Which THREE statements are correct for the angles shown on the figure? A) x° + 4x° - 85° = 90°
B) x° + 4x° - 85° = 180°
C) ∠ABD and ∠CBD are supplementary
D) ∠ABD = 35°
E) ∠CBD = 55°

pls help!!

A D E

Step-by-step explanation:

the figure shows that ABC is 90 degrees. So the two smaller angles add to 90 making A correct. (B isn't for obvious reasons - 180 is not 90.)

x + 4x - 85 = 90               Solve this to find the other 2 correct statements

5x - 85 = 90                    Add 85 to both sides.

5x = 90 + 85                    Combine

5x = 175                            Divide by 5

5x/5 = 175/5

x = 35

Since ABD is a single x, that statement (D) is true.

4x - 85 = 4*35 - 85 = 140 - 85 = 55 which makes E true as well

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