Angles abc and dbe are vertical
angles. if the measure of abc is 40, than what is the measure of abd?

 Angle ABD  is 140 degrees.

Step-by-step explanation:

Angle ABC = 40 and vertical angles are equal so Angle DBE is also 40.

In order to find Angle ABD you would take the degrees in a full circle which is 360 degrees and substract the two vertical angles you have.

360 (full circle) - 40 (Angle ABC) - 40 (Angle DBE) = 280 degrees.

The two remaining angles would also be vertical angles so divide the 280 degrees by 2.

280/2 =  140

4 angles:  40 + 40 + 140 + 140 = 360

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.