Mathematics, 19.07.2019 17:30 blink182lovgabbie

Circle 1 is centered at 4,3 and has a radius of 5 centimeters circle 2 is centered at 6,-2 and has a radius of 15 centimeters. what transformatons can be applied to circle one to prove that the aircles are similar?

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We know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that
Circle 1 is centered at (4,3) and has a radius of 5 centimeters
Circle 2 is centered at (6,-2) and has a radius of 15 centimeters

step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)> (x+2,y-5)
so
(4,3)> (4+2,3-5)> (6,-2)
so
center circle 1 is now equal to center circle 2
The circles are now concentric (they have the same center)

step 2
A dilation is needed to increase the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1> 15/5> 3

radius circle 1 will be=5*scale factor> 5*3> 15 cm
radius circle 1 is now equal to radius circle 2

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

Answer from: Quest

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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Circle 1 is centered at 4,3 and has a radius of 5 centimeters circle 2 is centered at 6,-2 and has a...

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