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Salsk061 [2.6K]
2 years ago
14

Choose the smallest fraction? 3/4 1/5 3/10 1/7

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
5 0

Answer:

Hey there!

3/4= 0.75

1/5=0.2

3/10=0.3

1/7=0.14

Thus, 1/7 is the smallest fraction.

Hope this helps :)

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Angle X measures 110 Degrees if angle x is rotated 60 degrees what is the measure of angle x ?
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Rotatation could be done to left or right.

110 + 60 = 170 degrees => Rotation to the right side.

110 - 60 = 50 degrees= > Rotation to the left side.

We can see in the choices that 170 degrees is the right choice.

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Start with

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1=\dfrac{3}{3n^2}+\dfrac{n^2-4n-5}{3n^2} = \dfrac{n^2-4n-2}{3n^2}

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1=\dfrac{1}{1}+\dfrac{1+4-5}{3} \iff 1 = 1+0

which is true

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Find the area of the shaded region ​
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so hmmm let's get the area of the whole hexagon, and then get the area of the circle inside it, then <u>subtract the area of the circle from that of the hexagon's</u>, what's leftover is what we didn't subtract, namely the shaded part.

\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cot\stackrel{\stackrel{degrees}{\downarrow }}{\left( \frac{180}{n} \right)}~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ n=\stackrel{hexagon}{6}\\ s=\frac{9}{2} \end{cases}\implies A=\cfrac{1}{4}(6)\left( \cfrac{9}{2} \right)^2 \cot\left( \cfrac{180}{6} \right)

A=\cfrac{1}{4}(6)\cfrac{9^2}{2^2} \cot(30^o)\implies A=\cfrac{243}{8}\cot(30^o)\implies A=\cfrac{243\sqrt{3}}{8} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{4}{5} \end{cases}\implies A=\pi \left( \cfrac{4}{5} \right)^2\implies A=\cfrac{16\pi }{25} \\\\[-0.35em] ~\dotfill

\stackrel{\textit{area of the hexagon}}{\cfrac{243\sqrt{3}}{8}}~~ - ~~\stackrel{\textit{area of the circle}}{\cfrac{16\pi }{25}}\implies \cfrac{6075\sqrt{3}-128\pi }{200}

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