Each week peggy drives two routes, route x and route y. One week she drives route x three times a d route y twice. She drives a total of 144 miles that week. Another week she drives route x twice and route y five times. She drives a total of 217 miles that week. Find the length of each route

x = 26 , y = 33

Step-by-step explanation:

3x + 2y = 144 (1)

2x + 5y = 217 (2)

3x + 2y = 144

(divide the equation by 3)

x + (2/3)y = 48

x = 48 - (2/3)y

Plug into (2)

2[48 - (2/3)y] + 5y = 217

96 - (4/3)y + 5y = 217

11y/3 = 217 - 96

11y/3 = 121

y = 121×3/11

y = 33

x = 48 - (2/3)y

x = 48 - (2/3)(33)

x = 48 - 22

x = 26

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