16}{25}) }

⇒ Tan\alpha  = \frac{-5}{4}\sqrt{(\frac{25-16}{25}) }

⇒ Tan\alpha  = \frac{-5}{4}(\frac{3}{5}) }

⇒ Tan\alpha  = \frac{-3}{4} , since in third quadrant . Tan\alpha  = \frac{-3}{4} remains same .

Now , Tan2x = \frac{2tanx}{1-(tanx)^{2}}}

⇒ Tan2x = \frac{2tanx}{1-(tanx)^{2}}}

⇒ Tan2x = \frac{2(\frac{-3}{4})}{1-(\frac{-3}{4})^{2}}}

⇒ Tan2x = \frac{-3}{2}(\frac{16}{7})

⇒ Tan2x =\frac{-24}{7}

Therefore, Tan2x =\frac{-24}{7} .

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