Answer:
DOGS is a parallelogram.
Step-by-step explanation:
Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4), G(5, 6), and S(4,3).
To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:
Using the Distance Formula
![Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=Distance%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
For D(1, 1) and O(2, 4)
![|DO|=\sqrt{(2-1)^2+(4-1)^2}=\sqrt{1^2+3^2}=\sqrt{10} \:Units](https://tex.z-dn.net/?f=%7CDO%7C%3D%5Csqrt%7B%282-1%29%5E2%2B%284-1%29%5E2%7D%3D%5Csqrt%7B1%5E2%2B3%5E2%7D%3D%5Csqrt%7B10%7D%20%5C%3AUnits)
For G(5, 6), and S(4,3).
![|GS|=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{10}\:Units](https://tex.z-dn.net/?f=%7CGS%7C%3D%5Csqrt%7B%284-5%29%5E2%2B%283-6%29%5E2%7D%3D%5Csqrt%7B%28-1%29%5E2%2B%28-3%29%5E2%7D%3D%5Csqrt%7B10%7D%5C%3AUnits)
For O(2, 4) and G(5, 6)
![|OG|=\sqrt{(5-2)^2+(6-4)^2}=\sqrt{(3)^2+(2)^2}=\sqrt{13}\:Units](https://tex.z-dn.net/?f=%7COG%7C%3D%5Csqrt%7B%285-2%29%5E2%2B%286-4%29%5E2%7D%3D%5Csqrt%7B%283%29%5E2%2B%282%29%5E2%7D%3D%5Csqrt%7B13%7D%5C%3AUnits)
For S(4,3) and D(1, 1)
![|SD|=\sqrt{(1-4)^2+(1-3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}\:Units](https://tex.z-dn.net/?f=%7CSD%7C%3D%5Csqrt%7B%281-4%29%5E2%2B%281-3%29%5E2%7D%3D%5Csqrt%7B%28-3%29%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B13%7D%5C%3AUnits)
Since:
Then, quadrilateral DOGS is a parallelogram.
12 people liked neither.
30-11-7= 12
30: total class
11: people that like chocolate cake
7: people that like white cake
Answer:
the width is 360 ft
Step-by-step explanation:
The computation of the width of the flag is shown below:
Let us assume the width be x
So the length would be x + 340
And, the perimeter is 2,120 ft
So the formula is
Perimeter = 2(length + width)
2,120 = 2(x + 340 + x)
2,120 = 2x + 680 + 2x
2,120 = 4x + 680
4x = 2,120 - 680
x = 360
hence, the width is 360 ft
Answer:
131
Step-by-step explanation:
8×16+3=131 because there are 16 ounces in a pound
Answer:
4x^2 + 12x + 9
Step-by-step explanation:
(2x + 3)^2
it is in the form of (a + b)^2
(a + b)^2 = a^2 + 2*a*b + b^2
(2x + 3)^2
(2x)^2 + 2*2x*3 + (3)^2
4x^2 + 12x + 9