Bd bisects abc so that m abd is x-5 and m cbd is 2x-6. find the value of x

We are given m<ABC is bisected by segment BD.

There form two angles m<ABD and m<CBD.

m<ABD = x-5.

m<CBD = 2x-6.

Angle bisector divide an angle into two equal angles.

Therefore,

Angle m<ABD = angle m<CBD

Plugging given values of m<ABD and m<CBD, we get

x-5 = 2x-6

Adding 6 on both sides, we get

x-5+6 = 2x-6+6

x+1 =2x.

Subtracting x from both sides, we get

x-x+1 =2x-x

1=x.

Therefore, the value of x is 1.

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

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.