If x meters, is the distance of the foot of the ladder from the wall.

cos `47^@` = `x/7`
`:.`    x = 5 cos `47^@`
          = `5 xx 0.6820`
          = 3.410
          = 3.41 (correct to 3 sig. fig.).
The foot of the ladder is 3.41 m from the wall.

x + 2)`2x^2` + 7x+6( 2x + 3
      `2x^2` + 4x
       ------------
              3x + 6
              3x + 6
             ----------
                 0

The quotient is 2x + 3

`x^2` - 3x - 1 ) `4x^4` -  `3x^3` + `2x^2` - 5x + 6 ( `4x^2` + 9x + 33
                       `4x^4` - `12x^3` -  `4x^2` 
                       ---------------------------------
                                    `9x^3` +  `6x^2` - 5x
                                    `9x^3` - `27x^2` - 9x
                                    -----------------------------
                                                  `33x^2` + 4x +   6
                                                  `33x^2` - 99x - 33
                                                  ---------------------
                                                               103x + 39 

The quotient is `4x^2` + 9x + 33; the reminder is 103x + 39.

 `x^2` - 2x + 4
x + 2 ) `x^3`             + 8(
          `x^3` + 2`x^2`
           -----------------
                     - 2`x^2`
                     - 2`x^2` - 4x
                    -----------------
                                     4x + 8
                                     4x + 8
                                     --------

The quotient is `x^2` - 2x + 4.

A parallelogram is a quadrilateral with its opposite sides parallel.

\\begin{graph}

width=200;
line((-2,3),(3,3))
line((3,3),(2,-3))
line((-3,-3),(2,-3))
line((-3,-3),(-2,3))

\\end{graph}Properties(1) Both pairs of opposite sides are equal.(2) A diagonal bisect the area of a parallelogram.(3) Both pairs of opposite angles are equal.(4) The diagonals bisect each other.Theorem: The opposite sides of a parallelogram are equal; the opposite angles are equal; the opposite angles are equal; and a diagonal bisects the parallelogram.Theorem: The diagonals of a parallelogram bisect each other.Theorem: If the opposite sides of a quadrilateral are equal are equal, then the quadrilateral must be a parallelogram.Theorem: If the opposite angles of a quadrilateral are equal are equal, then the quadrilateral must be a parallelogram.Theorem: If the diagonals of a quadrilateral bisect each other,then the quadrilateral must be a parallelogram. Theorem: If one pair of opposite sides of a quadrilateral are equal are parallel, then the  other sides must be equal and parallel and the quadrilateral must be a parallelogram.