My friend and i both have the same math homework one day. i work at a rate of $p$ problems per hour and it takes me $t$ hours to finish my homework. my friend works at a rate of $2p-4$ problems per hour and it only takes him $t-2$ hours to finish his homework. given that $p$ and $t$ are positive whole numbers and i do more than $10$ problems per hour, how many problems did i do?

If you do problems per hour, after hours you do problems.

Similarly, your friend does problems per hour, so after he has completed problems.

Since you have the same number of problems, we deduce

which we can rewrite as

If we solve this equation for one of the two variables, for example t, we have

Since p and t are positive integers, p must be at least 4.

Finding integers solutions require a bit of trial and error, and you can figure out that the only positive and integer solution where p > 10 is

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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what is the graph

step-by-step explanation: