parallel streets main and second are intersected by cross streets as shown. if m∠1=114° and m∠4=(9x)° and m∠7=(6x)° , what is the value of x?

x = 12

Step-by-step explanation:

Main Street and Second Street are parallel lines.

Angles 3 and 4 form a linear pair and are supplementary, so their measures add to 180 deg.

m<3 + m<4 = 180

Angles 3 and 7 are congruent since they are corresponding angles.

m<7 + m<4 = 180

6x + 9x = 180

15x = 180

x = 12

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