Answer:
Trapezoid
Step-by-step explanation:
The two sloped opposite sides are congruent. The two uncongruent opposite sides are parallel. There are no right angles. You can do this by finding the distance and slopes of the lines.
Not triangle because has four vertices.
Answer:
False
Step-by-step explanation:
If this number is larger than 6, then its square is larger than 36.
If x > 6, then x² > 36
The number is not larger than 6.therefore Its square is not larger than 36.
x ≤ 6; therefore, x² ≤ 36
-7 is < 6; however -7² > 36 as -7² = 49
Answer:
The polynomial is:
![p(x) = x^3 + 2x^2 - 3x + 20](https://tex.z-dn.net/?f=p%28x%29%20%3D%20x%5E3%20%2B%202x%5E2%20-%203x%20%2B%2020)
Step-by-step explanation:
A third degree polynomial can be written in function of it's zeros
the following way:
![p(x) = a(x - x_1)(x - x_2)(x - x_3)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%20-%20x_1%29%28x%20-%20x_2%29%28x%20-%20x_3%29)
In which a is the leading coefficient.
Integer coefficient that have zeros: 1+2i, 1-2i, -4
Leading coefficient: 1
So
![p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))](https://tex.z-dn.net/?f=p%28x%29%20%3D%201%28x%20-%20%281%2B2i%29%29%28x%20-%20%281-2i%29%29%28x%20-%20%28-4%29%29)
![p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%20-%201%20-2i%29%28x%20-%201%20%2B%202i%29%28x%20%2B%204%29)
![p(x) = ((x-1)^2 - (2i)^2)(x + 4)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28%28x-1%29%5E2%20-%20%282i%29%5E2%29%28x%20%2B%204%29)
![p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%5E2%20-%202x%20%2B%201%20-%204i%5E2%29%28x%20%2B%204%29)
Since ![i^2 = -1](https://tex.z-dn.net/?f=i%5E2%20%3D%20-1)
![p(x) = (x^2 - 2x + 1 + 4)(x + 4)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%5E2%20-%202x%20%2B%201%20%2B%204%29%28x%20%2B%204%29)
![p(x) = (x^2 - 2x + 5)(x + 4)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%5E2%20-%202x%20%2B%205%29%28x%20%2B%204%29)
![p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20](https://tex.z-dn.net/?f=p%28x%29%20%3D%20x%5E3%20%2B%204x%5E2%20-%202x%5E2%20-%208x%20%2B%205x%20%2B%2020)
![p(x) = x^3 + 2x^2 - 3x + 20](https://tex.z-dn.net/?f=p%28x%29%20%3D%20x%5E3%20%2B%202x%5E2%20-%203x%20%2B%2020)