answer:First, let's determine Tom's current age. If Tom will be 30 in five years, then he is currently 30 - 5 = 25 years old. Two years ago, Tom would have been 25 - 2 = 23 years old. Now, let's consider Jared's age. Jared is currently 48 years old. Two years ago, Jared would have been 48 - 2 = 46 years old. The ratio of Jared's age to Tom's age two years ago is therefore 46 (Jared's age two years ago) to 23 (Tom's age two years ago). To simplify the ratio, we divide both numbers by the greatest common divisor, which is 23 in this case. 46 ÷ 23 = 2 23 ÷ 23 = 1 So, the ratio of Jared's age to Tom's age two years ago is boxed{2:1} .

answer:First, we need to find out the total number of seconds that should be in the film if each player gets an average of 2 minutes. Since there are 5 players on the team, and 2 minutes is equal to 120 seconds, we multiply 120 seconds by 5 players: 120 seconds/player * 5 players = 600 seconds Now, we need to find out the total number of seconds Patricia already has for the other four players: 130 seconds (point guard) + 145 seconds (shooting guard) + 85 seconds (small forward) + 60 seconds (power forward) = 420 seconds Finally, we subtract the total seconds of the four players from the total seconds needed for all five players to find out how many seconds of the center Patricia has: 600 seconds (total needed for all players) - 420 seconds (total of four players) = 180 seconds So, Patricia has boxed{180} seconds of the center.

answer:For the system to have exactly one solution, the intersection between the line and the piecewise function (defined by absolute values) must be unique. Analyzing the piecewise function, we have: [ y = begin{cases} -4x + (a+b+c+d), & text{if } x < a -2x + (-a+b+c+d), & text{if } a leq x < b 0x + (-a-b+c+d), & text{if } b leq x < c 2x + (-a-b-c+d), & text{if } c leq x < d 4x + (-a-b-c-d), & text{if } d leq x. end{cases} ] The graph consists of five lines with slopes -4, -2, 0, 2, and 4, and corners at (a, -3a+b+c+d), (b, -a-b+c+d), (c, -a-b-c+d), and (d, -a-b-c+3d). The linear equation, 3x + y = 3005, has a slope of -3. For the graphs to intersect at just one point, this point must be a suitable corner. Consider intersection at (d, -a-b-c+3d): 3d + (-a-b-c+3d) = 3005 6d - a - b - c = 3005 Assuming a, b, and c are consecutive integers (minimal increment scenario), let a = d-3, b = d-2, and c = d-1. Then, 6d - (d-3) - (d-2) - (d-1) = 3005 6d - 3d + 6 = 3005 3d = 2999 d = 999 Thus, the minimum value of d, assuming consecutive integers, is boxed{999}.

answer:(1) Since line BC passes through points B(2,1) and C(-2,3), by the two-point form of a line, the equation of BC can be written as frac{y-1}{3-1}= frac{x-2}{-2-2}, which simplifies to x+2y-4=0. So the equation of the line containing side BC is: [ boxed{x+2y-4=0} ] (2) The midpoint D of side BC can be easily found to have coordinates (0,2). Since median AD passes through points A(-3,0) and D(0,2), by the intercept form of a linear equation, the equation of line AD can be written as frac{x}{-3}+ frac{y}{2}=1, which simplifies to 2x-3y+6=0. So the equation of the median AD of side BC is: [ boxed{2x-3y+6=0} ]