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A baby mango tree stands 2.6 meters above the ground. Its roots extend (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. |-(7)/(5)-2.6| B |2.6+(7)/(5)| c. |2.6-(7)/(5)|

A baby mango tree stands 22.66 meters above the ground. Its roots extend 75 \frac{7}{5} meters below the ground.\newlineWhich 22 of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots?\newlineChoose 22 answers:\newlineA. ∣−75−2.6∣ \left|-\frac{7}{5}-2.6\right| \newlineB ∣2.6+75∣ \left|2.6+\frac{7}{5}\right| \newlinec. ∣2.6−75∣ \left|2.6-\frac{7}{5}\right|

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Q. A baby mango tree stands 22.66 meters above the ground. Its roots extend 75 \frac{7}{5} meters below the ground.\newlineWhich 22 of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots?\newlineChoose 22 answers:\newlineA. ∣−75−2.6∣ \left|-\frac{7}{5}-2.6\right| \newlineB ∣2.6+75∣ \left|2.6+\frac{7}{5}\right| \newlinec. ∣2.6−75∣ \left|2.6-\frac{7}{5}\right|
  1. Understand the problem: Understand the problem.\newlineWe need to find the total vertical distance between the top of the mango tree and the tips of its roots. The tree's height above ground is 2.62.6 meters, and the roots extend 75\frac{7}{5} meters below the ground.
  2. Calculate total vertical distance: Calculate the total vertical distance. The total vertical distance is the sum of the height of the tree above the ground and the length of the roots below the ground. Total vertical distance = 2.62.6 meters + 75\frac{7}{5} meters
  3. Convert fraction to decimal: Convert the fraction to a decimal to make addition easier. \newline75\frac{7}{5} meters is equivalent to 1.41.4 meters.\newlineTotal vertical distance = 2.62.6 meters + 1.41.4 meters
  4. Add lengths together: Add the two lengths together.\newlineTotal vertical distance = 2.6+1.42.6 + 1.4\newlineTotal vertical distance = 4.04.0 meters
  5. Express as absolute values: Express the total vertical distance as absolute values.\newlineThe total vertical distance can be expressed as the absolute value of the sum of the tree's height and the root's length, which is ∣2.6+75∣|2.6 + \frac{7}{5}|.
  6. Check answer choices: Check the answer choices.\newlineWe need to find two expressions that represent the total vertical distance correctly. The correct expression based on our calculation is ∣2.6+75∣\lvert 2.6 + \frac{7}{5}\rvert, which corresponds to choice BB.
  7. Analyze other choices: Analyze the other choices.\newlineChoice A is ∣−75−2.6∣|-\frac{7}{5} - 2.6|, which is the absolute value of the negative sum of the tree's height and the root's length. This is not the correct representation of the total vertical distance because it implies a subtraction, not an addition.\newlineChoice C is ∣2.6−75∣|2.6 - \frac{7}{5}|, which is the absolute value of the difference between the tree's height and the root's length. This does not represent the total vertical distance because it does not account for the full length of the roots.

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