Question

already started running, while amari has not yet run any miles this month. the graph below shows the number of miles they plan to run compared to the number of days. james plan is represented by j(x), and amaris plan is represented by a(x). (a) a james had already ran 6 miles when they started tracking miles they plan to run b james ran at a rate of 6 miles per day when tracking miles he ran for the month. c james ran 0 miles when they started tracking miles they plan to run d james ran at a rate of 3 miles per day when tracking miles he ran for the month. (b) part b: choose two statements below that are true. a j(4) < a(4) b j(7) > a(7) c j(2) < a(3) d j(6) = a(6) e j(1) > a(2)

Explanation:

Step1: Analizar la intersección con el eje - y para James

La función \(J(x)\) de James intersecta el eje - y en \(y = 6\). Esto significa que cuando comenzaron a llevar un registro de las millas que planean correr (es decir, cuando \(x = 0\) días), James ya había corrido 6 millas.

Step2: Analizar valores de las funciones en puntos específicos

• Para \(x = 4\): Observando el gráfico, \(J(4)=18\) y \(A(4)=12\), entonces \(J(4)>A(4)\).
• Para \(x = 7\): \(J(7)\approx27\) y \(A(7)\approx21\), entonces \(J(7)>A(7)\).
• Para \(x = 2\): \(J(2)=12\) y para \(x = 3\), \(A(3)=9\), entonces \(J(2)>A(3)\).
• Para \(x = 6\): \(J(6)=24\) y \(A(6)=18\), entonces \(J(6)>A(6)\).
• Para \(x = 1\): \(J(1)=9\) y para \(x = 2\), \(A(2)=6\), entonces \(J(1)>A(2)\).

Answer:

(a) A. James had already ran 6 miles when they started tracking miles they plan to run
(b) B. \(J(7)>A(7)\)
E. \(J(1)>A(2)\)