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FromTheMoon [43]
3 years ago
6

Find the perimeter of the polygon with vertices A(-6,-4), B(-3,6), C(4,0), and D(2,-1)?

Mathematics
1 answer:
EleoNora [17]3 years ago
6 0
Check the picture below.

so the perimeter of the polygon is the sum of all its sides, namely, AB + BC + CD + DA.

now, let's check how long each side is,

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&A&(~{{ -6}} &,&{{ -4}}~) 
%  (c,d)
&B&(~{{ -3}} &,&{{ 6}}~)
\end{array}
\\\\\\
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\
-------------------------------\\\\
AB=\sqrt{[-3-(-6)]^2+[6-(-4)]^2}
\\\\\\
AB=\sqrt{(-3+6)^2+(6+4)^2}
\\\\\\
AB=\sqrt{3^2+10^2}\implies \boxed{AB=\sqrt{109}}\\\\
-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&B&(~{{ -3}} &,&{{6}}~) 
%  (c,d)
&C&(~{{ 4}} &,&{{ 0}}~)
\end{array}
\\\\
-------------------------------\\\\
BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2}
\\\\\\
BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\
-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&C&(~{{ 4}} &,&{{0}}~) 
%  (c,d)
&D&(~{{ 2}} &,&{{ -1}}~)
\end{array}
\\\\
-------------------------------\\\\
CD=\sqrt{(2-4)^2+(-1-0)^2}\implies CD=\sqrt{(-2)^2+(-1)^2}
\\\\\\
\boxed{CD=\sqrt{5}}\\\\
-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&D(~{{ 2}} &,&{{-1}}~) 
%  (c,d)
&A&(~{{ -6}} &,&{{ -4}}~)
\end{array}\\\\
-------------------------------\\\\
DA=\sqrt{[-6-2]^2+[-4-(-1)]^2}\\\\\\ DA=\sqrt{(-6-2)^2+(-4+1)^2}
\\\\\\
DA=\sqrt{(-8)^2+(-3)^2}\implies \boxed{DA=\sqrt{73}}

sum those sides up, and that's the perimeter of the polygon.

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Zigmanuir [339]

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Step-by-step explanation:

3 0
3 years ago
Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600
Alisiya [41]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

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-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                             \frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

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                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

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3 years ago
What is the equation of a line that passes through (7,8) and has a slope of -3
Komok [63]
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Answer choice A
3 0
3 years ago
Read 2 more answers
Verify that the roots of 5x²- 6x -2 = 0 are <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%20%2B%20%5Csqrt%7B19%7D%20%7D%7B5%7D%2
Mice21 [21]

Answer:

Proof below.

Step-by-step explanation:

<u>Quadratic Formula</u>

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

<u>Given quadratic equation</u>:

5x^2-6x-2=0

<u>Define the variables</u>:

  • a = 5
  • b = -6
  • c = -2

<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:

\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(5)(-2)}}{2(5)}

\implies x=\dfrac{6 \pm \sqrt{36+40}}{10}

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\implies x=\dfrac{6 \pm2\sqrt{19}}{10}

\implies x=\dfrac{3 \pm \sqrt{19}}{5}

Therefore, the exact solutions to the given <u>quadratic equation</u> are:

x=\dfrac{3 + \sqrt{19}}{5} \:\textsf{ and }\:x=\dfrac{3 - \sqrt{19}}{5}

Learn more about the quadratic formula here:

brainly.com/question/28105589

brainly.com/question/27953354

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