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hammer [34]
3 years ago
7

Find the perimeter of pentagon STUVW WITH VERTICES S(0,0) T(3,-2) U(2,-5) V(-2,-5) W(-3,-2)

Mathematics
1 answer:
andrew11 [14]3 years ago
4 0
Use the distance formula.

\sqrt{( x_{2} - x_{1} )^2 + (y_{2} - y_{1})^2}

 
Points S and W.
\sqrt{(3)^2 + (2)^2}

\sqrt{9+4}

\sqrt{13}

~3.6

Points S and T
\sqrt{(3 - 0)^2 + (-2 - 0)^2}

\sqrt{(3)^2 + (-2)^2}

\sqrt{9+4}

\sqrt{13}

~3.6

Points T and U
\sqrt{(3 - 2)^2 + (-2 + 5)^2}

\sqrt{(1)^2 + (3)^2}

\sqrt{1+9}

\sqrt{10}

~3.1

Points U and V
\sqrt{(2+2)^2 + (-5 + 5)^2}

\sqrt{(4)^2 + (0)^2}

\sqrt{16}

~4

Points V and W
\sqrt{(-2+3)^2 + (-5 + 2)^2}

\sqrt{(1)^2 + (-3)^2}

\sqrt{2+9}

\sqrt{11}

~3.3

Add all these together.

3.3 + 3.1 + 4 + 3.1 + 3.6
≈17
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Joel is designing a ramp for a bike trick. He draws this diagram. What is the value of x?
inn [45]

Answer:

x = -1

x = 5

Step-by-step explanation:

Use pythagorean theorem: a² + b² = c²

x² + (2x + 2)² = (2x + 3)²

Since these are quantities, you'll have to make them into quadratic equations.

(2x + 2)(2x + 2) = 4x² + 4x + 4x + 4

(2x + 3)(2x + 3) = 4x² + 6x + 6x + 9

x² + 4x² + 4x + 4x + 4 = 4x² + 6x + 6x + 9

Combine like terms

5x² + 8x + 4 = 4x² + 12x + 9

Move one side to set the equation equal to 0

x² - 4x - 5 = 0

Solve

x² - 5x + x - 5 = 0

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<em>We</em><em> </em><em>can</em><em> </em><em>check</em><em> </em><em>that</em><em> </em><em>these</em><em> </em><em>are</em><em> </em><em>correct</em><em> </em><em>by</em><em> </em><em>plugging</em><em> </em><em>them</em><em> </em><em>in</em><em> </em><em>for</em><em> </em><em>x</em><em> </em><em>and</em><em> </em><em>seeing</em><em> </em><em>if</em><em> </em><em>they</em><em> </em><em>are</em><em> </em><em>equal</em>

<em>For</em><em> </em><em>example</em>

<em>(</em><em>-1</em><em>)</em><em>²</em><em> </em><em>+</em><em> </em><em>(</em><em>2</em><em>(</em><em>-1</em><em>)</em><em> </em><em>+</em><em> </em><em>2</em><em>)</em><em>²</em><em> </em><em>=</em><em> </em><em>(</em><em>2</em><em>(</em><em>-1</em><em>)</em><em> </em><em>+</em><em> </em><em>3</em><em>)</em><em>²</em>

<em>1</em><em> </em><em>=</em><em> </em><em>1</em>

3 0
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