Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius. What value of x would make Line R Q tangent to circle P at point Q?
x =Determine the measure of the following angles.
The measure of ∠QML is degrees.
The measure of ∠PMN is degrees.

Sal is tiling his entryway. the floor plan is drawn on a unit grid. each unit length represents 1 foot. tile costs $1.35 per square foot. how much will sal pay to tile his entryway? round your answer to the nearest cent.

Luke started a weight-loss program. the first week, he lost x pounds. the second week, he lost pounds less than times the pounds he lost the first week. the third week, he lost 1 pound more than of the pounds he lost the first week. liam started a weight-loss program when luke did. the first week, he lost 1 pound less than times the pounds luke lost the first week. the second week, he lost 4 pounds less than times the pounds luke lost the first week. the third week, he lost pound more than times the pounds luke lost the first week.

Stefania pours 2 liters of orange juice and 1.5 liters of pineapple juice into a punch bowl. how many liters are in the punch bowl?