A. what is the sum of the squares of the roots of $x^2 - 5x - 4 = 0$? b. one root of $x^2 + 12x + k = 0$ is twice the other root. find $k.$ c. what is the sum of the roots of the quadratic $4x^2 - 4x - 4$? d. jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ he assumes that it will factor in the form \[ax^2 + bx + c = (ax + b)(cx + d),\]where $a,$ $b,$ $c,$ and $d$ are integers. if $a = 4,$ and jimmy wants to find the value of $a,$ what are the possible values he should check, in order to find $a$? e. brandy is trying to factor the quadratic $3x^2 - x - 10.$ she starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + b)(3x + d),\]for some integers $b$ and $d.$ after some work, brandy successfully factors the quadratic. find the ordered pair $(b, d).$

Atrain traveled for 1.5 hours to the first station, stopped for 30 minutes, then traveled for 4 hours to the final station where it stopped for 1 hour. the total distance traveled is a function of time. which graph most accurately represents this scenario? a graph is shown with the x-axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the origin and moves upward for 1.5 hours. the line then continues upward at a slow rate until 2 hours. from 2 to 6 hours, the line continues quickly upward. from 6 to 7 hours, it moves downward until it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y axis labeled total distance (in miles). a line is shown beginning at the origin. the line moves upward until 1.5 hours, then is a horizontal line until 2 hours. the line moves quickly upward again until 6 hours, and then is horizontal until 7 hours a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the y-axis where y equals 125. it is horizontal until 1.5 hours, then moves downward until 2 hours where it touches the x-axis. the line moves upward until 6 hours and then moves downward until 7 hours where it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at y equals 125 and is horizontal for 1.5 hours. the line moves downward until 2 hours, then back up until 5.5 hours. the line is horizontal from 5.5 to 7 hours