Question

The table below shows the surface area y, in square feet, of a shrinking lake in x days:

Answer 1

1A) The points are all on the line y=110-x, so the correlation coefficient is -1.

1B) The slope of the graph everywhere is -1 (square feet per day). This represents the change in area each day (-1 ft²).

1C) The data represents correlation. There is no reason to believe the change in area is caused by the passage of time. Rather, we expect the change to be caused by some process that removes water from the lake. In fact, we expect surface area to increase with time if water is being added (as by rain, for example).


2A) (h+t)(x) = h(x) +t(x) = (5x -2) +(4x +6) = 9x +4

2B) (h·t)(x) = h(x)·t(x) = (5x -2)·(4x +6) = 20x² +22x -12

2C) h(t(x)) = h(4x +6) = 5(4x +6) -2 = 20x +28


3A) 3x²y² -2xy² -8y² = y²(3x² -2x -8) = y²(x -2)(3x +4)
  we made use of the factoring -24 = -6·4 to form factors (3x-6)/3·(3x+4)

3B) x² +10x +25 = (x +5)² . . . . . matches the form for the square of a binomial

3C) x² -36 = (x -6)(x +6) . . . . . . matches the form for the difference of squares


4A) The discriminant is b²-4ac = (-12)² -4(4)(10) = 144 -160 = -16. The radicand is negative, so the solutions will be complex.

4B) A graph shows the solutions to be x ∈ {3, 3.5}.
  The "steps of the method" consisted of typing the expression into a graphing calculator and highlighting the x-intercepts. I chose this method as it requires the least amount of work.