Answers:
- Distance = 20 meters
- Displacement = 4 meters North
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Explanation:
To find the distance traveled, we add the two values to get 8+12 = 20 meters.
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For the displacement, I recommend drawing a vertical number line. Mark the values 0, -8 and 4 on the number line. Going from 0 to -8 represents going 8 meters south. From -8, move up 12 units and you should arrive at 4 on the number line, which represents being 4 meters north of the original position 0. The displacement only cares about the start and end points, more specifically, the change between the two. The direction is also important for the displacement.
In other words, Michael started at 0, did a bunch of movements, and ended up at 4 on the number line. So we can simplify all those movements to one single movement of "move north 4 meters" to represent the displacement.
As you can see, it's possible to get a displacement of 0 meters, which is not the case for the distance traveled in the previous section.
Answer:
5a) 2 sides are equal to each other
5b)
6) 16
Step-by-step explanation:
5b) I'm assuming that in this question you are trying to find the hypotenuse? So you use the pythagorean theorum, which is a^2+b^2=c^2. c represents the hypotenuse, so it would be 10^2+10^2=c^2 because the two sides are equal. Then 100+100=200 and the square root of that is 10\sqrt{2}.
6)a^2+b^2=32^2
since a=b you can write the equation as, 2a^2=1024
a^2=1024/2 , which equals a=\sqrt{512}
and simplify it to 16
Answer: 25%
Step-by-step explanation: So first make the number of people who ran the marathon and the number of people who finished the marathon into a ratio
1200:4800
then make that into a fraction, 1200/4800
then make the percent of people who reached the marathon into a fraction, using 100 as the denominator and a variable as the numerator.
for example. p/100 (p, represents the percent)
then cross multiply.
1200x100=1200000
Last divide 1200000 by 4800 to get 25%.
Answer:
-1 5/6
Step-by-step explanation:
-2/3 + (-1 1/6)
Look carefully at he number line. Each space between whole numbers is divided into 6. That means that from one mark on the line to the very next one, the distance is 1/6.
Start at -2/3. Since we are dealing with 1/6's, convert -2/3 to 6ths.
-2/3 * 2/2 = -4/6
-2/3 is the same as -4/6, so start at -4/6. Locate 0 on the number line, and move 4 marks to the left. That is -4/6 which is the same as -2/3 and is your starting point.
Now you need to add -1 1/6. Adding a negative number is the same as subtracting a positive number. Adding -1 1/6 is the same as subtracting 1 1/6. That means you need to go left 1 1/6. Since each unit is divided into 6 equal parts, 1 1/6 is 7 marks on the number line. Starting at -4/6, count 7 marks to the left. Where you end up is the answer which is -1 5/6.
Answer: -2/3 + (-1 1/6) = -1 5/6
