Triangles \( \triangle A O B \) and \( \triangle A O C \) have vertices \( A(0,7), B(-1,-2), C(2,-1) \), and \( O(0,0) \). Show that \( m \angle A O B>m \angle A O C \). Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to the nearest thousandth as needed.) A. Since \( A B=\square \) and \( A C=\square, \overline{A B}>\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). B. Since \( A B=\square \) and \( A C=\square, \overline{A B}=\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). C. Since \( A B=\square \) and \( A C=\square, \overline{A B}<\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \).

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 21 feet. The length of the ladder is

What is the slope of the line that passes through the points \( (6,-8) \) and \( (6,-3) \) ? Write your answer in simplest form.

5. The volume of a cone is given by \( V=\frac{1}{3} \pi r^{2} / \% \). Determine the volume of the cone in simplificd form if the radius is increased by \( x \) and the height is increased by \( 2 x \).

En cada uno de los siguientes pares de rectas, determinar: 1. Cuál par de rectas son paralelas no coincidentes (en cuyo caso, calcular la distancia entre ellas). 2. Cuál par son perpendiculares. 3. Cuál par se intersectan en un punto, en cuyo caso, obtener el punto de intersección. 4. Cuál par son coincidentes, en cuyo caso, calcular su distancia al origen. 5. Cuál par no son paralelas, ni perpendiculares, ni se intersectan en un punto, ni son a) \( \mathrm{L}_{1} \) : coincidentes (en cuyo caso, calcular el ángulo entre ellas). \( \mathrm{L}_{2} \) : contiene al punto \( (0,-2,1) \) y es paralela al vector \( \bar{u}=-10 i-10 j+4 j \)

A Which graph is non-proportional?