As a decimal = 0.83
fraction = 5/6
find common denominators!
Because you seem to have an understanding of the material, I will write my math, but no explanations for my work. Comment on this answer for an explanation, or if I did something wrong.
1. Find the length of the South side of the field.
![(5x+2)+(x^2-9)+(x^2-7x+12)\\5x+2+x^2-9+x^2-7x+12\\2x^2+5x+2-9-7x+12\\2x^2-2x+2-9+12\\2x^2-2x+5](https://tex.z-dn.net/?f=%285x%2B2%29%2B%28x%5E2-9%29%2B%28x%5E2-7x%2B12%29%5C%5C5x%2B2%2Bx%5E2-9%2Bx%5E2-7x%2B12%5C%5C2x%5E2%2B5x%2B2-9-7x%2B12%5C%5C2x%5E2-2x%2B2-9%2B12%5C%5C2x%5E2-2x%2B5)
2.Find the perimeter of the pumpkin field.
![2(5x+2)+2(5x-2)\\(5x+2)+(5x+2)+(5x-2)+(5x-2)\\20x+4-4\\20x](https://tex.z-dn.net/?f=2%285x%2B2%29%2B2%285x-2%29%5C%5C%285x%2B2%29%2B%285x%2B2%29%2B%285x-2%29%2B%285x-2%29%5C%5C20x%2B4-4%5C%5C20x)
3. Find the perimeter of the whole field.
![2(4x+5x-2)+2(5x+2+x^2-9+x^2-7x+12)\\2(9x-2)+2(2x^2-2x-5)\\18x-4+4x^2-4x+10\\4x^2+14x+6](https://tex.z-dn.net/?f=2%284x%2B5x-2%29%2B2%285x%2B2%2Bx%5E2-9%2Bx%5E2-7x%2B12%29%5C%5C2%289x-2%29%2B2%282x%5E2-2x-5%29%5C%5C18x-4%2B4x%5E2-4x%2B10%5C%5C4x%5E2%2B14x%2B6)
4. If
, what is the total perimeter?
![P=4x^2+14x+6\\P=4(30)^2+14(30)+6\\P=4(900)+420+6\\P=1026ft](https://tex.z-dn.net/?f=P%3D4x%5E2%2B14x%2B6%5C%5CP%3D4%2830%29%5E2%2B14%2830%29%2B6%5C%5CP%3D4%28900%29%2B420%2B6%5C%5CP%3D1026ft)
Random Tangent:
If you want to involve
in finding these answers for whatever reason, your math is going to get messy. Here's what I tried before I realized you could multiply each side by
to get the total perimeter:
![xy+1+x+6=4x+5x-2\\xy-8x=-9\\x(y-8)=-9\\y-8=-\frac{9}{x}\\y=-\frac{9}{x}+8](https://tex.z-dn.net/?f=xy%2B1%2Bx%2B6%3D4x%2B5x-2%5C%5Cxy-8x%3D-9%5C%5Cx%28y-8%29%3D-9%5C%5Cy-8%3D-%5Cfrac%7B9%7D%7Bx%7D%5C%5Cy%3D-%5Cfrac%7B9%7D%7Bx%7D%2B8)
Now the other side. This one's even worse.
![xy-1+6x+x=5x+2+x^2-9+x^2-7x+12\\xy+9x-2x^2=5\\x(y+9+2x)=5\\2x+9+y=\frac{5}{x}\\y=\frac{5}{x}-2x-9](https://tex.z-dn.net/?f=xy-1%2B6x%2Bx%3D5x%2B2%2Bx%5E2-9%2Bx%5E2-7x%2B12%5C%5Cxy%2B9x-2x%5E2%3D5%5C%5Cx%28y%2B9%2B2x%29%3D5%5C%5C2x%2B9%2By%3D%5Cfrac%7B5%7D%7Bx%7D%5C%5Cy%3D%5Cfrac%7B5%7D%7Bx%7D-2x-9)
At this point, was realizing I wasn't going about the problem correctly, but did one last try by setting
. At this point in the equation, I simply had to stop, both due to complexity and technological problems.
![\frac{5}{x}-2x-9=-\frac{9}{x}+8\\\frac{14}{x}=2x+17\\ 14=2x^2+17x\\0=2x^2+17x-13\\](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7Bx%7D-2x-9%3D-%5Cfrac%7B9%7D%7Bx%7D%2B8%5C%5C%5Cfrac%7B14%7D%7Bx%7D%3D2x%2B17%5C%5C%2014%3D2x%5E2%2B17x%5C%5C0%3D2x%5E2%2B17x-13%5C%5C)
I could possibly continue to solve, but I don't see a point. It was clear that this was NOT the right path to take finding the perimeter. It was here I realized that I could just multiply the two sides without
in them by
and--without as much difficulty--reach the correct answer.
First off, we are looking for the area of a poster that's in the shape of a rectangle.
Since we are looking for the area of a rectangle, we need to know the formula for the area of a rectangle.
The area of a rectangle is defined as Length times Width (L x W).
Our length is 3 ft and our width is 2 ft.
Given this information, we are ready to solve.
(L x W) = A
Plug in 3 for the length.
(3 x W) = A
Plug in 2 for the width.
(3 x 2) = A
3 x 2 = 6.
The area is 6 ft^2.
I hope this helps!
![\bf -\sqrt{\cfrac{1-\frac{2}{\sqrt{11}}}{11}}\implies -\sqrt{\cfrac{~~\frac{\sqrt{11}-2}{\sqrt{11}}~~}{\frac{11}{1}}}\implies -\sqrt{\cfrac{\sqrt{11}-2}{11\sqrt{11}}}](https://tex.z-dn.net/?f=%5Cbf%20-%5Csqrt%7B%5Ccfrac%7B1-%5Cfrac%7B2%7D%7B%5Csqrt%7B11%7D%7D%7D%7B11%7D%7D%5Cimplies%20-%5Csqrt%7B%5Ccfrac%7B~~%5Cfrac%7B%5Csqrt%7B11%7D-2%7D%7B%5Csqrt%7B11%7D%7D~~%7D%7B%5Cfrac%7B11%7D%7B1%7D%7D%7D%5Cimplies%20-%5Csqrt%7B%5Ccfrac%7B%5Csqrt%7B11%7D-2%7D%7B11%5Csqrt%7B11%7D%7D%7D)
I don't see it simplifying further, there are other ways that can change it to
, but that won't really be that simplified per se.
PEMDAS is
Parenthesis
Exponets
Multiply
Divide
Add
Subtract
therefore, you would do 40*0=0+40+1=41