The product of the slopes of perpendicular lines (excluding vertical lines) always equals -1. true or false

This is true.  The slope of the perpendicular line is equal to the negative reciprocal.  This means that you "flip" the fraction and multiply by negative 1.  Since the reciprocal is also the multiplicative inverse (something you multiply by a number to get 1), and the signs are different (one is positive, one is negative) it equals -1.

Hope this helps!

she will most likely have 33  

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq