Mr. and mrs. patton and their daughter carolyn own three cars. carolyn drives 10 miles per week farther with her car than her father does with his. mr. patton does twice as many miles per week as mrs. patton. if their total mileage per week is 160 miles, how many miles per week does each drive?

Lindsay used two points, (x,y; ) and (+2.82), to find the equation of the line, y = mx + b, that passes through the points. y2-y, first, she used the definition of slope and determined that the value of mis x, - . given this information, which expression must represent the value of b?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.