A baby mango tree stands $2$ . $6$ meters above the ground. Its roots extend $\frac{7}{5}$ meters below the ground. $\newline$ Which $2$ of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots? $\newline$ Choose $2$ answers: $\newline$ (A) $\left|-\frac{7}{5}-2.6\right|$ $\newline$ (B) $\left|2.6+\frac{7}{5}\right|$ $\newline$ (C) $\left|2.6-\frac{7}{5}\right|$

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Q. A baby mango tree stands

2

6

meters above the ground. Its roots extend

\frac{7}{5}

meters below the ground.

\newline

Which

2

of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots?

\newline

Choose

2

answers:

\newline

(A)

\left|-\frac{7}{5}-2.6\right|

\newline

(B)

\left|2.6+\frac{7}{5}\right|

\newline

(C)

\left|2.6-\frac{7}{5}\right|

Add Heights: To find the vertical distance between the top of the mango tree and the tips of its roots, we need to add the height of the tree above the ground to the length of the roots below the ground.
Calculate Heights: The height of the tree above the ground is $2.6$ meters.
Convert Length: The length of the roots below the ground is $(7)/(5)$ meters, which is $1.4$ meters when converted to a decimal.
Total Vertical Distance: To find the total vertical distance, we add the two lengths together: $2.6\,\text{meters} + 1.4\,\text{meters}$ .
Perform Addition: Performing the addition gives us $2.6 + 1.4 = 4$ meters.
Final Vertical Distance: The vertical distance between the top of the mango tree and the tips of its roots is $4$ meters. This distance is a positive value, so taking the absolute value will not change the result.
Evaluate Options: Now, let's evaluate the given options: $\newline$ A. $\left|\frac{-7}{5}-2.6\right| = \left|-1.4 - 2.6\right| = \left|-4\right| = 4$ , which is the correct vertical distance.
Evaluate Options: Now, let's evaluate the given options: $\newline$ A. $\left|\frac{-7}{5}-2.6\right| = \left|-1.4 - 2.6\right| = \left|-4\right| = 4$ , which is the correct vertical distance.B. $\left|2.6+\frac{7}{5}\right| = \left|2.6 + 1.4\right| = \left|4\right| = 4$ , which is also the correct vertical distance.
Evaluate Options: Now, let's evaluate the given options: $\newline$ A. $|\frac{-7}{5}-2.6| = |-1.4 - 2.6| = |-4| = 4$ , which is the correct vertical distance.B. $|2.6+\frac{7}{5}| = |2.6 + 1.4| = |4| = 4$ , which is also the correct vertical distance.C. $|2.6-\frac{7}{5}| = |2.6 - 1.4| = |1.2| = 1.2$ , which is not the total vertical distance but the difference between the height of the tree and the length of the roots.