Answer:
1) 60
2) 60
3) 119
4) 59
Step-by-step explanation:
All triangle angles add up to 180 degrees. All lines with transversals add to 180 degrees. Use these rules and the measurements given to solve.
Answer: 108
Explanation:
GCF(36,54) = 18
LCM(36,54) = ( 36 × 54) / 18
LCM(36,54) = 1944 / 18
LCM(36,54) = 108
![\bf \begin{array}{llll} -5x-y=5\\ -5x+y=5\\ -------\\ -10x+0=10 \end{array}\implies -10x=10\implies x=-1](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bllll%7D%0A-5x-y%3D5%5C%5C%0A-5x%2By%3D5%5C%5C%0A-------%5C%5C%0A-10x%2B0%3D10%0A%5Cend%7Barray%7D%5Cimplies%20-10x%3D10%5Cimplies%20x%3D-1)
so if x = -1, let's plug that in the second equation
-5(-1)+y = 5
5+y = 5
y = 0
QUESTION A
The total number of bottles Ella collected is
![50](https://tex.z-dn.net/?f=50)
The number of bottles that are plastic is
![19](https://tex.z-dn.net/?f=19)
The percentage of bottles that are plastic is
![= \frac{number \: of \: plastic \: bottles}{total \: number \: of \: bottes} \times 100\%](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7Bnumber%20%5C%3A%20of%20%5C%3A%20plastic%20%5C%3A%20bottles%7D%7Btotal%20%5C%3A%20number%20%5C%3A%20of%20%5C%3A%20bottes%7D%20%20%5Ctimes%20100%5C%25)
![= \frac{19}{50} \times 100\%](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B19%7D%7B50%7D%20%20%5Ctimes%20100%5C%25)
![= 19 \times 2\%](https://tex.z-dn.net/?f=%20%3D%2019%20%5Ctimes%202%5C%25)
![= 38\%](https://tex.z-dn.net/?f=%20%3D%2038%5C%25)
Therefore 38% of the bottles are plastic.
QUESTION B
The total number of bottles that are glass is
![50 - 19 = 31](https://tex.z-dn.net/?f=50%20-%2019%20%3D%2031)
The total number of bottles Ella collected is
![50](https://tex.z-dn.net/?f=50)
The percentage of bottles that is glass is
![= \frac{number \: of \: glass \: bottles}{total \: number \: of \: bottles} \times 100\%](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7Bnumber%20%5C%3A%20of%20%5C%3A%20glass%20%5C%3A%20bottles%7D%7Btotal%20%5C%3A%20number%20%5C%3A%20of%20%5C%3A%20bottles%7D%20%20%5Ctimes%20100%5C%25)
![= \frac{31}{50} \times 100\%](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B31%7D%7B50%7D%20%20%5Ctimes%20100%5C%25)
![= 31 \times 2\%](https://tex.z-dn.net/?f=%20%3D%2031%20%5Ctimes%202%5C%25)
![= 62\%](https://tex.z-dn.net/?f=%20%3D%2062%5C%25)
Therefore 62% of the bottles are glass
Before we solve for anything, let's remember what our formula is.
The circumference of a circle is 2PiR (2 x Pi x R).
Our radius is 157.64.
Pi is 3.14 (estimated).
Let's plug our numbers into the formula.
Circumference = 2 x 3.14 x 157.64.
2 x 3.14 = 6.28
6.28 x 157.64 = 989.979 (990 if estimated).
Your circumference is:
989.979 ft^2.
I hope this helps!