It is given that m || n , m∠1 = 65° , m∠2 = 60° , and BD bisects ∠ABC .
Because of the triangle sum theorem, m∠3 = 55°.
By the definition of bisector, m∠ABC = 110°. (unsure of this one, but no other choice seems right)
m∠5 = 110° because vertical angles are congruent.
Because of the same-side interior angles theorem, m∠5 + m∠6 = 180°.
Substituting gives 110° + m∠6 = 180° .
So, by the subtraction property of equality, m∠6 = 70°
To find sin( pi/3 ) , we can start with an equilateral triangle with side length 1 .
Now draw a line that bisects an angle and the opposite side. The length of this line is sin(pi/3) .
By the Pythagorean theorem...
(1/2)2 + ( sin(pi/3) )2 = 12
Subtract (1/2)2 from both sides of the equation.
( sin(pi/3) )2 = 12 - (1/2)2
Take the positive sqrt of both sides.
sin(pi/3) = √[12 - (1/2)2]
sin(pi/3) = √[1 - 1/4]
sin(pi/3) = √[3/4]
sin(pi/3) = √3 / 2
Whatever x value we choose to plug in to (g + f)(x) has to be in the domain of both g(x) and f(x) .
For instance, we can't find g(1) + f(1) because we can't find g(1) .
The domain of g + f is all real x values such that x ≥ -14 and x ≤ -11
The domain of g + f is all real x values such that -14 ≤ x ≤ -11
The minimum value in that domain is -14 .