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crimeas [40]
3 years ago
5

A root of x2 – 5x – 1 = 0 is

Mathematics
2 answers:
yan [13]3 years ago
8 0
x^2-5x-1=0\\\\
a=1,\ b=-5,\ c=-1\\\\
\Delta=b^2-4ac=(-5)^2-4*1*(-1)=25+4=29\\\\
\sqrt{\Delta}=\sqrt{29}\\\\
x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{29}}{2*1}=\frac{5-\sqrt{29}}{2}\\\\
x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*1}=\frac{5+\sqrt{29}}{2}\\

Natasha2012 [34]3 years ago
8 0

<em><u>Answer:</u></em>

The roots are \frac{5+\sqrt{29}}{2} and \frac{5-\sqrt{29}}{2}

<em><u>Explanation:</u></em>

<u>The general form of the quadratic equation is:</u>

ax² + bx + c = 0

<u>The given equation is:</u>

x² - 5x - 1 = 0

<u>By comparison:</u>

a = 1

b = -5

c = -1

To get the roots of the equation, we will use the quadratic formula shown in the attached image.

<u>This means that:</u>

either x = \frac{5+\sqrt{(-5)^2-4(1)(-1)}}{2(1)}  = \frac{5+\sqrt{29}}{2}

or x = \frac{5-\sqrt{(-5)^2-4(1)(-1)}}{2(1)}  = \frac{5-\sqrt{29}}{2}

Hope this helps :)

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3 years ago
How is the series 5+11+17…+251 represented in summation notation?
NISA [10]

Answer:

\displaystyle \large{\sum_{n=1}^{42}(6n-1)

Step-by-step explanation:

Given:

  • Series 5+11+17+...+251

To find:

  • Summation notation of the given series

Summation Notation:

\displaystyle \large{\sum_{k=1}^n a_k}

Where n is the number of terms and \displaystyle \large{a_k} is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

  • Arithmetic Series

A series that has common difference.

  • Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

  • 11-5 = 6
  • 17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

\displaystyle \large{a_n=a_1+(n-1)d}

Where \displaystyle \large{a_n} is the nth term, \displaystyle \large{a_1} is the first term and \displaystyle \large{d} is the common difference:

So for our general term:

\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}

And for number of terms, substitute \displaystyle \large{a_n} = 251 and solve for n:

\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}

Now we can convert the series to summation notation as given the formula above, substitute as we get:

\displaystyle \large{\sum_{n=1}^{42}(6n-1)

5 0
2 years ago
HELP ME PLEASSDJDJXKKCKCKC
attashe74 [19]

the answers is

1 Inch = 4 Feet


Here is the explanation -


the side of square = 12


length of Ground - 48


ratio of length = 12 /48


= 1/4


1 : 4

bye

7 0
2 years ago
Plz help<br> Thank you!<br> If you can
aleksklad [387]

Answer: 140

Step-by-step explanation: It doesn't change because they arethe same proportional angle.

8 0
3 years ago
Read 2 more answers
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