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icang [17]
3 years ago
5

Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multi

media sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria.
No Common Tangents


Diagram:








Justification:

Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0

I made mine from google drawings

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Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, whe
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Rationalizing the denominator involves exploiting the well-known difference of squares formula,

a^2-b^2=(a-b)(a+b)

We have

(\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14

so that

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}

Rewrite 16 and 32 as powers of 2, then simplify:

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}

\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7

So we have <em>A</em> = 8, <em>B</em> = 2, <em>C</em> = 4, and <em>D</em> = 7, and thus <em>A</em> + <em>B</em> + <em>C</em> + <em>D</em> = 21.

3 0
3 years ago
A painter used 3/4 of a gallon of paint to cover 1/4 of a wall. How many gallons of paint will the painter use for the entire wa
Ivahew [28]
3 gallons because 3/4 of a gallon covers 1/4 of a wall so you multiply the amount of gallons used for a wall times 4 which is 12/4 (keep the denominator the same ) and then divide 12 by 4 which is 3 gallons
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3 years ago
A rectangle is 4 units long and 2 units wide. What is its area?
Irina18 [472]

rectangle area = l * w

2 * 4 =

8 units²

7 0
3 years ago
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Which number is the smallest? 4.4 ⋅ 10−5, 3.99 ⋅ 10−6, 2.6 ⋅ 102, 1.85 ⋅ 103
harina [27]
The answer is:  [B]:  " 3.99 * 10⁻⁶ " .
______________________________________________
  Note:
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We are given the following answer choices, and we are asked which one is the "smallest number" :
_______________________________________________
  [A]:  4.4 * 10⁻⁵
_________________________________________
  [B]:  3.99 ⋅ 10⁻⁶
______________________
  [C]:  2.6 ⋅ 10²
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  [D]:  1.85 ⋅ 10³
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         We can rule out answer choices: [C] and [D]; since these values, essentially "direct us" to move the decimal point FORWARD "2 places" and "3 places", respectively;  whereas choices [A] and [B] essentially "direct us" to move the decimal point BACKWARD "5 places" and "6 places" respectively.  Note that all values given in the answer choices are written in proper "scientific notation" —that is, beginning with a "single integer followed by (a) decimal point(s) and then additional digits (when needed).  So, the answer choice that essentially "directs us" to move the decimal point BACKWARD "6 places" —
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             →   Answer choice:  [B]:  " 3.99 * 10⁻⁶ "  ;
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                  is the smallest value ; and as such, the correct answer.
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7 0
3 years ago
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mrs papica bought 20 cupcakes for her class. one-half of them have chocolate frosting and one-fourth of them have vanilla frosti
Jobisdone [24]
Chocolate- 20×.5= 10  Vanilla-20×.25=5  Strawberry- 20×.25=5   10+5+5=20
8 0
4 years ago
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