The table shows the elevation of 6 cities in California
1 answer:
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Answer: Choice C) Multiplication property of inequality
The rule basically says that if you start with a < b and you multiply both sides by some positive number c, then a*c < b*c. The sign doesn't flip if you multiply both sides by a positive number.
The sign will flip if c is negative. So we'll go from a < b to a*c > b*c if c is negative.
Example 1:
1 < 5
-2 > -10 ... multiplied both sides by -2; sign flips
Example 2:
3 < 7
9 < 21 ... multiplied both sides by 3; sign does not flip
Similar rules apply to a > b,
and 
The rule basically says that if you start with a < b and you multiply both sides by some positive number c, then a*c < b*c. The sign doesn't flip if you multiply both sides by a positive number.
The sign will flip if c is negative. So we'll go from a < b to a*c > b*c if c is negative.
Example 1:
1 < 5
-2 > -10 ... multiplied both sides by -2; sign flips
Example 2:
3 < 7
9 < 21 ... multiplied both sides by 3; sign does not flip
Similar rules apply to a > b,
9514 1404 393
Answer:
k = 5
Step-by-step explanation:
Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...
speed = distance/time = 1 / 30 . . . . units per minute
When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = 1/30(t +10)
Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = (1/30)(t +5)
We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...
d = 1/20t
To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...
(1/30)(2k +5) = (1/20)(2k)
4k +10 = 6k . . . . . multiply by 60
10 = 2k . . . . . . . . . subtract 4k
5 = k . . . . . . . . . . . divide by 2
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The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.
