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5 +10 + 7 + 3  =  25

1/3 + 2/9 + 5/9  =  3/9 +2/9 + 5/9  =  10/9  =  1 1/9

25 + 1 1/9  =  26 1/9

Whole numbers are  0, 1, 2, 3, 4, ...

2.333... isn't a whole number; 2.333...  is 2 1/3  which is  7/3.

AS you entered it (with 16 decimal places), it is   23 333 333 333 333 333 / 100 000 000 000 000 000.

Call the intersection point of the two diagonals X.

Looking at Triangle BCX:  ∠BCX =  85°,  BX  =  10  and  CX  =  7.

Law of Sines for Triangle BCX:  sin(∠BCX) / BX  =  sin(∠CBX) / CX

                        --->               sin(85°) / 10  =  sin(∠CBX) / 7

                        --->               7 x sin(85°) / 10   =  sin(∠CBX)

1)  Find ∠CBX.

2)  Use ∠CBX and ∠BCX to find ∠BXC.

3)  Use ∠BXC to find ∠BXA.

4)  Use the Law of Cosines on Triangle AXB to find AB.

5)  Use the Law of Sines on Triangle AXB to find ∠ABX.

6)  Find ∠ABC.

7)  Find ∠BAD.

I posted this and I can't do it either

7(9+x)=84

divide both sides by 7

9+x=12

minus 9 from both sides

x=3

done

Since you know a point and a slope, use the point-slope form:  y - y₁  =  m(x - x₁)

     m  =  34     (x₁, y₁)  =  (1, -2)     --->     y - -2  =  34(x - 1)

                                                     --->     y + 2  =  34x - 34

                                                     --->     y  =  34x - 36

Oh gawd

Your welcome lol I just made an account

Ah, I almost overlooked the question, but the answer is (-6+10)-3=1

Yes Melody he was here......for half an hour...then he went!

Think of it this way....

Total amount =  Amount per day  x  number of days......

Geno....thanks for all those great answers to those geometry questions...!!!

Let me expand on Melody's answer just a bit....

The median of a trapezoid is just (1/2) the sum of the lengths of the bases. So....calling the length of the unknown base, "x," we have

(5 + x ) / 2   = 8

5 + x = 16

x = 11

And that's just as Melody found.....

Yeah, Melody, using "x" for the length probably would have made it easier.....I just didn't think to do it that way.....!!!

binary  1 1 0 1 0 0 1 0 1

=  1(2⁸) + 1(2⁷) + 0(2⁶) + 1(2⁵) + 0(2⁴) + 0(2³) + 1(2²) + 0(2¹) + 1(2⁰)

=  1(256) + 1(128) + 0(64) + 1(32) + 0(16) + 0(8) + 1(4) + 0(2) + 1

=  421

Draw a picture of this rectangle with its diagonals.

This picture contains four triangles. You know that two sides of each of these interior triangles are each 6 cm long. In two of the triangles, the angle contained between these sides is 30° and in the other two triangles, the angle is 150°.

One formula for the area of a triangle is:  Area  =  ½ · a · b · sin(C)  Where  a  and  b  are the lengths of the two sides that contain  ∠C.

So the area of two of the triangles is each:               Area  =  ½ · 6 · 6 · sin(30°) 

while the area of each of the other two triangles is:   Area  =  ½ · 6 · 6 · sin(150°) 

Add these four triangular areas to get the area of the rectangle.

Start by drawing a picture of a rhomus with its diagonals.

The diagonals of that rhombus are perpendicular to each other; therefore, you have a picture that contains 4 congruent right triangles.

Since the diagonals are 6 cm and 8 cm, the sides of each of the right triangles are 3 cm and 4 cm. Calculate the hypotenuses of the right triangles (they are all the same size) and add these four sides together to get the perimeter of the rhombus.

One formula for the area of a parallelogram is:  Area  =  a · b · sin(C)  where  a  and  b  are two consecutive sides of the parallelogram and  ∠C  is the enclosed angle.

One formula for the area of a parallelogram is:  Area  =  a · b · sin(C)  where  a  and  b  are two consecutive sides of the parallelogram and  ∠C  is the enclosed angle.

Area  =  15 · 16 · sin(60°)

The area of a trapezoid can be found by using:  Area  =  ½·h·(b₁ + b₂)

--->   180  =  ½ · h · (16 + 14)

Can you take it from here?

One formula for the area of a parallelogram is:  Area  =  a · b · sin(C)  where  a  and  b  are two consecutive sides of the parallelogram and  ∠C  is the enclosed angle.

Since a rhombus is a type of parallelogram:  Area  =  6 · 6 · sin(42°) 

Since π is an irrational number, it will remain an irrational number if it is multiplied by a non-zero integer (8) and divided by an integer (3).

A rational number is a number that is (or can be placed into) a fraction of integers (but the denominator cannot be zero). Although 8π/3 is a fraction, it is not a fraction of integers.

@@ End of Day Wrap        Mon 29/12/14 /12/14       Sydney,   Australia      Time 11:20pm      ♪ ♫ 

Hello all,

There were a number of good questions today.  Our industrious and learned answerers were CPhill, Rosala, Alan, Juhaszbenedek08, Tiagunix and geno3141.  Thanks all.     

Now for some interest posts:

The first four were all suggested by CPhill. I am always pleased when people request interest posts to be included.  Thanks Chris  

1)  Simplifying indices - A pretty cool question

Tues 30/12/14

1)  How do you change different base numbers to base 10 ?  In this case base 2.  Thanks Gino