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the measure of angle ABC = 48 degrees

thank you.

Thank you.

That sounds like a commonly used one.

I think some people use Python.

I guess when I am ready to learn I will work out the best one for me.

(probably the easiest one that I can download for free)

C++.

xxxxxxxxxx

Thanks   

What coding language did you use?

One of these days I will learn to code in some modern language.   

Guest is correct 

But maybe this will explain better where the 2 came from.

\(y=a(x-5)(x+4)(x-1)\)

just sub in x=-3 and y=64 

Solve for a

And yes you do have to expand it.

Sorry, you got it spot on. It is: 1656 / 7776 =23 / 108. I just verified it by a computer code. The first stupid answer I worked out was for "at least 3 specific numbers, such as 3 ones"

You did not need to appologize :)

Could you elaborate on your answer please.

6^5 =7776 possible outcomes (order counts)

N,A and B represent different numbers that can be thrown

NNNNN       6 ways

NNNNA       6*5*5 =150ways

NNNAA       6*5*5C2=30*10 = 300 ways

NNNAB       6*5*4 *5C2= 120*10= 1200 ways

1200+300+150+6 = 1656  (order counts)

P(at least 3 the same) =   1656/7776 = 23/108

I do not guarantee my answers, especially not counting and probability answers.

This answer does seem higher than I would have expected.

(x-5)(x+4)(x-1) = 0      subbing in x = -3   yields   32    so there must be a 2 multiplier

2 (x-5)(x+4)(x-1) =    multiply all of this out :

2x^3-4x^2-38x+40

Ohhhh.... yes.  I'm going to take some time off.  This is the second time I've overlooked the simplest thing. 

natural log?  The way I read it was that 2e was the question number ... as in 2a, 2b, 2c, etc.  What would be the purpose in saying the word "Question" at the beginning of a question? 

(5 nCr 3 * 5^2) + (5 nCr 4 * 5^1) + (5 nCr 5 * 5^0) = 276 / 6^5 =23 /648

[Sorry Melody. Didn't know you were working on it]

\((a+b)\sqrt{cd}\)       Replace  a  with  2 ,  b  with  4 ,  c  with  3 ,  and  d  with  12

\(=\ (2+4)\sqrt{(3)(12)}\)       Now we can simplify this expression

\(=\ (6)\sqrt{36}\)

\(=\ (6)(6)\)

\(=\ 36\).

I could find only one triplet:

[2  x  5  x  7] / [ 2  +  5  +  7] ==5

(-9x^2 + 12x^2)         - x + 7

AB = sqrt [(4 + 2)² + (4 - 2)²] 

There is a lot more than that.

Guest has only found the simplest ones.

Look again guest.

draw it!

The only really important thing that you may not know is that

the tangent to a circle is perpendicular (at right angles) to the radius that it intersects with.

I think it either means  

\((2*10^4)*2n=4n*10^4\\ or\\ 2e^4*2n=4ne^4\)

I really dislike the e notation for scientific notation, it is always confusing.

In the diagram, triangle ABE, triangle BCE, and triangle CDE are right-angled, with angle AEB = angle BEC = angle CED = 60 degrees, and AE=24.  Find the perimeter of quadrilateral ABCD.

Perimeter = 24 + √432 + √108 + √27 + √9

Hi, thanks guest,

I did not realize this was already answered but I have made the pic already so I might as well post it.

Probability = 1 - [6 * 5 * 4 * 3] / 6^4 =1 - [360 / 1,296] =13 / 18