This question is all about dimensional analysis. The whole idea behind dimensional analysis is that you multiply a starting value with different conversion factors to cancel out units you don't want to tern the value into the units that you do want. The conversion for yards to feet can be written as 3 feet/yard (this is the conversion factor it can be written as 3feet/1yard or 1yard/3feet, it depends on what you are starting with). If you start out with yards and and want to go to feet you have to multiply the number of yards by 3feet/yard so that the yards cancel out leaving you with feet. If start out with feet and want to go to yards you divide the number of feet by 3feet/yard so that the feet cancel out and you are left with yards.
In your question Tom is trying to go from feet to yards. Therefore he has to divide the number of feet by 3feet/yard to get feet to cancel out. His mistake was that he multiplied by 3feet/yard instead of divide by 3feet/yard. The correct way do it is divide 379 feet by 3feet/yard to get 126.33 yards.
Let me know if anything is unclear to you in the comments. This is a very important skill to learn since this is the basis of many high school and college science classes.
I hope this helps.
Answer:
a : c = 7 : 10
Step-by-step explanation:
The two ratios (a : b and b : c) both have b in common, so to work out what a : c is, we can use b to 'bridge' the two ratios together.
However, in a : b, b is 4. But in b : c, b is 2. We need to make sure b is the same in both ratios before we can combine the ratios together. The easiest way to do this is to multiply b : c by 2 to get b : c = 4 : 10. Now b is 4 in both ratios.
So now, we can combine the two ratios together to get a : b : c = 7 : 4 : 10. Since we only want a : c though, we can just drop the b and get a : c = 7 : 10. No simplifying is necessary since the ratio is already in its simplest form.
Hope that helps! :)
Answer:
The equation of a parallel line in point-slope form would be y - 3 = -8(x + 3)
Step-by-step explanation:
To find this, we must first note that the original slope is -8. Parallel lines have the same slope, so we know that the new line will also have the slope of -8.
Given this information, we can use the point and slope and put them into the base form of point-slope form.
y - y1 = m(x - x1)
y - 3 = -8(x - -3)
y - 3 = -8(x + 3)
