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Norma-Jean [14]
3 years ago
11

Hello everyone, could you please solve this problem step by step. I don't have the exact solution and there are no options for i

t. Thanks a lot for your effort.

Mathematics
1 answer:
lara31 [8.8K]3 years ago
6 0

Answer:

<em>The area of the shaded part  = 61.46</em>

<em />

Step-by-step explanation:

Assume the hypotenuse of the triangle is c (c>0)

As the triangle inscribed in the semi circle is the right angle triangle, its hypotenuse is equal to the diameter of the circle.

The hypotenuse of the triangle can be calculated by Pythagoras theorem as following: c^{2} =a^{2} +b^{2} =(2\sqrt{5}) ^{2} + (4\sqrt{5}) ^{2} = 20 + 80 = 100

=> c = 10

So that the semi circle has the diameter = 10 => its radius = 5

  • The total area of 2 semi circles is equal to the area of the circle with radius =5

    => The total area of 2 semi circles is: \pi x 5^{2} = 25\pi

  • The area of a triangle inscribed in the semi circle is: 1/2 x a x b = 1/2 x 2\sqrt{5\\ x 4\sqrt{5} = 20

    => The area of 2 triangles inscribed in 2 semi circles is: 2 x 20 = 40

  • The area of the square is: c^{2} = 10^{2} =100

It can be seen that:

<em>The area of the shaded part = The area of the square - The total area of 2 semi circles + The total are of 2 triangles inscribed in semi circles </em>

<em>= 100 -  25</em>\pi<em> + 40 = 61.46</em>

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Answer:

x = 7.5

y = 75

Step-by-step explanation:

if one angle of an equilateral triangle is 60 degrees (180/3) then 4x + 2x + 2x = 8x = 60, so x = 7.5

for y, we'll have to take the right triangle. we know that 2x = 15, and MON = 60, so 180 - 60 - 15 = 105.

180 - 105 will give us y, which is 75

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3 years ago
How many gallons of a 70​% antifreeze solution must be mixed with 60 gallons of 20​% antifreeze to get a mixture that is 60​% ​a
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We have 60 gallons of 20% antifreeze.

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Source

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3 years ago
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Ludmilka [50]

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6 0
2 years ago
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A school district transported a total of 409 students and teachers to a zoo in buses and vans.
valina [46]

Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

Step-by-step explanation:

Since we have given that

Total number of students and teachers = 409

Let the number of vans be x

Let the number of buses be x+5

Number of students and teachers each bus transported = 55

Number of students and teachers each van transported = 12

According to question,

55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2

Total number of students and teachers who rode to the zoo in buses will be

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Total number of students and teachers who rode to the zoo in vans will be

12x\\\\=12\times 2=24

Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

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