geno3141

y =  (2 - x^-1) / (x + 3)

Using the quotient formula:

y'  =  [ (x + 3)(x^-2) - (2 - x^-1)(1) ] / (x + 3)²

y'  =  [ x^-1 + 3x^-2 - 2 + x^-1 ] / (x + 3)²

y'  =  ( 2x^-1 + 3x^-2 - 2 ) / (x + 3)²

x² + y²  =  26

x - y   =  6

Solve the second equation for x:  x - y  =  6   --->   x  =  y + 6

Replace this value into the first equation:  x² + y²  =  26   --->   (y + 6)² + y²  =  26

Multiply out:  y² + 12y + 36 + y²  =  26

Simplify:       2y² + 12y + 36  =  26

Get all terms to one side:  2y² + 12y + 10  =  0

Divide by 2:                              y² + 6y + 5  =  0

Factor:                                 (y + 5)(y + 1)  =  0

Solve:                       y  =  -5     or     y  -1

Place these values into the linear equation:  x  =  -5 + 6   --->   x  =  1   --->   (1, -5)

                                                           x  =  -1 + 6   --->   x  =  5   --->   (5, -1)

(If you replace back into the quadratic equation, you will get extraneous answers.)

log( a / b )  =  log(a) - log(b)

log( xy² / z³ )  =  log( xy² ) - log( z³ )  

                        =  log( x ) + log( y² ) - log( z³ )

                        =  log( x ) + 2log( y ) - 3log(z)

Drawing a triangle from the point on the ground to the base of the tree to the top of the tree and back to the point on the ground creates a right triangle.

From the point of view of the point on the ground, the side of the triangle from that point to the base of the tree (the shadow = 6m) is the adjacent side and the height of the tree (8.5m) is the opposite side.

Tangent is defined as opposite / adjacent   --->   tan(Angle)  =  8.5 / 6

                                                                                        Angle  =  tan^-1(8.5/6)

                                                                                        Angle  =  54.8°  (approximately)

If you mean:  what do you do when you are subtracting a larger number from a smaller number ---

For example:  How much is  345 - 789 ?

Reverse the problem:  789 - 345  to get  444 and attach a negative sign, because your answer is a negative number:         345 - 789  =  -444

                                  45/100 · x  =  180

Multiply both sides by 100:  45x  =  18000

Divide both sides by 45:          x  =  400

19x² + 25x²  =  (19 + 25)x²  =  45x²

Never change exponents when you are adding terms together  --  just add the coefficients and attach the variable.

Factor the denominator:

1 / [ 5m - 20 ]  =  1 / [ 5(m - 4) ]

You're done!

First, I would get rid of fractions:

---   multiply the first equation by 6:   6(x/2) + 6(y/3)  =  6(-1)   --->   3x + 2y  =  -6

---   multiply the second equation by 2:   2(x/2) + 2(2y)  =  2(4)   --->   x + 4y  =  8

Now, combine these:  3x + 2y  =  6

                                      x + 4y  =  8

If you want to eliminate the x-terms, leave the top equation alone and multiply the bottom equation by -3:

3x + 2y  =  -6   --->                                        3x + 2y  =  -6

  x + 4y  =   8   --->   multiply by -3   --->   -3x - 12y  =  -24

Add down the columns:                                      -10y  =  -30

                                                                                 y  =  3

Substitue this value back into an original equation:  x + 4y  =  8   --->   x + 4(3)  =  8   --->   x + 12  = 8

                                                                        --->   x  =  -4

                                                  2a - b  =  3

                                                  -a + b  =  4

Add down the columns:             a          =  7

--->   2a - b  =  3   --->   2(7) - b  =  3   --->   14 - b  =  3   --->   -b  =  -11   --->   b  =  11