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3 years ago

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A regular pentagon has an apothem of 3.2m and an area of 37.2m squared. What is the length of one side of the pentagon?

1 answer:

Shtirlitz [24]3 years ago

3 0

Area=5/2*apothem*side
so
side=(2*area)/(5*apothem)
in your case
side=(2*37.2)/(5*3.2)=4.65m

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Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

5 0

3 years ago

Miguel tells his teacher1/5 is the same as 20%. Which best justifies Miguel’s answer? a.5 goes into 100 twenty times, so 20% is

svetoff [14.1K]

Answer:

C. 5 goes into 100 twenty times, and 1 times 20 is 20

Step-by-step explanation:

Since, we know that when we multiply both numerator and denominator of a fraction by a same number then we obtain an equivalent fraction,

Here, the given fraction,

$\frac{1}{5}$

By the above statement,

$\frac{1}{5}=\frac{1\times 20}{5\times 20}=\frac{20}{100}$

Now,

$a\%=\frac{a}{100}$

$\implies \frac{20}{100}=20\%$

Hence,

$\frac{1}{5}=20\%$

Option C is correct.

3 0

3 years ago

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What value of x makes the equation -5x - (-7 - 4x) = -2(3x - 4) tru

Aloiza [94]

Answer: 1/10 or 0.1

Step-by-step explanation:

-(-7 - 4x) = -2(3x - 4)

7 + 4x = -6x + 8

* subtract 7 from both sides

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* Add 6x to both sides

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* Divide both sides by 10

x = 1/10 or 0.10

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2 years ago

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What is 1.08 to the power of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D" id="TexFormula1" title="\frac{1}{5}" alt="

OlgaM077 [116]

Answer:

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Step-by-step explanation:

No it isn't, because:

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3 years ago