Kaitlin the trainer has two solo workout plans that she offers her clients: plan a and plan b. each client does either one or the other (not both). on monday there were 5 clients who did plan a and 2 who did plan b. on tuesday there were 3 clients who did plan a and 8 who did plan b. kaitlin trained her monday clients for a total of 6 hours and her tuesday clients for a total of 7 hours. how long does each of the workout plans last?
length of each plan a workout: -hour(s)
length of each plan b workout: -hour(s)

Write 2 equations:

Monday: 5A + 2B = 6 hours

Tuesday: 3A + 8B = 7 hours

Multiply Monday by -4:

Monday: -20A -8B = -24

Now add Monday and Tuesday together:

-17A = -17 hours

Divide both sides by -17

A = -17/ -17 = 1

Plan A is 1 hour long.

Now replace A in Monday with 1 and solve for B:

5(1) + 2B = 6

5 + 2B = 6

Subtract 5 from both sides:

2B = 1

Divide both sides by 2:

B = 1/2

Plan A is 1 hour, Plan B is 1/2 hour.

for the points

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