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In music, a dotted note has  the duration of the original note. 

You misspoke there. 

A dot adds duration to the original note, the addition being half the original note. 

In other words, the duration of a dotted note becomes 150% of what it was without the dot. 

What fraction of a whole note is a dotted eighth note?   

Boiling it down to terms simple enough for me to understand,

1/8 is 2/16,   half of 2/16 is 1/16,   2/16 + 1/16 = 3/16.   

Thus, a dotted 1/8 note is 3/16 of a whole note, in those terms. 

_.

2x^2 = -2y^2 + 2x - 4y + 20

\(2x^2 = -2y^2 + 2x - 4y + 20\\ x^2 = -y^2 + x - 2y + 10\\ (x^2-x)\;\;\;+(y^2 +2y) = 10\\ (x^2-x+0.25)\;\;\;+(y^2 +y+1) = 10+0.25+1\\ (x-0.5)^2\;\;\;+(y+1)^2 = 11.25\\\)

This is a circle with a radius of  \(\sqrt{11.25}\)

What will the diameter be?

So what is the area of the square that circumscribes this circle?   Hint:  sketch it.

LaTex:

2x^2 = -2y^2 + 2x - 4y + 20\\ 
x^2 = -y^2 + x - 2y + 10\\
 (x^2-x)\;\;\;+(y^2 +2y) = 10\\
 (x^2-x+0.25)\;\;\;+(y^2 +y+1) = 10+0.25+1\\
 (x-0.5)^2\;\;\;+(y+1)^2 = 11.25\\

A dotted note actually has the duration of one and a half of the original  (not as you have said)

I will assume you are talking 4 4 otherwise known as common time.

An eighth note is a quaver worth 1/2 a beat.   A half of a half is 1/4  that is a semiquaver.

1/2  +  1/4 =  3/4

So a doted quaver (or doted 8th note) is worth 3/4 of a beat.   

(remembering that there are 4 beats in a whole note - which is a semibreve)

Added:

And     3 /4 of 1/4 = 3/16     

So a dotted quaver is a dotted eigth note and is worth 3/16 of a whole note.  (3/16 of a semibreve)

Maybe this will help.

Thanks Mathy.

Now it comes out perfectly well.

If you still need help with it please put this correct version, along with the explantatory note,  on the original thread.   

I can help you over there is you still want me too,

What is the minimum value of the expression x^2 + y^2 + 2x - 4y + 8 - 10y + 3y for real x and y?

Hello Guest!

\(x^2 + y^2 + 2x - 4y + 8 - 10y + 3y\\ =x^2+2x+4+y^2-14y+49-45\\ =(x+2)^2+(y-7)^2-45\\ =(x+2)^2+(y-7)^2-45\\ \color{blue}x=-2\\ \color{blue}y=7\\ 0^2+0^2-45=\color{blue} -45 \)

The minimum value of the expression is - 45.

  !

Using this equation, we can calculate the length of a longer leg:  b ≈ 23.204

Let's see if this equation works:

Angle A = 25.528 degrees

c = sqrt(b² - 10²) + tan(A) * 10

c ≈ 25.714

a = sqrt(c² - b²)

a ≈ 11.082

a + b + c = 11.082 + 23.204 + 25.714 = 60

If this is a legitamate unit test, you are cheating. Nevertheless, I will help you. When two triangles are similar, their angles are equal. Therefore, 

Angle A = Angle E

Angle B = Angle F

Angle C = Angle G

Angle A = 61°

Angle B = Angle F

52° = Angle G

Angle A + Angle C + Angle B = 180

61°+52°+ Angle B =180

Angle B =67

Find all real solutions to  \(x^2 + 4x + 4 =100x^2 - 20x + 1 \).

Hello Guest!

\(x^2 + 4x + 4 =100x^2 - 20x + 1\\ 99x^2-24x-3=0 \)

 a         b           c

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {24 \pm \sqrt{576-4\cdot 99\cdot (-3)} \over 2\cdot 99}\\ \)

\(x\in \{-\frac{1}{11},\frac{1}{3}\}\)

  !

What makes you think that a+b = 50 ? Would you explain, please?

a + b + c = 60

according to the pythagorean theorem, a^2 + b^2(the two legs) = c^2

we also know that a + b + c = 60

a + b = 50

a^2 + b^2 = 100

(a+b)^2 = 50^2: a^2+b^2+2ab = 2500

a + b = 50

a*b = 2400

you can solve from there to get the two legs. 

https://web2.0calc.com/questions/geometry_84069#r1

https://web2.0calc.com/questions/question-help_7

The area of the square is 80.

Im sorry that there is no diagram. I cant upload pictures for some reason

angle CDE = 60 degrees

This might be wrong..

First strip can be colored by = 4ways

2nd strip can be colored by = 3ways

3rd strip can be colored by = 3ways

4th strip can be colored by = 3ways

5th strip can be colored by = 3ways

6th strip can be colored by = 3ways

Then total ways = 4×3×3×3×3×3=12×3^4=12×81= 972

The smallest palindrome that will divide: 1, 2, 3, 4, 6, 7, 8, 9 = \(\fbox{48,384}\)

im just guessing:

the factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

the factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

the factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

the factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

the ones that appear in all 4 are 1, 2, 4, 5, 10, and 20

(I think... dont blame me if I get this wrong)

Assume all are a bit different.

I will assume that ever person is unique.   I will also (just for the working) assume every card is unique

There are 9! ways to line up the cards but for each of those there are  3! ^3 doubling up  9!/(3!)^3 = 1680 ways total sample space

There are 3! ways to give the reds one to each person then   6!/2^3 = 90     

90*3! = 540 ways for the desirable outcome

540/1680 = approx 32%

I don't know if it is right or not.   My answer seems to be in line with Catmg's.  :)  It also seems to be a reasonable answer.

I would  like to know why ItsFree is so certain their answer is correct though.  It is a bold statement to make.

First we know that ABC is an isosceles triangle. On line AB, there is a point P that makes CPB an isosceles triangle as well. Angle APC is 116. That means angle CPB is 180-116=64 degrees. Since triangle CPB is isosceles, angle PBC is also 64 degrees. That makes angle PCB 180-(64+64)=180-128=52 degrees. As you may recall, triangle ABC is isosceles, so angle ACP+52=64. Solving for the angle, we get ACP=64-52=12 degrees. (By the way, sorry there's no picture to show you my thinking.)

Arc YZ = 6pi       (Chord YZ is a diameter)

GingerAle and Catmg:

The correct answer is 1/1200

You have a denominator of 10x9x8x10 because that is the total amount of combinations.

The numerator is 6 because their are 3! ways to arange the 3 white balls.

<(-_-)>_It'sFree_>(-_-)<

This problem has already been answered: https://web2.0calc.com/questions/1-there-are-four-positive-integers-a-b-c-and-d-such

This question has been answered here: https://web2.0calc.com/questions/please-help_29192

This question has been answered here: https://web2.0calc.com/questions/help-plz_10265