How many unique triangles can be drawn with side lengths 12 cm and 16 cm and a 50 ° included angle

1 unique triangle

Step-by-step explanation:

There are several ways to determine if the information given about a triangle produces a unique triangle or not. One option is to provide two side lengths and the angle included between them, this is known as SAS (side-angle-side) congruence, this is not to be confused with SSA (side-side-angle) congruence.  Since this is one of the groups of givens that provides a unique triangle, then the number of unique triangles that can be drawn is 1 unique triangle.

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.