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3 years ago

Which angle is a vertical angle with

Mathematics

1 answer:

yuradex [85]3 years ago

8 0

The angle that is a vertical angle is ii believe DFB !

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A square building with an area of 225 m2 has a garden surrounding it that has an equal width on all sides. The area of the garde

xenn [34]

Answer:

The width of the garden is 1.16 m

Step-by-step explanation:

step 1

<em>Find the area of the garden</em>

To find out the area of the garden multiply by 1/3 the area of the building

$225(\frac{1}{3})=75\ m^2$

step 2

Find the length side of the square building

The area of a square is

$A=b^2$

where

b is the length side of the square

we have

$A=225\ m^2$

$b^2=225\\b=15\ m$

step 3

Find the width of the garden

Let

x ----> the width of the garden

we know that

The area of the building plus the area of the garden is equal to

$(15+2x)^2=225+75$

solve for x

$225+60x+4x^2=225+75\\4x^2+60x-75=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is x=1.16 m

see the attached figure

therefore

The width of the garden is 1.16 m

Find the exact value

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$4x^2+60x-75=0$

$a=4\\b=60\\c=-75$

substitute in the formula

$x=\frac{-60\pm\sqrt{60^{2}-4(4)(-75)}} {2(4)}$

$x=\frac{-60\pm\sqrt{4,800}} {8}$

$x=\frac{-60\pm40\sqrt{3}} {8}$

$x=\frac{-60+40\sqrt{3}} {8}\ m$ ----> exact value

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Answer:

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Step-by-step explanation:

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kotykmax [81]

Use distance formula: $\sqrt{(x_2- x_1)^2 + (y_2-y_1)^2$

$\sqrt{(-8-12)^2 + (18-6)^2} = \sqrt{544} = 23.3$

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Answer:

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Step-by-step explanation:

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