What is the slope of the line?
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Answer:
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Step-by-step explanation:
Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.
This implies that boxes are in multiples of 12
i.e. 12, or 24, or 36 or....
Let us say this as 12m for m an integer
Now additional boxes arrived =60
Total number of boxes now =
This when arranged in stacks of 14,nothing left out
Or this is multiple of 14
for some positive integer n.
By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.
So we say originally 24 boxes were there now 84 boxes there.
Hence both options are right.
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Required equation to determine two consecutive even number is and required numbers are 4 and 6.
<u>Solution:</u>
Given that product of two consecutive positive integer is 14 more that their sum. Need to create the equation and solve it to get two numbers.
Let’s assume first even number be represented by x.
So second consecutive even number will be
Sum of two consecutive number =
Sum of two consecutive number =
Product of two consecutive number =
Product of two consecutive number is 14 more that sum of two consecutive numbers, so if we subtract 14 from product, we will get sum.
One even number =
Other even number =
Hence required equation to determine two consecutive even number is and required numbers are 4 and 6.