Answer:
Step-by-step explanation:
By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other: 
, or equivalently, 
.
Given our linear equation 3x + y = 3 (or y = -3x + 3):
We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is 
.
To test whether this is correct, we can take first slope, 
, and multiply it with the negative reciprocal slope 
:
Therefore, we came up with the correct slope for the other line, which is .
Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:
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:
Step-by-step explanation:
is the least steeped graph
- The greater the slope, the steeper the line.
- Also you use the absolute values of the slopes when determining the steepness.
- So here it would be:
- Now, arrange them from least to greatest:
As you can see, 
is the smallest number/slope.
Hope this helps!
Answer:
A & C
Step-by-step explanation:
