1/7 *2 =2/7 take denominator with 1 over it and multiply by numerator
Answer:
Z = 0.198877274
Step-by-step explanation:
![(\frac{1}{4})^{3z-1} = 16^z + 2*16^{z-2}\\4^{1-3z} = 4^{2z} + 4^{\frac{1}{2}}*4^{2z-4}\\4^{1-3z} = 4^{2z} + 4^{2z-4+\frac{1}{2}}\\4^{1-3z} = 4^{2z} + 4^{2z-\frac{7}{2}}\\4^{1-3z} = 4^{2z} *(1+ 4^{-\frac{7}{2}})\\4^{1-3z} = 4^{2z} *(1+ 2^{-7})\\4^{1-3z} = 4^{2z} *(1+ \frac{1}{128} )\\4^{1-3z} = 4^{2z} *(\frac{129}{128} )\\Taking\;\; Logarithm\;\; with\;\; base\;\; 4\\Log_4(4^{1-3z}) = Log_4(4^{2z}) + Log_4(\frac{129}{128})\\1-3z = 2z + 0.005613627712 \\5z = 0.994386372\\z = 0.198877274](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B3z-1%7D%20%3D%2016%5Ez%20%2B%202%2A16%5E%7Bz-2%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2A4%5E%7B2z-4%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B2z-4%2B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B2z-%5Cfrac%7B7%7D%7B2%7D%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%204%5E%7B-%5Cfrac%7B7%7D%7B2%7D%7D%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%202%5E%7B-7%7D%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%20%5Cfrac%7B1%7D%7B128%7D%20%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%28%5Cfrac%7B129%7D%7B128%7D%20%29%5C%5CTaking%5C%3B%5C%3B%20Logarithm%5C%3B%5C%3B%20with%5C%3B%5C%3B%20base%5C%3B%5C%3B%204%5C%5CLog_4%284%5E%7B1-3z%7D%29%20%3D%20Log_4%284%5E%7B2z%7D%29%20%2B%20Log_4%28%5Cfrac%7B129%7D%7B128%7D%29%5C%5C1-3z%20%3D%202z%20%2B%200.005613627712%20%5C%5C5z%20%3D%200.994386372%5C%5Cz%20%3D%200.198877274)
Hence, the value of Z = 0.198877274
Answer: 4x² + 5x + 3
<u>Step-by-step explanation:</u>
![\dfrac{4x^3+5x^2+3x}{x}\\\\\\=\dfrac{x(4x^2+5x+3)}{x}\qquad \text{factored out the common term from the numerator}\\\\\\=4x^2+5x+3\qquad \text{canceled out x from numerator and denominator}](https://tex.z-dn.net/?f=%5Cdfrac%7B4x%5E3%2B5x%5E2%2B3x%7D%7Bx%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7Bx%284x%5E2%2B5x%2B3%29%7D%7Bx%7D%5Cqquad%20%5Ctext%7Bfactored%20out%20the%20common%20term%20from%20the%20numerator%7D%5C%5C%5C%5C%5C%5C%3D4x%5E2%2B5x%2B3%5Cqquad%20%5Ctext%7Bcanceled%20out%20x%20from%20numerator%20and%20denominator%7D)
Each pack of batteries cost $21 each.
And then you have $63.
The operation to be used: Division.
63 ÷ 21 ==
Answer: 3
= You can buy 3 packs of batteries with your $63.
Answer: $134.40
Step-by-step explanation: Just find 80% of 168. That is because 100 - 20 is 80. The question says 20% OFF.