Manny wants to cover the windows in his home with either wood blinds or curtains. he has 35 windows that he would like to cover, but he only have $2100 to spend. wood blinds cost $100 per window. curtains cost $60 per window. which system of inequality's represents the number of wood blinds, x, and curtains, y, manny can purchase?

Step-by-step explanation:

Call x the amount of blinds that Manny buys.

Let's call and the amount of curtains that Manny buys

There are only 35 windows, so the number of curtains and windows can not be greater than 35.

Manny can only spend $ 2100

Then we can represent this by an inequality in the following way.

and

We can write this as a single inequality:

Finally, the set of inequalities to model this problem is:

250

step-by-step explanation:

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