What is the domain of the function y=ln(12-4x/5)

x < 15

Step-by-step explanation:

Important:  The domain of y = ln x is (0, ∞).

Thus, to answer this question, we set the argument 12 - 4x/5 = to 0 and solve for x:

12 - 4x/5 = 0,or 12 = 4x/5.

Mult. both sides by 5, we clear out the fractions:  60 = 4x.

Solving for x:  x = 60/4 = 15

Supposing we let x = 14, is 12 - 4x/5 = to 0

Choose a test number based upon this 15:  14 is smaller and 16 is larger.  

Let x = 14.  Is    12 - 4x/5 ≥ 0, as it must be?

Is 12 - 4(14)/5 ≥ 0?

Is 60 - 56 ≥ 0?  Yes.  Thus, the domain of the given function includes all real numbers less than 15.

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

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