The figure of the prism is attached below.
The total surface area of the prism equals the sum of areas of two triangles and the three rectangles.
Surface Area of Prism = Area of 2 Triangles + Area of 3 Rectangles.Area of a Triangle = 0.5 x Base x Height
Area of a Triangle = 0.5 x 3 x 4 = 6 square units
There are 3 rectangles. From the figure we can see that the bottom most rectangle has the dimensions 4 by 6. The left most rectangle has the dimensions 3 x 6 and the right most rectangle has the dimensions 5 by 6.
So, the Area of 3 rectangles will be = (4 x 6) + (3 x 6) + (5 x 6) = 72 square units
The Surface Area of the prism will be:
Surface Area = 2 (4) + 72 = 84 square units
Thus the correct answer is option A
Since the two lines are parallel and it is cut by a transversal,
75+X+5=180
=>80+X=180
=>X=180-80
==>X=100
Hope this helps u...!!!!!
If the distance to work<span> is 1 mile and you can walk at 4 miles per hour, then you can walk 1 mile in ¼ hr = 15 minutes.</span>
Answer:

Step-by-step explanation:



![b) [Kindly\ refer\ the\ graph\ attachment]\\\\We've\ drawn\ the\ graph\ fixing\ the\ scale\ of\ 1\ unit\ to\ be\ 20\ heads (Adults\ or\ Children).\\The\ red\ slope\ and\ the\ red\ area\ shaded\ below\ it,\ represent\ Inequality\ 1.\\The\ blue\ slope\ and\ the\ blue\ area\ shaded\ below\ it,\ represent\ Inequality\ 2.\\As\ we\ already\ know\ that,\\The\ overlapped\ region\ contains\ the\ solutions\ to\ the\ system\ of\ Inequalities.](https://tex.z-dn.net/?f=b%29%20%5BKindly%5C%20refer%5C%20the%5C%20graph%5C%20attachment%5D%5C%5C%5C%5CWe%27ve%5C%20drawn%5C%20the%5C%20graph%5C%20fixing%5C%20the%5C%20scale%5C%20of%5C%201%5C%20unit%5C%20to%5C%20be%5C%2020%5C%20heads%20%28Adults%5C%20or%5C%20Children%29.%5C%5CThe%5C%20red%5C%20slope%5C%20and%5C%20the%5C%20red%5C%20area%5C%20shaded%5C%20below%5C%20it%2C%5C%20represent%5C%20Inequality%5C%201.%5C%5CThe%5C%20blue%5C%20slope%5C%20and%5C%20the%5C%20blue%5C%20area%5C%20shaded%5C%20below%5C%20it%2C%5C%20represent%5C%20Inequality%5C%202.%5C%5CAs%5C%20we%5C%20already%5C%20know%5C%20that%2C%5C%5CThe%5C%20overlapped%5C%20region%5C%20contains%5C%20the%5C%20solutions%5C%20to%5C%20the%5C%20system%5C%20of%5C%20Inequalities.)


![I]Substituting\ x=20,\ y=100\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*20+250*100 \leq 44000\\4000+25000 \leq 44000\\29000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=20,\ y=100\ in\ Inequality\ 2:\\x+y \leq 150\\20+100 \leq 150\\120 \leq 150\\This\ is\ TRUE\ too.](https://tex.z-dn.net/?f=I%5DSubstituting%5C%20x%3D20%2C%5C%20y%3D100%5C%20in%5C%20Inequality%5C%201%3A%5C%5C200x%2B250y%20%5Cleq%2044000%5C%5C200%2A20%2B250%2A100%20%5Cleq%2044000%5C%5C4000%2B25000%20%5Cleq%2044000%5C%5C29000%20%5Cleq%2044000%5C%5CThis%5C%20is%5C%20TRUE.%5C%5C%5C%5CSubstituting%5C%20x%3D20%2C%5C%20y%3D100%5C%20in%5C%20Inequality%5C%202%3A%5C%5Cx%2By%20%5Cleq%20150%5C%5C20%2B100%20%5Cleq%20150%5C%5C120%20%5Cleq%20150%5C%5CThis%5C%20is%5C%20TRUE%5C%20too.)
![II]\ Substituting\ x=100,\ y=20\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*100+250*20 \leq 44000\\20000+5000 \leq 44000\\25000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=100,\ y=20\ in\ Inequality\ 2:\\x+y \leq 150\\100+20 \leq 150\\120 \leq 150\\This\ is\ TRUE\ too.](https://tex.z-dn.net/?f=II%5D%5C%20Substituting%5C%20x%3D100%2C%5C%20y%3D20%5C%20in%5C%20Inequality%5C%201%3A%5C%5C200x%2B250y%20%5Cleq%2044000%5C%5C200%2A100%2B250%2A20%20%5Cleq%2044000%5C%5C20000%2B5000%20%5Cleq%2044000%5C%5C25000%20%5Cleq%2044000%5C%5CThis%5C%20is%5C%20TRUE.%5C%5C%5C%5CSubstituting%5C%20x%3D100%2C%5C%20y%3D20%5C%20in%5C%20Inequality%5C%202%3A%5C%5Cx%2By%20%5Cleq%20150%5C%5C100%2B20%20%5Cleq%20150%5C%5C120%20%5Cleq%20150%5C%5CThis%5C%20is%5C%20TRUE%5C%20too.)
![III]\ Substituting\ x=40,\ y=40\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*40+250*40 \leq 44000\\8000+10000 \leq 44000\\18000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=40,\ y=40\ in\ Inequality\ 2:\\x+y \leq 150\\40+40 \leq 150\\80 \leq 150\\This\ is\ TRUE\ too.](https://tex.z-dn.net/?f=III%5D%5C%20Substituting%5C%20x%3D40%2C%5C%20y%3D40%5C%20in%5C%20Inequality%5C%201%3A%5C%5C200x%2B250y%20%5Cleq%2044000%5C%5C200%2A40%2B250%2A40%20%5Cleq%2044000%5C%5C8000%2B10000%20%5Cleq%2044000%5C%5C18000%20%5Cleq%2044000%5C%5CThis%5C%20is%5C%20TRUE.%5C%5C%5C%5CSubstituting%5C%20x%3D40%2C%5C%20y%3D40%5C%20in%5C%20Inequality%5C%202%3A%5C%5Cx%2By%20%5Cleq%20150%5C%5C40%2B40%20%5Cleq%20150%5C%5C80%20%5Cleq%20150%5C%5CThis%5C%20is%5C%20TRUE%5C%20too.)
![IV]\ Substituting\ x=80,\ y=60\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*80+250*60 \leq 44000\\16000+15000 \leq 44000\\31000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=80,\ y=60\ in\ Inequality\ 2:\\x+y \leq 150\\80+60 \leq 150\\140 \leq 150\\This\ is\ TRUE\ too.](https://tex.z-dn.net/?f=IV%5D%5C%20Substituting%5C%20x%3D80%2C%5C%20y%3D60%5C%20in%5C%20Inequality%5C%201%3A%5C%5C200x%2B250y%20%5Cleq%2044000%5C%5C200%2A80%2B250%2A60%20%5Cleq%2044000%5C%5C16000%2B15000%20%5Cleq%2044000%5C%5C31000%20%5Cleq%2044000%5C%5CThis%5C%20is%5C%20TRUE.%5C%5C%5C%5CSubstituting%5C%20x%3D80%2C%5C%20y%3D60%5C%20in%5C%20Inequality%5C%202%3A%5C%5Cx%2By%20%5Cleq%20150%5C%5C80%2B60%20%5Cleq%20150%5C%5C140%20%5Cleq%20150%5C%5CThis%5C%20is%5C%20TRUE%5C%20too.)
