6.1 A man places a 5 m ladder to reach a point of x m high on the wall. The distance from of the wall to the foot of the latter is 3 m . Calculate the height of the wall.

A farmer buys 58 feet of fencing material to build a rectangular livestock pen. Fill in the second columi of the table to find the length of the pen if the width is \( 4,6,8,10 \), or 12 feet. Then find the area of each of the pens formed.

Con una escalera de \( z=36 u \) se desea subir al extremo de una barda de \( x=18 u \) de altura. ¿A qué distancia se necesita colocar la base de la escalera para que el otro extemo coincida con la punta de la torre?

6. Jennifer wants to plant a flower garden in the space shown. She wants to add a fountain that is 3 feet wide and 3 feet long. What is the area of the space left to plant flowers?

4. Identify each of the following as an ellipse, circle, or hyperbola. Show how you determined it. a) \( x^{2}-2 x-4 y^{2}-16 y=19 \) answer: b) \( 2 y^{2}-6 y+2 x^{2}+36 x-45=0 \) answer: c) \( x^{2}+9 y^{2}+36 y-45=0 \) answer:

3 ¿A qué altura llega una escalera de \( z=8 u \) di largo en un muro vertical, si su base está situada a \( x=6 u \) del muro?