Notice that
11/12 = 1/6 + 3/4
so that
tan(11π/12) = tan(π/6 + 3π/4)
Then recalling that
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
⇒ tan(x + y) = (tan(x) + tan(y))/(1 - tan(x) tan(y))
it follows that
tan(11π/12) = (tan(π/6) + tan(3π/4))/(1 - tan(π/6) tan(3π/4))
tan(11π/12) = (1/√3 - 1)/(1 + 1/√3)
tan(11π/12) = (1 - √3)/(√3 + 1)
tan(11π/12) = - (√3 - 1)²/((√3 + 1) (√3 - 1))
tan(11π/12) = - (4 - 2√3)/2
tan(11π/12) = - (2 - √3) … … … [A]
Answer:
for #1: 70x = y
for #2: 70x + 100 = y
Step-by-step explanation:
you pay $70 for x amount of time with will equal your total therefore it's 70x = y
if you have to pay a one-time fee of $100.00 then you have to add that to your equation giving you 70x + 100 = y
hope this is right
hope it helps too :)
It is a line that divides the space into two.. The line is y=-x-3
Answer:
See attached diagram
Step-by-step explanation:
Graph the solution of the inequality 
First, draw the dotted line 
(dotted because the sign of the inequality is <). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (red part on the diagram).
Graph the solution of the inequality 
First, draw the solid line 
(solid because the sign of the inequality is ≥). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (blue part on the diagram).
The intersection of both regions is the solution of the system of two inequalities.
THe LCD is x(x^2 - 4)
so multiplying through by this we get:-
2x(x + 2) + 7x = 5(x^2 - 4)
2x^2 + 4x + 7x = 5x^2 - 20
3x^2 - 11x - 20 = 0
(3x + 4)(x - 5 ) = 0
so x = 5 , -4/3
Its the second choice
