Darnell is building a triangular community garden plot.
Which set of lengths can be used to create the plot perimeter?
Recall the triangle inequality theorem which states that the sum of any two sides must be greater than the third side.
![\begin{gathered} a+b>c \\ b+c>a_{} \\ a+c>b \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%20b%2Bc%3Ea_%7B%7D%20%5C%5C%20a%2Bc%3Eb%20%5Cend%7Bgathered%7D)
Let us analyze each of the given options.
Option A:
a = 20 feet
b = 12 feet
c = 34 feet
![\begin{gathered} a+b>c \\ 20+12>34 \\ 32>34\quad (\text{not satified)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%2020%2B12%3E34%20%5C%5C%2032%3E34%5Cquad%20%28%5Ctext%7Bnot%20satified%29%7D%20%5Cend%7Bgathered%7D)
Option B:
a = 8 feet
b = 10 feet
c = 19 feet
![\begin{gathered} a+b>c \\ 8+10>19 \\ 18>19\quad (\text{not satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%208%2B10%3E19%20%5C%5C%2018%3E19%5Cquad%20%28%5Ctext%7Bnot%20satisfied%29%7D%20%5Cend%7Bgathered%7D)
Option C:
a = 5 feet
b = 8 feet
c = 14 feet
![\begin{gathered} a+b>c \\ 5+8>14 \\ 13>14\quad (\text{not satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%205%2B8%3E14%20%5C%5C%2013%3E14%5Cquad%20%28%5Ctext%7Bnot%20satisfied%29%7D%20%5Cend%7Bgathered%7D)
Option D:
a = 12, feet
b = 14 feet
c = 20 feet
![\begin{gathered} a+b>c \\ 12+14>20 \\ 26>20\quad (\text{satisfied)} \\ b+c>a \\ 14+20>12 \\ 24>12\quad (\text{satisfied)} \\ a+c>b \\ 12+20>14 \\ 22>14\quad (\text{satisfied)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Ec%20%5C%5C%2012%2B14%3E20%20%5C%5C%2026%3E20%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5C%5C%20b%2Bc%3Ea%20%5C%5C%2014%2B20%3E12%20%5C%5C%2024%3E12%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5C%5C%20a%2Bc%3Eb%20%5C%5C%2012%2B20%3E14%20%5C%5C%2022%3E14%5Cquad%20%28%5Ctext%7Bsatisfied%29%7D%20%5Cend%7Bgathered%7D)
As you can see, only option D satisfies the triangle inequality theorem
Therefore, option D is the correct answer.
Answer:
x = 3 and y = -18
Step-by-step explanation:
y = -6x
y = -8x + 6
Both equations are equal to y. So,
y = -6x = -8x + 6
Solve for x first.
-6x = -8x + 6
Add 8x to both sides.
2x = 6
x = 3
Substitute x = 3 into y = -6x
y = -6 * 3
y = -18
Now, double check to see if this is correct.
y = -8x + 6
-18 = -8 * 3 + 6
-18 = -24 + 6
-18 = -18
x = 3 and y = -18 are correct.
I hope this helps! Feel free to ask any questions!
The monomial factor is (4)(4) = 16. Notice that 4 is a common factor of the first expression in parentheses, and that 4 is again a common fact. of the second expression in parentheses. You will be left with 2 binomials, as desired. Show your work, please.
Answer:
22
Step-by-step explanation:
Once you fill in the variables your equation will look like this::4^2+4(1.5)::you will the go multiply both parts of the equation leaving you with 16+6 and when you add those together you get 22.
Hope This Helps!
Answer:
10 k cal
Step-by-step explanation:
the ecosystem has ecological of 10%
the producer level is 1000 kilo-calories
the primary consumer will contain 10 % of the producer:
10000*10%=1000
the secondary consumer will contain 10% of the primary:
1000*10%=100 k cal
the tertiary will get 10% of the secondary: 100*10%=10 kcal