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2 years ago

Solve for x by completing the square: x2 − 8x + 13 = 0. show all work

1 answer:

5 0

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

<h3>How to find the roots of a polynomial by completing the square</h3>

In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:

x² - 8 · x + 13 = 0

x² - 8 · x + 16 = 3

(x - 4)² = 3

x - 4 = ± √2

x = 4 ± √2

There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.

To learn more on quadratic equations: brainly.com/question/2263981

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Racheal used a total of 5 1/6 gallons of gas while driving her car. Each hour she was driving, she used 5/9 gallons of gas. What

Andreyy89

Answer: The correct answer is: " 9.3 hours " .

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Step-by-step explanation:

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To calculate:

Let "gal" represent "gallons (of gas)" ;

Let "h" represent "hour(s)" ;

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5 $\frac{1}{6}$ gal * (  1 h  ) = ? h ;

( 5/9 gal ) ;

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Note: On the "left-hand side" of the equation;

The units of "gal" ["gallons"] — "cancel out" ;

→ {since: "gal/ gal = 1"} ;

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and we can rewrite our equation as:

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( 5 $\frac{1}{6}$ )

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( 5/9 )

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To solve:

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5 1/6 ÷ (5/9) =

5 1/6 * (9/5) ;

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Note: Dividing by a fraction is the same as multiplying by that very fraction's reciprocal form.

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Now, let us convert "5 1/6" ; which is a "mixed fraction" ; into an

"Improper fraction" ;

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To do this, we can use the "MAD" method:

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M: Multiply the "denominator number" of the "fraction portion" [within the "mixed fraction"]—by the "whole number" [within the "mixed fraction" ; In this case: "6" , multiplied by "5" ; to get "30" ;

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Then:

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A: Add this obtained value; to the "numerator number" of the

"fraction portion" [within the "mixed fraction"] ;

In this case: "30" ; added to "1" ; to get 31:

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Then:

D: Divide this number by the "denominator number" of the "fraction portion" [within the "mixed fraction"] ; but instead of solving for the quotient—write in the format of a fraction:

In this case: " $\frac{31}{6}$ " .

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Now, substitute this "improper fraction" into our original problem; and rewrite:

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" $\frac{31}{6} * \frac{9}{5}$ " hours;

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We can reduce the "9" to "3" ; and the "6" to "2" ;

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{Since "9/6 = 3/2" };

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And rewrite as:

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" $\frac{31}{2} * \frac{3}{5}$ " hours ;

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Note: " \frac{31}{2} * \frac{3}{5} " ;

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= " $\frac{(31*3)}{(2*5)} = \frac{93}{10}$ " ;

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= 93 ÷ 10 ;

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= 9.3 hours.

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The answer is: " 9.3 hours " .

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Hope this explanation is helpful!

Best of luck to you in your academic pursuits!

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3 0

3 years ago

2*2 <img src="https://tex.z-dn.net/?f=%20%5Ccos%28300%29%20" id="TexFormula1" title=" \cos(300) " alt=" \cos(300) " align="ab

ankoles [38]

Step-by-step explanation:

$\cos(300 \degree) \\ \\ = \cos(360 \degree - 60\degree) \\ \\ = \cos( 60\degree) \\ \\ = \frac{1}{2} \\ \\ \huge \orange{ \boxed{ \therefore \: \cos(300 \degree) = \frac{1}{2} }}$

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3 years ago

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zaharov [31]

Answer:

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Find the diagram attached

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l = √6400+3600

l = √10,000

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3 years ago

What's 16,048 ÷by 1/8? and can you please explain it

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16, 048÷ 1/8

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4 years ago

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Greeley [361]

Hi ;-)

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3 years ago

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