Answer:
-4.6
6.6
16.2
Step-by-step explanation:
This question is all about how far the ant walks, but you just need to split it up into little pieces to make it seem less daunting.
First you need to figure out where the ant is on the number line after all of that walking. We can break it down into a more mathematical sense. When the ant walks Left, it represents negative numbers, or numbers you should subtract since whenever the ant walks left, it is getting closer to the zero, or becoming a smaller number. Right represents positive numbers, or numbers you should add, since when the ant walks right, it is getting further away from the zero or becoming a bigger number. Now, we need to add the numbers together. 3.5 centimeters left should be -3.5 for the reason above, and 4.8 centimeters right should be + 4.8 for the reason above. Finally, 7.9 Centimeters left should be -7.9.
Now, we need to add them together in order. The ant starts at positive 2 centimeters. Then, it goes 3.5 centimeters left. 2 minus 3.5 is -1.5 cm. Then, the ant travels 4.8 centimeters right. -1.5 cm plus 4.8 is 3.3 cm. Finally, the ant moves 7.9 cm left. 3.3 minus 7.9 is -4.6 cm. This is the new position of the ant, for part A.
Part B you just need to find the difference between 2, and -4.6. This involves absolute value. How far away from the zero is -4.6 centimeters. 4.6 centimeters. It is that easy. Now, you add the two absolute values together. The absolute value of 2 is 2, because it is 2 centimeters away from zero, and 2 plus 4.6 is 6.6. That is the answer to part B.
The total distance the ant travels is also about absolute value. Remember that absolute value numbers can NEVER be negative because a number cannot be negative units away from zero. So you just add all of the values together to get the total distance the ant travelled. 3.5 plus 4.8 plus 7.9. DON'T add your two into this value, because that's where the ant started, not a distance that it traveled. The answer should be 16.2 for part C.
You're welcome, stranger :)
The position of the ant is required at various times.
The ant is at [tex]-4.6[/tex]
Distance from original location is 6.6 cm.
Distance covered is 16.2 cm.
The situation will be, the ant is at +2 and walks 3.5 cm right then 4.8 cm left then 7.9 cm right.
The ant's initial location is at [tex]+2[/tex].
If the distance is left then the added number will be negative.
If the distance is right then the added number will be positive.
[tex]2-3.5=-1.5[/tex]
[tex]-1.5+4.8=3.3[/tex]
[tex]3.3-7.9=-4.6[/tex]
So, the ant is at [tex]-4.6[/tex] on the number line.
Distance between initial and final location is
[tex]2-(-4.6)=6.6\ \text{cm}[/tex]
Total distance the ant covered is
[tex]3.5+4.8+7.9=16.2\ \text{cm}[/tex]
The situation will be, the ant is at +2 and walks 3.5 cm right then 4.8 cm left then 7.9 cm right.
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