Astorekeeper wishes to sell 100 pounds of mixed nuts for $1.75 a pound. he mixes peanuts worth $1.65 a pound with cashews worth $1.90 a pound. how many pounds of each does he use?

Step-by-step explanation:

Let c represent the weight of cashews in the mix. Then (100 -c) is the weight of peanuts, and the total cost of the 100 lbs of mix will be ...

... 1.90c +1.65(100 -c) = 1.75·100 . . . . total cost of the mix

... 0.25c +165 = 175 . . . . . . . . simplify

... 0.25c = 10 . . . . . . . . . . . . . subtract 165

... c = 40 . . . . . . . . . . . . . . . . . divide by 0.25

There will be 40 lbs of cashews and 100-40 = 60 lbs of peanuts in the mix.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752