Question

If $3x-y = 12$, what is the value of ${8^x}/{2^y}$?

A) $2^{12}$
B) $4^4$
C) $8^2$
D) The value cannot be determined from the information given.

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Answer 1

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One approach is to express

8x2y

so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 2^3 for 8 in the numerator of 8x2y gives

(23)x2y

which can be rewritten

2^3x2y

Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that

8x2y=2^12

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Answer 2

:Think of the equation as an equation for a line. $$y=mx+b$$. where in this case..

You can see the slope of the graph is ${5}/{9}$, which means that for an increase of 1 degree Fahrenheit, the increase is ${5}/{9}$ of 1 degree Celsius.

$$C= {5}/{9} (F)$$

$$C= {5}/{9} (1)= {5}/{9}$$

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of ${9}/{5}$ degrees Fahrenheit.

An increase of $5/9$ degree Fahrenheit leads to an increase of ${25}/{81}$, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.

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