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kolezko [41]
3 years ago
11

What is the probability that a point chosen at random in the regular hexagon lies in the shaded region? A 1/3 B 2/5 C 1/2 D 2/3

Mathematics
2 answers:
kondaur [170]3 years ago
8 0
Answer: option A) 1/3

Justification:

1) The probability that a point chosen at random <span>in the regular hexagon lies in the shaded region is equal to:

  area of the shaded region
---------------------------------------
     area of the hexagon

2) The hexagon is formed by 6 equal triangles and the shaded area is formed by 2 of those triangles.

3) Therefor,naming x the area of one triangle, the the above fraction is equal to:

  area of two triangles           2x        
------------------------------- =    --------   = 2/6 = 1/3
  area of six triangles            6x

And that is the answer: 1/3
</span>
aleksandr82 [10.1K]3 years ago
7 0
C Is the final answer
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P is the midpoint of HR. Given HP = 7x + 2 and PR = 58; find the value of x
Zielflug [23.3K]

Answer:

x = 8

Step-by-step explanation:

Since P is at the midpoint of HR, then

HP = PR ← substitute values

7x + 2 = 58 ( subtract 2 from both sides )

7x = 56 ( divide both sides by 7 )

x = 8

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3 years ago
5+7k&gt;=-30 and -4k +4&gt;20​
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Answer:

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Step-by-step explanation:

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Please help with question ​
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Step-by-step explanation:

8 0
3 years ago
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Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims
hjlf

Answer:

12 miles

Step-by-step explanation:

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 1/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

Total distance Alyssa cycled and ran =

\frac{4}{5} + \frac{1}{8}

\frac{32 + 5}{40} = \frac{37}{40}

Distance she swam =  1 - 37/40 = 3/40

3/40 of the distance is 0.9

the total distance = 40/3 x 0.9 = 12 miles

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2 years ago
Write and equation of the translated or rotated graph in general form (picture below)
WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ (\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=

 ( \frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0

* Lets open the bracket

∴ \frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0

* Lets add the like terms

∴ \frac{-4xy}{2}-16=0

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

6 0
3 years ago
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