geno3141

Since  a = 15  b = 12  and  c = 10

then  s  =  ( 15 + 12 + 10 ) / 2         --->         s  =  37/2  =  18.5

Area  =  √( 18.5 x ( 18.5 - 15 ) x ( 18.5 - 12 ) x ( 18.5 - 10 ) )     =  √ ( 18 x 3.5 x 6.5 x 8.5 )

         =  √ 3480.75  ≈  59.0

This formula is known as Hero's Formula or Heron's Formula.

(x + y)^2  =  (x + y)(x + y)  =  x² + xy  + xy + y²  =  x² + 2xy + y²

(x + y)^3  =  (x + y)(x + y)(x +y)                                                                                                                                =  (x + y)(x² + 2xy + y²)  =  x³ + 2x²y + xy² + x²y + 2xy² + y³  =  x³ + 3x²y + 3xy²+ y³ 

(x + y)^4  =  (x + y)(x + y)(x +y)(x + y)  =  (x + y)(x³ + 3x²y + 3xy²+ y³)                                                                 =  x^4 + 3x³y + 3x²y² + xy³ + x³y + 3x²y² + 3xy³ + y^4                                                                           = x^4 + 4x³y + 6x²y² + 4xy³ + y^4

Look at the coefficients:

(x + y)^2  -->  1  2  1

(x + y)^3  -->  1  3  3  1

(x + y)^4  -->  1  4  6  4  1

Can you find the pattern?  You may want to look up "Pascal's Triangle" for a fuller explanation.

If you're still confused, ask again ...

35 x 26  =  910

(1/2) · (8 - x)  =  (8 - x) / 2

So, we have:         (8 - x) / 2  =  8 - x / 2

Multiply each term by 2 to eliminate fractions:    8 - x  =  16 - x

Add  x  to both sides:  8  =  16

Since this is not possible the original "equation" was not really an equation.

If the diameter is  1.905 cm  then the radius is  0.9525 cm.

V  =  π · (0.9525 cm)² · (0.124 cm)   =  0.335 cm³

Cats have eyes; potatoes have eyes; so count the number of eyes on the potato and divide by 2.

These seem to be the three sides of a triangle. Is it a right triangle; and, if so where is the right angle?

A rational number is a number that can be put into the form  a/b  where  a  and  b  are integers and b ≠ 0.

Every common fraction is a rational number. Every mixed fration is a rational number.

Decimals that terminate (such as 12.375) or repeat (such as -2.34343434...) are rational numbers.

12.375  =  12 3/8  =  99/8.                -2.3434...  =  -2 34/99  =  -232/99  

Decimals that neither terminate nor repeat, such as √2 and π are not rational.

√121 =  11    because   11 x 11 = 121

It is a rational number; not an irrational number.

The Pythagorean Theorem is  c²  = a² + b²

where  c  is the hypotenuse and  a  and  b  are the other two sides.

For this problem,  c = √74  and  a = 5:    ( √74 )²  =  ( 5 )² +  b²

     --->  74  =  25 + b²

     --->  49  =  b²

     --->  b  =  √49

     --->  b  =  7

[The sides  a  and  b  are interchangeable.]