Answer:
-10x² - 7x + 7
Step-by-step explanation:
Subtract:
- -5x² - 8x - 1 - (5x² - x - 8)
- -5x² - 5x² - 8x + x - 1 + 8
- -10x² - 7x + 7
Remember: subtracting a negative number is adding that number
-Chetan K
Answer:
135ft²
Step-by-step explanation:
Width = w
Length = w + 6
Perimeter = 48
Perimeter = 2(l + w)
Perimeter = 2(w + 6 + w) = 48
2(2w + 6) = 48
4w + 12 = 48
4w = 48 - 12
4w = 36
w = 36/4
width = 9
length = w + 6 = 9 + 6 = 15
Area = length × width
= 15 × 9
= 135 ft²
Answer:
The answer is below
Step-by-step explanation:
Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:
Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:
![z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\](https://tex.z-dn.net/?f=z_%7Bk%3D0%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%280%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%280%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D0%7D%3D3%5Bcos%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B3%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5Cz_%7Bk%3D1%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%281%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%281%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D1%7D%3D3%5Bcos%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B19%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5C)
![z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]](https://tex.z-dn.net/?f=z_%7Bk%3D2%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%282%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%282%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D2%7D%3D3%5Bcos%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B35%5Cpi%7D%7B32%7D%29%5D%5C%5C%5C%5Cz_%7Bk%3D3%7D%3D81%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%28cos%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%283%29%5Cpi%7D%7B4%7D%20%29%2Bisin%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B8%7D%20%20%2B2%283%29%5Cpi%7D%7B4%7D%20%29%29%3D3%5Bcos%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%29%5D%20%5C%5Cz_%7Bk%3D3%7D%3D3%5Bcos%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%20%29%2Bisin%28%5Cfrac%7B51%5Cpi%7D%7B32%7D%29%5D)
Answer:
$500
Step-by-step explanation:
substitute the values for X & S in the equation from part A:
y=20x + 0.15s
x=($20x25) + (0.15x$0)
= $500
Answer:
60 feet
Step-by-step explanation:
a - 2x
b - x
c - 3x
120/6 = 20
20 x 3 = 60
