Solve for x:
x^9 = n x
Subtract n x from both sides:
x^9 - n x = 0
Factor x and constant terms from the left hand side:
-x (n - x^8) = 0
Multiply both sides by -1:
x (n - x^8) = 0
Split into two equations:
x = 0 or n - x^8 = 0
Subtract n from both sides:
x = 0 or -x^8 = -n
Multiply both sides by -1:
x = 0 or x^8 = n
Taking 8^th roots gives n^(1/8) times the 8^th roots of unity:
Answer: x = 0 or x = -n^(1/8) or x = -i n^(1/8) or x = i n^(1/8) or x = n^(1/8) or x = -(-1)^(1/4) n^(1/8) or x = (-1)^(1/4) n^(1/8) or x = -(-1)^(3/4) n^(1/8) or x = (-1)^(3/4) n^(1/8)
Answer:
y=7(x-5)+3
Step-by-step explanation:
Answer:
56 eggs
Step-by-step explanation:
If
of all eggs are green,
of all are blue, then
![1-\dfrac{2}{7}-\dfrac{1}{4}=\dfrac{28-2\cdot 4-7}{28}=\dfrac{13}{28}](https://tex.z-dn.net/?f=1-%5Cdfrac%7B2%7D%7B7%7D-%5Cdfrac%7B1%7D%7B4%7D%3D%5Cdfrac%7B28-2%5Ccdot%204-7%7D%7B28%7D%3D%5Cdfrac%7B13%7D%7B28%7D)
of all eggs are red.
We know that there are 26 red eggs
![26\text{ eggs }-\dfrac{13}{28}\\ \\x\text{ eggs }- 1[=\dfrac{28}{28}]](https://tex.z-dn.net/?f=26%5Ctext%7B%20eggs%20%7D-%5Cdfrac%7B13%7D%7B28%7D%5C%5C%20%5C%5Cx%5Ctext%7B%20eggs%20%7D-%201%5B%3D%5Cdfrac%7B28%7D%7B28%7D%5D)
Make a proportion
![\dfrac{26}{x}=\dfrac{\frac{13}{28}}{1}\\ \\26\cdot 1=x\cdot \dfrac{13}{28}\ [\text{Cross multiply}]\\ \\13x=26\cdot 28\ [\text{Multiply by 28 to get rid of fraction}]\\ \\x=\dfrac{26\cdot 28}{13}\ [\text{Divide by 13 to get x}]\\ \\x=2\cdot 28\\ \\x=56](https://tex.z-dn.net/?f=%5Cdfrac%7B26%7D%7Bx%7D%3D%5Cdfrac%7B%5Cfrac%7B13%7D%7B28%7D%7D%7B1%7D%5C%5C%20%5C%5C26%5Ccdot%201%3Dx%5Ccdot%20%5Cdfrac%7B13%7D%7B28%7D%5C%20%5B%5Ctext%7BCross%20multiply%7D%5D%5C%5C%20%5C%5C13x%3D26%5Ccdot%2028%5C%20%5B%5Ctext%7BMultiply%20by%2028%20to%20get%20rid%20of%20fraction%7D%5D%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B26%5Ccdot%2028%7D%7B13%7D%5C%20%5B%5Ctext%7BDivide%20by%2013%20to%20get%20x%7D%5D%5C%5C%20%5C%5Cx%3D2%5Ccdot%2028%5C%5C%20%5C%5Cx%3D56)
Answer:
iii) a=3b/2
Step-by-step explanation:
7a-2b= 5a+b
7a-5a=2b+b
2a=3b
a=3b/2