For second one the answer is 14
Answer:
There are 14 horses and 21 chickens.
Step-by-step explanation:
First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :
![4x + 2y = 98](https://tex.z-dn.net/?f=4x%20%2B%202y%20%3D%2098)
( horse has 4 feet and chicken has 2 feet )
There are a total of 35 heads so the other equation will be :
![x + y = 35](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2035)
Lastly, you have to solve it :
![4x + 2y = 98](https://tex.z-dn.net/?f=4x%20%2B%202y%20%3D%2098)
![2(2x + y) = 98](https://tex.z-dn.net/?f=2%282x%20%2B%20y%29%20%3D%2098)
![2x + y = 49 - - - (1)](https://tex.z-dn.net/?f=2x%20%2B%20y%20%3D%2049%20-%20%20-%20%20-%20%281%29)
![x + y = 35 - - - (2)](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2035%20-%20%20-%20%20-%20%282%29)
![(1) - (2)](https://tex.z-dn.net/?f=%281%29%20-%20%282%29)
![2x + y - x - y = 49 - 35](https://tex.z-dn.net/?f=2x%20%20%2B%20y%20-%20x%20-%20y%20%3D%2049%20-%2035)
![x = 14](https://tex.z-dn.net/?f=x%20%3D%2014)
![substitute \: x = 14 \: into \: (2)](https://tex.z-dn.net/?f=substitute%20%5C%3A%20x%20%3D%2014%20%5C%3A%20into%20%5C%3A%20%282%29)
![14 + y = 35](https://tex.z-dn.net/?f=14%20%2B%20y%20%3D%2035)
![y = 35 - 14](https://tex.z-dn.net/?f=y%20%3D%2035%20-%2014)
![y = 21](https://tex.z-dn.net/?f=y%20%3D%2021)
Answer:
i got 6.70820393
Step-by-step explanation:
We can sum two fractions if they have the same denominator, so we have to rewrite both fractions so that they'll have the same denominator.
We can generate equivalent fractions by multiplying both numerator and denominator by the same number.
So, we have
![-\dfrac{7}{9} = -\dfrac{7\cdot 10}{9\cdot 10} = -\dfrac{70}{90}](https://tex.z-dn.net/?f=-%5Cdfrac%7B7%7D%7B9%7D%20%3D%20-%5Cdfrac%7B7%5Ccdot%2010%7D%7B9%5Ccdot%2010%7D%20%3D%20-%5Cdfrac%7B70%7D%7B90%7D)
Similarly, we have
![-\dfrac{5}{10} = -\dfrac{5\cdot 9}{10\cdot 9} = -\dfrac{45}{90}](https://tex.z-dn.net/?f=-%5Cdfrac%7B5%7D%7B10%7D%20%3D%20-%5Cdfrac%7B5%5Ccdot%209%7D%7B10%5Ccdot%209%7D%20%3D%20-%5Cdfrac%7B45%7D%7B90%7D)
Now we can sum the fractions:
![-\dfrac{7}{9}-\dfrac{5}{10} = -\dfrac{70}{90}-\dfrac{45}{90} = \dfrac{-70-45}{90} = -\dfrac{115}{90} = -\dfrac{23}{18}](https://tex.z-dn.net/?f=-%5Cdfrac%7B7%7D%7B9%7D-%5Cdfrac%7B5%7D%7B10%7D%20%3D%20-%5Cdfrac%7B70%7D%7B90%7D-%5Cdfrac%7B45%7D%7B90%7D%20%3D%20%5Cdfrac%7B-70-45%7D%7B90%7D%20%3D%20-%5Cdfrac%7B115%7D%7B90%7D%20%3D%20-%5Cdfrac%7B23%7D%7B18%7D)
Answer:
12 a. 4605 feet 12 b. 1,459,063 square feet
Step-by-step explanation:
For the perimeter, we simply add the lengths of each of the 5 sides together (or multiply 5 times one side length).
P = 5(921)
P = 4605 feet
For the area, we will use composition...add the area of the triangle to the area of the trapezoid.
For the area of the triangle, the formula is
.
Filling in our values gives us
and
A = 403,045 square feet.
Now for the trapezoid. The formula for a trapezoid is
![A=\frac{1}{2}(b_{1}+b_{2})(h)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28b_%7B1%7D%2Bb_%7B2%7D%29%28h%29)
where the b's represent the bases and the h represents the height. Filling in our values gives us
![A=\frac{1}{2}(921+1490)(876)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28921%2B1490%29%28876%29)
Work inside the parenthesis first:
and
A = 1,056,018
Now we add those together to get that area of the Pentagon is 1,459,063 square feet