A curve has equation y=2x^2-3x
Find the set of values of x for which y>9

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Step-by-step explanation:

Here we have to solve this inequality 2x² - 3x - 9 > 0 for x.

In order to solve this inequality we need to factorize the expression at first:

2x² - 3x - 9 = 2x² - 3x - 3x + 3x - 9

                  = 2x² + 3x - (6x + 9)

                 = x(2x + 3) - 3(2x + 3)

                 = (2x + 3)(x - 3)

check the attached picture

conclusion:

the set of values of x for which y>9 is :

(-∞ , -3/2)∪(3 , +∞)

:)

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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b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.