(4) A rectangular toom has an area of \( 6+8 \sqrt{7} \mathrm{~m}^{2} \). The leng the of the room is \( 5+\sqrt{7} \mathrm{~m} \). find the width of the room, gicking the answer as an exact surd in its simglest form.

Draw a graph of the line that contains the given point and has the given slope. \( (0,1) ; m=-3 \)

Si \( P=(1,1) \) y \( Q=(2,2) \), la magnitud \( (|\overrightarrow{P Q}|) \) y dirección \( (\theta) \) del vector \( \overrightarrow{P Q} \) son, respectivamente

7. A village with an actual area of \( 1 \mathrm{~km}^{2} \) is represented by an area of \( 4 \mathrm{~cm}^{2} \) on a map. (a) Express the scale of this map in the form \( 1: n \), where \( n \) is an integer.

coordinate grid below. Find the coordinates of a fourth point o that the four points form the vertice of a rectangle.

Graph the line containing the point \( P \) and having slope \( m \). \( P=(-6,3) ; m=0 \)