The length of three sides in a right triangle has the rule of hypotenuse^2=leg one ^2 + leg two ^2. So the square of the length of hypotenuse equals to 9^2+40^2. So the length is 41 cm.
Answer:
![5s^2 +13s-10](https://tex.z-dn.net/?f=5s%5E2%20%2B13s-10)
Step-by-step explanation:
Given the expression
![5s(3+s)-(2s+10)](https://tex.z-dn.net/?f=5s%283%2Bs%29-%282s%2B10%29)
First, use distributive property:
![5s(3+s)=5s\cdot 3+5s\cdot s=15s+5s^2\\ \\-(2s+10)=(-1)\cdot (2s+10)=(-1)\cdot 2s+(-1)\cdot 10=-2s-10](https://tex.z-dn.net/?f=5s%283%2Bs%29%3D5s%5Ccdot%203%2B5s%5Ccdot%20s%3D15s%2B5s%5E2%5C%5C%20%5C%5C-%282s%2B10%29%3D%28-1%29%5Ccdot%20%282s%2B10%29%3D%28-1%29%5Ccdot%202s%2B%28-1%29%5Ccdot%2010%3D-2s-10)
Now, the given expression is equivalent to the following expression:
![15s+5s^2-2s-10](https://tex.z-dn.net/?f=15s%2B5s%5E2-2s-10)
Rewrite this expression using commutative property:
![5s^2+15s-2s-10\\ \\=5s^2 +13s-10 \ [\text{Add the like terms}]](https://tex.z-dn.net/?f=5s%5E2%2B15s-2s-10%5C%5C%20%5C%5C%3D5s%5E2%20%2B13s-10%20%5C%20%5B%5Ctext%7BAdd%20the%20like%20terms%7D%5D)
If you meant 2x + 2x + 1 = 17: x = 4
Solve for x by simplifying both sides of the equation, then isolating the variable.<span>
</span>
If you meant <span>x2 + 2x + 1 = 17:</span> <span>x ≈ 3.1231056,−5.1231056x</span>
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula. <span><span>x = −1 ± <span>√17</span></span>x</span>
Answer:
![DF = 38](https://tex.z-dn.net/?f=DF%20%3D%2038)
![GE = 40](https://tex.z-dn.net/?f=GE%20%3D%2040)
Step-by-step explanation:
Given
![DH = 2y + 6,](https://tex.z-dn.net/?f=DH%20%3D%202y%20%2B%206%2C)
![HF = 4x + 1,](https://tex.z-dn.net/?f=HF%20%3D%204x%20%2B%201%2C)
![HE = 3x + 2](https://tex.z-dn.net/?f=HE%20%3D%203x%20%2B%202)
![GH = 20.](https://tex.z-dn.net/?f=GH%20%3D%2020.)
See attachment for parallelogram.
Required
Find GE and DF
From the attachment:
![GH= HE](https://tex.z-dn.net/?f=GH%3D%20HE)
Substitute values for GH and HE
![20 = 3x + 2](https://tex.z-dn.net/?f=20%20%3D%203x%20%2B%202)
Subtract 2 from both sides
![20-2 = 3x + 2-2](https://tex.z-dn.net/?f=20-2%20%3D%203x%20%2B%202-2)
![20-2 = 3x](https://tex.z-dn.net/?f=20-2%20%3D%203x)
![18= 3x](https://tex.z-dn.net/?f=18%3D%203x)
![3x = 18](https://tex.z-dn.net/?f=3x%20%3D%2018)
Divide both sides by 3
![x = \frac{18}{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B18%7D%7B3%7D)
![x=6](https://tex.z-dn.net/?f=x%3D6)
![GE = GH + HE](https://tex.z-dn.net/?f=GE%20%3D%20GH%20%2B%20HE)
![GH= HE](https://tex.z-dn.net/?f=GH%3D%20HE)
So:
![GE = GH + GH](https://tex.z-dn.net/?f=GE%20%3D%20GH%20%2B%20GH)
![GE = 20 + 20](https://tex.z-dn.net/?f=GE%20%3D%2020%20%2B%2020)
![GE = 40](https://tex.z-dn.net/?f=GE%20%3D%2040)
To find DF, we find y first:
![DH = HF](https://tex.z-dn.net/?f=DH%20%3D%20HF)
![2y + 6 = 4x + 1](https://tex.z-dn.net/?f=2y%20%2B%206%20%3D%204x%20%2B%201)
Subtract 6 from both sides
![2y +6- 6 = 4x + 1-6](https://tex.z-dn.net/?f=2y%20%2B6-%206%20%3D%204x%20%2B%201-6)
![2y = 4x + 1-6](https://tex.z-dn.net/?f=2y%20%3D%204x%20%2B%201-6)
Substitute 6 for x
![2y = 4*6 + 1-6](https://tex.z-dn.net/?f=2y%20%3D%204%2A6%20%2B%201-6)
![2y = 19](https://tex.z-dn.net/?f=2y%20%3D%2019)
Divide both sides by 2
![y = \frac{19}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B19%7D%7B2%7D)
![y = 9.5](https://tex.z-dn.net/?f=y%20%3D%209.5)
DF is then calculated as"
![DF = DH + HF](https://tex.z-dn.net/?f=DF%20%3D%20DH%20%2B%20HF)
![DF = 2y+6 + 4x+1](https://tex.z-dn.net/?f=DF%20%3D%202y%2B6%20%2B%204x%2B1)
Substitute values for x and y
![DF = 2*9.5+6 + 4*3+1](https://tex.z-dn.net/?f=DF%20%3D%202%2A9.5%2B6%20%2B%204%2A3%2B1)
![DF = 38](https://tex.z-dn.net/?f=DF%20%3D%2038)