given that bisects ∠dbc, which statement must be true?
m∠abd = m∠abc
ab ≅ bc
b is the midpoint of dc.
m∠dbc = 90°

Only statement 1 is true.

Step-by-step explanation:

It can be clearly seen that the the points D, B, and C lie on the straight line. Therefore, the angle DBC must be 180 degrees. This means that the fourth statement is false. If a line is cutting an angle right in the middle, that line is called an angle bisector. It can be seen in the diagram that the line AB is bisecting the able DBC. Since the angle bisector equally cuts the angle, therefore the angles ABD and ABC are equal. So angle ABD = angle ABC = 180 degrees / 2 = 90 degrees. So the first option is correct. The second statement is false because the angle bisector can start from any point in the plane. This means that its length is ambiguous. Same is the case for the line BC. Statement 3 is true if the line AB acts as a perpendicular bisector as well, other than the angle bisector. Just like latter, former equally cuts the line from the middle. If the line AB is not a perpendicular bisector, then statement 3 is not true. If the line AB is a perpendicular bisector, then statement 3 is true!!!

54.864 meters

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!