Question

a baby mango tree stands 2.6 meters above the ground. its roots extend $\frac{7}{5}$ meters below the ground. which 2 of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots? choose 2 answers: a $left|-\frac{7}{5}-2.6
ight|$ b $left|2.6 - \frac{7}{5}
ight|$ c $left|2.6+\frac{7}{5}
ight|$

Explanation:

Step1: Define positions

Let the ground - level be 0. The height of the tree above the ground is 2.6 meters (a positive value), and the depth of the roots below the ground is $\frac{7}{5}=1.4$ meters (a negative value).

Step2: Calculate vertical distance

The vertical distance between the top of the tree and the tips of the roots is the sum of the absolute - value of the height above the ground and the absolute - value of the depth below the ground. Mathematically, if the height above the ground is $h = 2.6$ and the depth below the ground is $d=-\frac{7}{5}$, the vertical distance $D=\vert h - d\vert=\vert2.6-(-\frac{7}{5})\vert=\vert2.6+\frac{7}{5}\vert$. Also, we can think of it as $\vert-\frac{7}{5}-2.6\vert$ because distance is always non - negative.

Answer:

A. $\vert-\frac{7}{5}-2.6\vert$, C. $\vert2.6+\frac{7}{5}\vert$