Question 1023751: simplify the expression shown 5x/2*1/x
Found 2 solutions by Theo, Fombitz:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the car's value is 31,700.
it depreciates 1,800 per year.
in how many year will the value be 15,500.
for its value to be 15,500, it must have depreciated 31,700 - 15,500 = 16,200.
16,200 / 1,800 = 9
the car's value will be 15,500 in 9 years.
this can be modeled by a linear equation of y = -1,800 * x + 31,700.
graph the equation and find the intersection with the line of y = 15,500.
the graph is shown below:
since this is linear, it can also be treated as an arithmetic progression.
the formula is An = A1 + (n-1) * d
A1 = 31,700
d = 1,800
An = 15,500
use the formula to solve for n.
you get 15,500 = 31,700 - (n-1) * 1,800
subtract 31,700 from both sides of the equation to get 15,500 - 31,700 = - (n-1) * 1,800.
combine like terms to get -16,200 = - (n-1) * 1,800.
divide both sides of the equation by 1,800 to get -16,200 / 1,800 = - (n-1)
simplify to get -9 = - (n-1)
remove parentheses to get -9 = -n + 1
subtract 1 from both sides of the equation to get -9 - 1 = -n
combine like terms to get -10 = -n
multiply both sides of the equation to get n = 10.
the tenth term in the progression is equal to 15,500.
since the progression starts at n = 1, then the tenth term is 9 years away from the first term.
the difference between the graphical solution and the arithmetic progression solution is that the graph starts at n = 0 and the arithmetic progression starts at n = 1.
that's why the tenth term in the arithmetic progression is equivalent to the ninth term in the graphical solution.
the algebraic solution and the graphical solution correspond.
the equation is y = 31,700 - 1,800 * x.
x is the number of years (same as n in the progression).
set y = 15,500 and the equation becomes 15,500 = 31,700 - 1,800 * x.
subtract 31,700 from both sides of the equation to get -16,200 = -1,800 * x.
divide both sides of the equaiton by 1,800 to get -9 = -x.
multiply both sides of the equation by -1 to get 9 = x which is the same as x = 9.
Answer by Fombitz(32388)  (Show Source):
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