Answer: 23.89 thousands of pounds is more wheat that was gathered from the second field than from the first field.
Step-by-step explanation:
Since we have given that
the area of one field = 16 acres
Area of second field is given by
![1\frac{1}{4}\times 16\\\\=\frac{5}{4}\times 16\\\\=5\times 4\\\\=20\ acres](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B4%7D%5Ctimes%2016%5C%5C%5C%5C%3D%5Cfrac%7B5%7D%7B4%7D%5Ctimes%2016%5C%5C%5C%5C%3D5%5Ctimes%204%5C%5C%5C%5C%3D20%5C%20acres)
A barn of wheat on the first field makes up
![3\frac{7}{12}\times 16\\\\=\frac{43}{12}\times 16\\\\=57.33\text{ thousands of pounds.}](https://tex.z-dn.net/?f=3%5Cfrac%7B7%7D%7B12%7D%5Ctimes%2016%5C%5C%5C%5C%3D%5Cfrac%7B43%7D%7B12%7D%5Ctimes%2016%5C%5C%5C%5C%3D57.33%5Ctext%7B%20thousands%20of%20pounds.%7D)
A barn of wheat on the second field makes up
![1\frac{2}{15}\times 20\\\\=\frac{43}{12}\times \frac{17}{15}\times 20\\\\=81.22\text{ thousands of pounds }](https://tex.z-dn.net/?f=1%5Cfrac%7B2%7D%7B15%7D%5Ctimes%2020%5C%5C%5C%5C%3D%5Cfrac%7B43%7D%7B12%7D%5Ctimes%20%5Cfrac%7B17%7D%7B15%7D%5Ctimes%2020%5C%5C%5C%5C%3D81.22%5Ctext%7B%20thousands%20of%20pounds%20%7D)
Now,
![81.22-57.33=23.89](https://tex.z-dn.net/?f=81.22-57.33%3D23.89)
Hence, 23.89 thousands of pounds is more wheat that was gathered from the second field than from the first field.
<span>x+(2x-4)=11
Answer is x=5.</span>
Answer:
Perimeter = 18.7 units
Area = 13.5 units²
Step-by-step explanation:
Perimeter of ADEC = AD + DE + EC + AC
Length of AD = 3 units
By applying Pythagoras theorem in ΔDBE,
DE² = DB² + BE²
DE² = 3² + 3²
DE = √18
DE = 4.24 units
Length of EC = 3 units
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
AC² = 6² + 6²
AC = √72
AC = 8.49 units
Perimeter of ADEC = 3 + 4.24 + 3 + 8.49
= 18.73 units
≈ 18.7 units
Area of ADEC = Area of ΔABC - Area of ΔBDE
Area of ΔABC = ![\frac{1}{2}(AB)(BC)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28AB%29%28BC%29)
= ![\frac{1}{2}(6)(6)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%286%29%286%29)
= 18 units²
Area of ΔBDE = ![\frac{1}{2}(BD)(BE)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28BD%29%28BE%29)
= ![\frac{1}{2}(3)(3)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%283%29%283%29)
= 4.5 units²
Area of ADEC = 18 - 4.5
= 13.5 units²
Average rate=(change in y)/(change in x)
if f(x)=-x/3
r=( f(2)-f(-2) )/(2--2)
r=(-2/3-2/3)/(2+2)
r=(-4/3)/4
r=-4/12
r=-1/3
For a line, this is always true, since all lines have a constant velocity, the average velocity over any interval is equal to the slope.