Subjects algebra

Animal Depths

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1. **Problem 25:** Which animal is represented by the point farthest from 0 on the number line? 2. **Step 1:** Identify the absolute values of each animal's location (distance from 0). - Bloodbelly comb jelly: $|-0.8|=0.8$ - Deep sea anglerfish: $\left|-\frac{2}{3}\right|=\frac{2}{3}\approx0.6667$ - Fanfin anglerfish: $\left|-2\frac{1}{4}\right|=2.25$ - Gulper eel: $|-1.1|=1.1$ - Pacific blackdragon: $|-0.3|=0.3$ - Slender snipe eel: $|-0.6|=0.6$ 3. **Step 2:** Compare these absolute values to find the greatest distance from 0. - The greatest absolute value is $2.25$ for the Fanfin anglerfish. 4. **Answer 25:** The Fanfin anglerfish is represented by the point farthest from 0 on the number line because it has the greatest distance from 0, $2.25$ km below the ocean's surface. 5. **Problem 26:** Which animal is closest to a depth of $-0.7$ km? 6. **Step 1:** Calculate the distance of each animal's depth from $-0.7$ km by finding the absolute value of the difference. - Bloodbelly comb jelly: $|-0.8 - (-0.7)| = | -0.1| = 0.1$ - Deep sea anglerfish: $\left|-\frac{2}{3} - (-0.7)\right| = | -0.6667 + 0.7| = 0.0333$ - Fanfin anglerfish: $|-2.25 - (-0.7)| = |-1.55| = 1.55$ - Gulper eel: $|-1.1 - (-0.7)| = |-0.4| = 0.4$ - Pacific blackdragon: $|-0.3 - (-0.7)| = |0.4| = 0.4$ - Slender snipe eel: $|-0.6 - (-0.7)| = |0.1| = 0.1$ 7. **Step 2:** Identify the smallest distance. - The smallest distance is $0.0333$ km for the Deep sea anglerfish. 8. **Answer 26:** The Deep sea anglerfish is closest to a depth of $-0.7$ km because its depth differs by only about $0.0333$ km from $-0.7$ km.