Answer:
If Angle 1 is 110,
then the second angle to complete the straight angle (180 degrees) is...
180 - 110 = 70
Angle 2 = 110 (same as Angle 1, plus it's obtuse)
Angle 3 = 70 (it's acute)
Angle 4 = 70 (same as Angle3, plus it's acute)
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points through which the line passes, so we can find the slope:
Thus, the equation is of the form:
We substitute one of the points and find "b":
Finally, the equation is of the form:
ANswer:
Answer:
-1/6
Step-by-step explanation:
To find the slope we use
m = (y2-y1)/(x2-x1)
= (-4-8)/( 1-3)
= -12/-2
=6
We want a line perpendicular, so we need the negative reciprocal
- (1/6)
-1/6
The property shown is commutative multiplication. This property says that the product of two factors is not affected by the order in which they're multiplied. In this case, the product remains the same i.e., 2*8*5 = 80 while 2*5*8 <em>also </em>equals 80.
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.")
