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Monica [59]
2 years ago
9

Giving 40 points!!! please help

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
5 0

Answer:

\textsf{D.} \quad x=4 \pm \sqrt{17}

Step-by-step explanation:

Rearrange the equation so it equals zero:

\begin{aligned} x^2+4 & =8x+5 \\ \implies x^2+4-8x-5 & = 0\\x^2-8x-1&=0\end{aligned}

Now use the quadratic formula to solve for x:

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

a=1, \quad b=-8, \quad c=-1

\implies x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(-1)}}{2(1)}

\implies x=\dfrac{8 \pm \sqrt{68}}{2}

\implies x=\dfrac{8 \pm \sqrt{4\cdot 17}}{2}

\implies x=\dfrac{8 \pm \sqrt{4}\sqrt{17}}{2}

\implies x=\dfrac{8 \pm 2\sqrt{17}}{2}

\implies x=4 \pm \sqrt{17}

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Answer:  The perimeter of each book is:  " 36 in. " .

__________________________________________________

Step-by-step explanation:

__________________________________________________

Note that the given units are all in "inches (in.)" .

Use the formula for the "perimeter of a rectangle" ;

{which happens to work for a "square" as well;

          since a "square" is a rectangle.}.

__________________________________________________

This is based on the assumption that the book is shaped like a

"rectangle"  (or "square" —which is a rectangle).

__________________________________________________

The formula for the Perimeter of a rectangle is:

  P = 2 L  + 2 w  ;

in which:

P =  the perimeter of the rectangle;

for which we shall solve;   [in "inches (in.)" ] ;

L =  the length of the rectangle = 10 in. (given) ;

w = the width of the rectangle = 8 in. (given) .

___________________________________________________

Now, plug the given values for the "length (L)" and the "width (w)" ;

 as follows:

___________________________________________________

    P = (2 * 10 in.)  +  (2 * 8 in.)  ;

    P = (20 in.)  +  (16 in.)  ;

   P = 36 in.

___________________________________________________

Answer:  The perimeter of each book is:  " 36 in. " .

___________________________________________________

Hope this helps!

    Best wishes in your academic pursuits

            — and within the "Brainly" community!

___________________________________________________

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