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dedylja [7]
3 years ago
14

I need help with #7. Please help. I have to show all work so please explain

Mathematics
1 answer:
Sveta_85 [38]3 years ago
5 0

Answer: 2√17 A website to use for this would be "M a t h w a y"!!! Good luck, hope I helped!!!

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Find the area of the shaded region ​
o-na [289]

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}

5 0
2 years ago
Solve each prportion. (2/y-4)=(y+3/4)
vampirchik [111]

Answer:

y = 5, -4

Step-by-step explanation:

To solve proportions you cross-multiply.

\frac{2}{y-4} =\frac{y+3}{4} \rightarrow 2\times4 = (y-4)\times(y+3) \rightarrow 8=y^2-y-12

Now that we have 8 = y^2 - y - 12, we must make the entire trinomial equal to 0 by subtracting 8 from both sides.

y^2 - y - 20 = 0

Factor the trinomial.

(y - 5)(y + 4) = 0

Make both factors equal to 0 to solve for both values of y.

  • y - 5 = 0 --> y = 5
  • y + 4 = 0 --> y = -4

y = 5, -4

4 0
3 years ago
Solve the system of linear equations below. Enter your solution as an ordered pair (x,y). Do not include spaces in your answer..
kotykmax [81]
Y=3
4x+y=19
4x+3=19
4x=19-3
4x=16
x=4

pair is 4,3
5 0
3 years ago
Read 2 more answers
1/7x7=1 what property is that
Wewaii [24]

Identity property of multiplication

Identity property of multiplication: The product of 1 and any number is that number. For example, 7 × 1 = 7 7 \times 1 = 7 7×1=77, times, 1, equals, 7.

8 0
2 years ago
it took margaret 2 hours and 14 minutes to clean her room(including her closet). write the time it took margaret to clean her ro
Tpy6a [65]
An hour has 60 minutes in it, so the simplified form would be
2 14/60 (The 2 should be the whole number in front of the fraction)

In order to change it into a decimal, change it into an improper fraction and divide
134/60
2.23
5 0
3 years ago
Read 2 more answers
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