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liubo4ka [24]
2 years ago
8

Prove that the two circles shown below are similar. (10 points)

Mathematics
1 answer:
____ [38]2 years ago
3 0

The translation will not affect the size and shape. Then the circle C and the circle E will be similar.

<h3>What is a circle?</h3>

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

There is only one parameter in the equation of the circle that is radius.

If the radius is changed, then the size of the circle is changed.

And the translation will not impact the size and shape.

Thus, the circle C and the circle E will be similar.

More about the circle link is given below.

brainly.com/question/11833983

#SPJ1

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Read 2 more answers
Find a number between 1 5/8 and 1.62501
Sauron [17]

Answer:

1 \frac{125001}{200000} or 1.625005

Step-by-step explanation:

To find a number between two numbers, if you're allowed to pick any number you want between those two numbers, one natural choice is the midpoint... the point that is exactly halfway between the two numbers.

<u>Finding a midpoint</u>

To find the midpoint of two numbers, divide their sum by 2:

\text{midpoint}=\dfrac{\text{first number}+\text{second number}}{2}

It is convenient to have both numbers in decimal form or both numbers in fraction form for adding and dividing by 2.

<u>Fraction form:</u>

To convert 1.62501 to a fraction, we note that the last decimal digit is in the hundred-thousandths place, so we'll need a fraction with 100,000 in the denominator.

1.62501=1\frac{62501}{100000}

Using our midpoint formula:

\text{midpoint} = \dfrac{ 1 \frac{5}{8} + 1 \frac{62501}{100000} } {2}

find a common denominator...

\text{midpoint} = \dfrac{ 1 +(\frac{5}{8})*\frac{12500}{12500} + 1 +\frac{62501}{100000} } {2}

\text{midpoint} = \dfrac{ 1 + \frac{62500}{100000}  + 1 +\frac{62501}{100000} } {2}

combining like terms...

\text{midpoint} = \dfrac{ 2 +\frac{125001}{100000} } {2}

rewriting the division as multiplication of a reciprocal....

\text{midpoint} =  \left(2 +\frac{125001}{100000} \right) *\dfrac{1}{2}

distributing...

\text{midpoint} =  \left(2 *\dfrac{1}{2} +\frac{125001}{100000} *\dfrac{1}{2}\right)

\text{midpoint} =  1 +\frac{125001}{200000}

\text{midpoint} =  1 \frac{125001}{200000}

So, 1 \frac{125001}{200000} is the midpoint of the two numbers, and is a number that is between them.

<u>Decimal form:</u>

To convert 1 \frac{5}{8}  to a decimal, we divide 5 by 8.  5 divided by 8 is 0.625.

So, 1 \frac{5}{8}=1.625

To find a midpoint of 1.625 and 1.62501, we use our midpoint formula:

Using our midpoint formula:

\text{midpoint} = \dfrac{ 1.625 + 1.62501} {2}

\text{midpoint} = \dfrac{ 3.25001} {2}

\text{midpoint} =1.625005

So, 1.625005 is midpoint of the two numbers, and is a number that is between them.

<u>Extension with decimals:</u>

Knowing the decimal form of the two numbers, 1.625 and 1.62501, we can include trailing zeros at the end of these numbers (since it is to the right of the decimal point), so that 1.625 is equivalent to 1.625000, and 1.62501 is equivalent to 1.625010.

Note that the last two digits are in the millionths place, and that changing the digit in the millionths place for the first number (while leaving all other digits as they are) will also be a number between the two numbers (all 9 of the numbers with a star written below):

1.625000

1.625001*

1.625002*

1.625003*

1.625004*

1.625005*

1.625006*

1.625007*

1.625008*

1.625009*

1.625010

8 0
2 years ago
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