Answer:
Area of triangle is 9.88 units^2
Step-by-step explanation:
We need to find the area of triangle
Given E(5,1), F(0,4), D(0,8)
We will use formula:
![Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}](https://tex.z-dn.net/?f=Area%5C%2C%5C%2Cof%5C%2C%5C%2Ctriangle%20%3D%5Csqrt%7Bs%28s-a%29%28s-b%29s-c%29%7D%20%5C%5Cwhere%5C%2C%5C%2C%20s%20%3D%20%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
We need to find the lengths of side DE, EF and FD
Length of side DE = a = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Length of side DE = a = ![=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%285-0%29%5E2%2B%281-8%29%5E2%7D%5C%5C%3D%5Csqrt%7B%285%29%5E2%2B%28-7%29%5E2%7D%5C%5C%3D%5Csqrt%7B25%2B49%7D%5C%5C%3D%5Csqrt%7B74%7D%5C%5C%3D8.60)
Length of side EF = b = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Length of side EF = b = ![=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%280-5%29%5E2%2B%284-1%29%5E2%7D%5C%5C%3D%5Csqrt%7B%28-5%29%5E2%2B%283%29%5E2%7D%5C%5C%3D%5Csqrt%7B25%2B9%7D%5C%5C%3D%5Csqrt%7B34%7D%5C%5C%3D5.8)
Length of side FD = c = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Length of side FD = c = ![=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%280-0%29%5E2%2B%288-4%29%5E2%7D%5C%5C%3D%5Csqrt%7B%280%29%5E2%2B%284%29%5E2%7D%5C%5C%3D%5Csqrt%7B0%2B16%7D%5C%5C%3D%5Csqrt%7B16%7D%5C%5C%3D4)
so, a= 8.60, b= 5.8 and c = 4
s = a+b+c/2
s= 8.6+5.8+4/2
s= 9.2
Area of triangle=![=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88](https://tex.z-dn.net/?f=%3D%5Csqrt%7Bs%28s-a%29%28s-b%29s-c%29%7D%5C%5C%3D%5Csqrt%7B9.2%289.2-8.6%29%289.2-5.8%29%289.2-4%29%7D%5C%5C%3D%5Csqrt%7B9.2%280.6%29%283.4%29%285.2%29%7D%5C%5C%3D%5Csqrt%7B97.5936%7D%5C%5C%3D9.88)
So, area of triangle is 9.88 units^2
The solution to the given expression negative four and one third ÷ two and one fifth is -1 32/33
<h3>Fraction division</h3>
negative four and one third ÷ two and one fifth
-4 1/3 ÷ 2 1/5
= -13/3 ÷ 11/5
- Multiply by the reciprocal of 11/5
- The reciprocal of 11/5 is 5/11
= -13/3 × 5/11
= (-13 × 5) / (3 × 11)
= -65 / 33
= -1 32/33
Therefore, the solution to the fraction is -1 32/33
Learn more about fraction:
brainly.com/question/11562149
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Answer:
The consecutive even numbers are 28, 30, 32, 34
Step-by-step explanation:
let the four consecutive even numbers be: b d f h,
such that:
b=b, d=b+2, f=b+4, h=b+6.
Therefore, 2(b+b+2)=3(b+6)+14
b=28,
d=(b+2)=30
f=(b+4)=32
h=(b+6)=34
Answer:
t = 350
Step-by-step explanation:
subtract 250 from each side, and then you'll have t = 350