Alocal school needs to paint the floor of its theater room, where the length of the floor, x, is at least 12 feet. the width of the floor is 4 feet less than the length. it will have a stage and a closet, and the remaining area of the floor will be painted. the dimensions are shown in the diagram:
rectangle with length of x ft and width of x minus 4 ft, right triangle inside labeled stage with height of x minus 4 ft and base of 8 ft, rectangle inside labeled closet with length of 8 ft and width of 4 ft, the rest of the rectangle is labeled floor
let a represent the painted area, in square feet, of the floor. choose the correct equation to solve for area (a).
a.)a = x(x − 4) − 0.5(8)(x − 4) − 4(8)
b.)a = x(x − 4) − (8)(x − 4) − 4(8)
c.)a = x(x − 4) + (8)(x − 4) + 4(8)
d.)a = x(x − 4) + 0.5(8)(x − 4) + 4(8)

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

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

step-by-step explanation:

left be aligning the decimal points is required to not required see the number of digits to the right