1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

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3 years ago

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A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

Nastasia [14]

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

$y =\frac{1}{10} x +60$

This is the equation of the line

using a graph tool

see the attached figure

Statements

case a) The slope of the function is $1.00

The statement is False

The slope of the function is equal to $\frac{1}{10} \frac{\$}{tokens}$

case b) The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

for $x=0$

$y =\frac{1}{10}*0 +60$

$y =\$60$

case c) The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to $y =\frac{1}{10} x +60$

case d) The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

case e) The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure

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3 years ago

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a landscaper is designing a park in the shape of a kite with a fountain in the center, F. AK = 28 ft, PF=48 ft and F=32 ft. He w

Keith_Richards [23]

Answer:

169.9

Step-by-step explanation:

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3 years ago