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The difference in the height is 2*sqrt(15)/3.

Yes may you specify

Could you specify which angles are which?

Is A=50, B=50, and C=80? because that was wrong

Summing all three equations together, every term on the left-hand side cancels out, yielding that \(0 = a + 15 - 7 \Longrightarrow a = \boxed{-8}\).

Add all three equations together to get a+8=0 so a is -8

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we can draw out the angle bisectors and set variable x to get the three angles are 50, 50, and 80

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Go to this link to find the answer 

https://web2.0calc.com/questions/help_51190 

Thank you!

If the exterior angle is 80, then the top angle is 100 and the congruent angles are 40 each. Because there's an altitude there is a right triangel with one angle 90 and the other 40. The other angle is 50 degrees.

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The first letter has 2 choices and the last 4 have 12 each so there are 2*12^4 or 41472 ways.

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Lets try a list of primes

2: 5^23 is odd 2^23 is even No

3: 5^23 is -1mod3 2^23 is -1mod3 No

5.: 5^23 is divisible by 5 2^23 is not No

7: 5 and 2 are additive inverses mod 7. Exponent is odd. Yessssss

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Thank you! :DD

The area of the quadrilateral is 4*sqrt(3).

The total age of the turtles is 440 and the average is 22. After 2 turtles escaped, there were 18 turtles left with an average of 21 so the total age is now 378. The sum of the ages of the two escaped turtles is 62 so one is 26 and the other is 36, so the age of the box tutle is 36.

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36/pi or just like you put it?

thanks a lot!!

The quadratic can be written as (x-3)^2+51 so b+c=48

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Assuming that you mean 3pi/4, we know that a circle has 2pi radians so 3pi/4 is 3/8 of it. The circumference is 96 mm so the length of the arrc is 36pi mm

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Out of 3 consecutive numbers, one must be divisible by 2 and one must be divisible by 3 so the product must be divisible by 6. There are 79 integers from 2 to 80. 

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Cases

3 is rolled before even numbers: 1/4

3 is rolled after 1 even numbers: 3/16

7/16

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What two numbers multiply to make 70 and are different by 3. 

Take the first part first.  What two numbers can we multiply to make 70. 

If you don't see it intuitively, try them all.  Which one(s) is different by 3 ? 

 1 • 70    no... the diff is 69...  

 2 • 35    no... the diff is 33...  

 5 • 14    no... the diff is 9...  

 7 • 10    winner winner, chicken dinner!  

Melody's excellent answer suggested to set it up and solve as a quadratic equation, which is the best way to do it.  Notice, that factoring the quadratic takes you to the same question as the first line of this posting.  However, this problem was simple.  You might get into a situation where factoring would be difficult, if not impossible.  Then you need the proposition in quadratic form so you can use the quadratic formula. 

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We're looking for (-3+5i)(-3-5i) which is 9+25=34.

For any z in the form a+bi, z multiplied by its conjugate will be equal to a^2+b^2.

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My idea:

Pick which attribute(s) (color, shape, number, shading) is similar. Make all of the other one's different. Count the cases and multiply.

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You have to pick 3 vertices of the hexagon so there are 6choose3= 20 ways

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Here are the numbers I got

111

123

132

213

222

231

312

321

333

9 numbers

1/3

:D