Megan earns a rebate each month on completing surveys and books. she earns $0.75 for each survey she completes and $1 for each book. last month megan completed 8 surveys and earned $21.

part a: create an equation that will determine the number of books she purchased.
art

b: solve this equation justifying each step with an algebraic property of equality

part c: how many books did megan purchase last month?

Answer and Step-by-step explanation:

Let b = books

Part A : 8(0.75) + b = 21

Part B : 8(0.75) + b = 21

Multiply:

6 + b = 21

Take out 6 from both sides:

b = 15

Part C : Megan purchased 15 books in total

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