Factor completely and then place the factors in the proper location on the grid. 4a 2 - 8a - 5
2 answers:
Answer:
Step-by-step explanation:
Given quadratic polynomial:
To factorize the given quadratic polynomial we use the "splitting of middle term" method that is the x term which is the sum of two factors and product equal to last term.
The product of first and last term =
The middle term of the given polynomial can be written as
, where -10a and 2a are the factors of
.
Now,
Hence,
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Answer:
The vertical distance from the ground to the bird's eyes is 47.67 m
Step-by-step explanation:
* Lets explain the situation of the problem
- There is a bird on the top of a tree
- The bird looks down on a field mouse at an angle of depression of 50°
- The field mouse is 40 meters from the base of the tree
* Consider that the vertical distance from the ground to the bird's eyes,
the distance from the field mouse to the base of the tree distance
from the bird eyes to the field mouse formed a right triangle
- The hypotenuse is the distance from the bird eyes to the field mouse
- The horizontal side is the distance from the field mouse to the base
of the tree
- The angle between the hypotenuse and the horizontal side is the
angle of depression which = 50°
- The opposite side to the angle of measure 50° is the vertical distance
from the ground to the bird's eyes
* Lets use trigonometry functions to find the vertical distance
∵ The length of the adjacent side to the angle of measure 50° is 40 m
∵ The length of the opposite side to the angle of measure 50° is h m
∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф
∵ Ф = 50°
∴ tan 50° = h/40 ⇒ by using cross multiplication
∴ 40 tan 50° = h
∴ h = 47.67 m
* The vertical distance from the ground to the bird's eyes is 47.67 m
