Answer:
![Area = \frac{1}{2}|x_1(y_2 - y_3)+x_2(y_3 - y_1)+x_3(y_1 - y_2)|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7Cx_1%28y_2%20-%20y_3%29%2Bx_2%28y_3%20-%20y_1%29%2Bx_3%28y_1%20-%20y_2%29%7C)
![Area = 2\ units^2](https://tex.z-dn.net/?f=Area%20%3D%202%5C%20units%5E2)
Explanation:
Given
![A = (x_1,y_1)](https://tex.z-dn.net/?f=A%20%3D%20%28x_1%2Cy_1%29)
![B = (x_2,y_2)](https://tex.z-dn.net/?f=B%20%3D%20%28x_2%2Cy_2%29)
![C = (x_3,y_3)](https://tex.z-dn.net/?f=C%20%3D%20%28x_3%2Cy_3%29)
Required
Determine the area
The area of a triangle is :
![Area = \frac{1}{2}|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7CA_x%28B_y%20-%20C_y%29%20%2B%20B_x%28C_y%20-%20A_y%29%20%2B%20C_x%28A_y%20-%20B_y%29%7C)
By substituting values for the x and y coordinates of A, B and C;
We have:
![Area = \frac{1}{2}|x_1(y_2 - y_3)+x_2(y_3 - y_1)+x_3(y_1 - y_2)|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7Cx_1%28y_2%20-%20y_3%29%2Bx_2%28y_3%20-%20y_1%29%2Bx_3%28y_1%20-%20y_2%29%7C)
So:
For instance
![A = (0,3)](https://tex.z-dn.net/?f=A%20%3D%20%280%2C3%29)
![B= (2,1)](https://tex.z-dn.net/?f=B%3D%20%282%2C1%29)
![C = (2,3)](https://tex.z-dn.net/?f=C%20%3D%20%282%2C3%29)
The area is:
![Area = \frac{1}{2}|0(1-3) + 2(3-3) + 2(3-1)|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C0%281-3%29%20%2B%202%283-3%29%20%2B%202%283-1%29%7C)
![Area = \frac{1}{2}| 2*0 + 2*2|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C%202%2A0%20%2B%202%2A2%7C)
![Area = \frac{1}{2}| 0 + 4|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C%200%20%2B%204%7C)
![Area = \frac{1}{2}|4|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C4%7C)
![Area = \frac{1}{2} * 4](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%204)
![Area = 2\ units^2](https://tex.z-dn.net/?f=Area%20%3D%202%5C%20units%5E2)
Answer:
First and last sentence .♀️
Explanation:
An important thing to keep in mind about the Reading Comprehension section of the GRE as we use PowerPrep online to study is that it is just that—reading comprehension. In other words, as difficult as it may seem, and it can be pretty tricky, the test makers will always give us all the information we need in the passage to answer the question.
Answer:
85.34g of NH3
Explanation:
Step 1:
The balanced equation for the reaction. This is given below:
N2 + 3H2 —> 2NH3
Step 2:
Determination of the number of moles of NH3 produced by the reaction of 2.51 moles of N2. This is illustrated below:
From the balanced equation above,
1 mole of N2 reacted to produce 2 moles of NH3.
Therefore, 2.51 moles of N2 will react to produce = (2.51 x 2)/1 = 5.02 moles of NH3.
Therefore, 5.02 moles of NH3 is produced from the reaction.
Step 3:
Conversion of 5.02 moles of NH3 to grams. This is illustrated below:
Molar mass of NH3 = 14 + (3x1) = 17g/mol
Number of mole of NH3 = 5.02 moles
Mass of NH3 =..?
Mass = mole x molar Mass
Mass of NH3 = 5.02 x 17
Mass of NH3 = 85.34g
Therefore, 85.34g of NH3 is produced.