9514 1404 393
Answer:
k = 10
Step-by-step explanation:
The useful shortcut* here is that the external angle is equal to the sum of the remote internal angles.
115° = (4k+5)° +(6k+10)°
100° = 10k° . . . . . . collect terms, subtract 15°
k = 10 . . . . . . . . . . divide by 10°
_____
* I call it a shortcut because you can get there from the relations ...
- the sum of angles in a triangle is 180°
- a linear pair has a sum of 180°
If we call the internal angles X, Y, and Z, then we have ...
X + Y + Z = 180° . . . triangle sum relation
Y + 115° = 180° . . . . . linear pair relation
Equating the expressions for 180° gives ...
X + Y + Z = Y + 115°
X + Z = 115° . . . . . . . . . subtract Y from both sides
To determine the perimeter of the trapezoid, we just have to determine the distance between the pair of points which can be calculated through the equation,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting,
(1,4) and (-2,0) d = √(1 - -2)² + (4 - 0)² = 5
(-2,0) and (7,0) d= √(-2 - 7)² + (0 - 0)² = 9
(7,0) and (3,4) d = √(7 - 3)² + (0 - 4)² = 5.66
(3,4) and (1,4) d = √(3 - 1)² + (0 - 0)² = 2
The perimeter is the sum of the distances. Thus, the answer is 21.66.
Add 5 then add 4 is the sequence
For this case we have the following expression:
h (t) = -16t ^ 2 + 64t + 80
For t = 0 we have:
h (0) = -16 (0) ^ 2 + 64 (0) + 80
h (0) = -0 + 0 + 80
h (0) = 80 feet
Therefore the number 80 represents the initial height of the rocket
Answer:
the 80 in the expression represented:
the initial height of the rocket
