Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
__
If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
Let n = 30
We are actually looking for a_30.
a_30 = 4(30) + 1
a_30 = 120 + 1
a_30 = 121
In this question , we have to find, which option represents inverse functions.
Let's check out option b
Let it be y
So we have
Switching x and y and solving for y,
Performing cross multiplication
Combining like terms
Which is same as of the other function.
So correct option is b .
Answer:(4,1)
Step-by-step explanation: over the x axis 4 and up 1 with the y axis
