2 years ago

6 is added a number x.then the result is multiplied by 9. the final answer is greater than 99

Mathematics

1 answer:

drek231 [11]2 years ago

6 0

So this inequality is going to be written as 9(x + 6) > 99

Firstly, you want to foil 9(x + 6), which will look like this: 9x + 54 > 99

Next, subtract 54 on both sides of the equation: 9x > 45

Lastly, divide both sides by 9, and your answer will be x > 5

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If log(x + y) = log 3 + ½log x + ½log y, prove that x² + y² = 7xy

Free_Kalibri [48]

Answer:

See Explanation

Step-by-step explanation:

$log(x + y) = log3 + \frac{1}{2} logx+ \frac{1}{2} logy \\ \\ log(x + y) = log3 + logx ^{\frac{1}{2}} + logy ^{\frac{1}{2}}\\ \\ log(x + y) = log3 + log(xy) ^{\frac{1}{2}} \\ \\ log(x + y) = log[3(xy) ^{\frac{1}{2}}] \\ \\ x + y = 3(xy) ^{\frac{1}{2}} \\ \\ squaring \: both \: sides \\ {(x + y)}^{2} = \bigg(3(xy) ^{\frac{1}{2}} \bigg)^{2} \\ \\ {x}^{2} + {y}^{2} + 2xy = 9xy \\ \\ {x}^{2} + {y}^{2} = 9xy - 2xy \\ \\ \purple{ \bold{{x}^{2} + {y}^{2} = 7xy}} \\ thus \: proved$