Megan's text message plan charges $0.20 for each message over 450 in addition to a $7 base charge. If she owes $34.20 for text messaging in the month of July how many text messages did she send that month?

Step-by-step explanation:

Let number of text messages sent be m, and amount owed, O

Then, O(m) = .25(m - 350) + 14, with m+%3E=+350

72.5 = .25m - 87.5 + 14 Substituting 72.5 for O(m)

72.5 = .25m - 73.5

72.5 + 73.5 = .25m

146 = .25m

m, or number of messages sent that month = highlight_green%28matrix%281%2C3%2C+146%2F.25%2C+%22=%22%2C+584%29%29

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)