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A fish finder shows a large fish at

feet below the surface of the water and a smaller fish located
feet below the surface of the water. Select ALL the expressions that are equivalent to the distance between the fish.

A
∣−13+(−4)∣\left|-13+\left(-4\right)\right|∣−13+(−4)∣

B
∣−13−(−4)∣\left|-13-\left(-4\right)\right|∣−13−(−4)∣

C
∣−13−4∣\left|-13-4\right|∣−13−4∣

D
∣−4+(−13)∣\left|-4+\left(-13\right)\right|∣−4+(−13)∣

E
∣−4−(−13)∣\left|-4-\left(-13\right)\right|∣−4−(−13)∣

1 answer

To find the distance between the two fish located at different depths, we can denote their positions below the surface as negative numbers. Let's assume:

  • The depth of the larger fish is \( -13 \) feet.
  • The depth of the smaller fish is \( -4 \) feet.

The distance between the two fish is the absolute value of the difference between their depths. This can be calculated as follows:

\[ \text{Distance} = \left|-13 - (-4)\right| = \left|-13 + 4\right| = \left|-9\right| = 9 \text{ feet} \]

Now, let's evaluate the given expressions to determine which are equivalent to this calculation.

A) \(\left|-13 + (-4)\right| = \left|-17\right| = 17\)

B) \(\left|-13 - (-4)\right| = \left|-13 + 4\right| = \left|-9\right| = 9\)

C) \(\left|-13 - 4\right| = \left|-17\right| = 17\)

D) \(\left|-4 + (-13)\right| = \left|-17\right| = 17\)

E) \(\left|-4 - (-13)\right| = \left|-4 + 13\right| = \left|9\right| = 9\)

The expressions that yield a distance of \(9\) are:

  • B: \(\left|-13 - (-4)\right| = 9\)
  • E: \(\left|-4 - (-13)\right| = 9\)

Thus, the equivalent expressions are B and E.