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GenaCL600 [577]
3 years ago
8

The area of a square in square feet is

Mathematics
1 answer:
Sedaia [141]3 years ago
4 0

Answer:

Part 1) The expression for the perimeter is P=4(25z-3) or  P=100z-12

Part 2) The perimeter when  z = 15 ft. is P=1,488\ ft

Step-by-step explanation:

Part 1)

we have

625z^{2}-150z+9

Find the roots of the quadratic equation

Equate the equation to zero

625z^{2}-150z+9=0

Complete the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

625z^{2}-150z=-9

Factor the leading coefficient  

625(z^{2}-(150/625)z)=-9

625(z^{2}-(6/25)z)=-9

Complete the square. Remember to balance the equation by adding the same constants to each side

625(z^{2}-(6/25)z+(36/2,500))=-9+(36/4)

625(z^{2}-(6/25)z+(36/2,500))=0

Rewrite as perfect squares

625(z-6/50)^{2}=0

z=6/50=0.12 -----> root with multiplicity 2

so

The area is equal to  

A=625(z-0.12)(z-0.12)=[25(z-0.12)][25(z-0.12)]=(25z-3)^{2}

The length side of the square is b=(25z-3)

therefore

The perimeter is equal to

P=4b

P=4(25z-3)

P=100z-12

Part 2) Find the perimeter when  z = 15 ft.

we have

P=100z-12

substitute the value of z

P=100(15)-12=1,488\ ft

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y

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5

The point-slope formula states:

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y

−

y

1

)

=

m

(

x

−

x

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Where

m

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(

x

1

y

1

)

is a point the line passes through.

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(

y

−

−

1

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=

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(

x

−

−

3

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y

+

1

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=

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5

(

x

+

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)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

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m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

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+

1

=

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