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.")
Answer:
40%
Step-by-step explanation:
amount of apples = 6
total amount of fruits = 15
percentage of apples
= 6/15 x 100%
= 40%
Should I answer all the questions? or a specific one?
Answer:
The equation of a parallel line in point-slope form would be f(x) = -5/3x - 14
Step-by-step explanation:
To find this, we must first find the slope of the original line. We can do this by solving for y.
5x + 3y = 8
3y = -5x + 8
y = -5/3x + 8/3
Now that we have the slope of the original line, we can use the point and slope and put them into the base form of point-slope form. Then we solve for y to get the final result.
y - y1 = m(x - x1)
y + 9 = -5/3(x + 3)
y + 9 = -5/3x - 5
y = -5/3x - 14
Then to get the function notation, we need to replace the y with f(x).
f(x) = -5/3x - 14
8 cups of raisins is the answer
