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vampirchik [111]
3 years ago
11

Bill’s car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to dete

rmine whether this relation is a function. Write the equation for the number of miles Bill travels, y, in terms of how much gas it uses, x.
Mathematics
1 answer:
pshichka [43]3 years ago
6 0

this relation is a function, y=30x

for every ax or 1 gallon, it goes 30 miles.

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Solve for x: 3/3x + 1/x+4 = 10/7x
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Given,

3/3x + 1/(x + 4) = 10/7x

1/x + 1/(x+4) = 10/7x

Because the first term on LHS has 'x' in the denominator and the second term in the LHS has '(x + 4)' in the denominator. So to get a common denominator, multiply and divide the first term with '(x + 4)' and the second term with 'x' as shown below

{(1/x)(x + 4)/(x + 4)} + {(1/(x + 4))(x/x)} = 10/7x

{(1(x + 4))/(x(x + 4))} + {(1x)/(x(x + 4))} = 10/7x

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(x + 4 + 1x) / (x(x + 4)) = 10/7x

(2x + 4) / (x(x + 4)) = 10/7x

In order to have the same denominator for both LHS and RHS, multiply and divide the LHS by '7' and the RHS by '(x + 4)'

{(2x+4) / (x(x + 4))} (7 / 7) = (10 / 7x) {(x + 4) / (x + 4)}

(14x + 28) / (7x(x + 4)) = (10x + 40) / (7x(x + 4))

Now both LHS and RHS have the same denominator. These can be cancelled. 

∴14x + 28 = 10x + 40
14x - 10x = 40 - 28
4x = 12
x = 12/4

∴x = 3



8 0
3 years ago
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