Answer:
(a) x = 
(b) x = 
Step-by-step explanation:
A. sum of angles in a polygon = (n - 2) 180
The polygon given is an irregular pentagon, where n = 5
So that;
sum of angles in a pentagon = (5 - 2) 180
= 3 x 180
= 
Thus,
x + 90 + 76 + 110 + 136 = 
x + 412 = 
x =
- 412
x = 
B. The polygon given is an irregular pentagon, where n = 5.
Let the supplementary angle with angle 38 be represented by y,
y + 38 = 180
y = 180 - 38
= 
y = 
Let the supplementary angle with x be represented by z, so that;
z + 72 + 120 + 100 + 142 = 
z + 434 = 
z =
- 434
= 
z = 
But, x + z = 
Then;
x +
= 
x =
- 
= 
x = 
Answer:
The area of the triangle is 18 square units.
Step-by-step explanation:
First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:
AB
![AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%285-2%29%5E%7B2%7D%2B%5B6-%28-1%29%5D%5E%7B2%7D%7D)

BC


AC
![AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%28-1-2%29%5E%7B2%7D%2B%5B4-%28-1%29%5D%5E%7B2%7D%7D)

Now we determine the area of the triangle by Heron's formula:
(1)
(2)
Where:
- Area of the triangle.
- Semiparameter.
If we know that
,
and
, then the area of the triangle is:


The area of the triangle is 18 square units.
Answer: c) There is not enough evidence to reject H0
Step-by-step explanation:
Step-by-step explanation:
Domain x belongs to [-4 , 0]
Range y belongs to [-4 , 4]