Solve the inequality and express your answer in interval notation.
x2 - 12x + 5 <0
Answers
Answer:
([tex]6 - \sqrt{31}[/tex], [tex]6 + \sqrt{31}[/tex])
Step-by-step explanation:
[tex]x^{2}-12x+5 < 0[/tex]
To solve this inequality, we can start by completing the square. To do this, we divide the x coefficient (-12) by 2 and then square it. We then add the result to the left side of the equation. To ensure the inequality remains true, we also subtract it.
[tex]x^{2}-12x+(-6^{2})-(-6^{2}) + 5 < 0\\x^{2}-12x+36-36 + 5 < 0\\[/tex]
We can then express the first trinomial as a perfect square.
[tex](x-6)^{2} - 31 < 0[/tex]
Add 31 to both sides:
[tex](x-6)^{2}< 31[/tex]
Then take the square root of both sides:
[tex]x-6<[/tex] ± [tex]\sqrt{31}[/tex]
Finally, add 6 to both sides:
x < 6 + [tex]\sqrt{31}[/tex]
x > 6 - [tex]\sqrt{31}[/tex]
The solution to the inequality in interval notation is shown by option A
What is inequality?
An inequality in mathematics describes how two expressions relate to one another by indicating whether one expression is greater, smaller, equal to, or not equal to the other. Inequalities are denoted by symbols.
We have to use the quadratic formula that states that;
x < (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
So we have that;
x < [12 ± √([tex](-12)^2[/tex] - 4 * 1 * 5)] / 2 * 1
Thus we would obtain in the end;
6 - √31 < x < 6 + √31
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What is a Decimal number?A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.
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I wrote notes on this question a while ago
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Answers
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Answers
Step-by-step explanation:
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Hope it helps.
Do comment if you have any query
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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--------------
5
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True
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Answers
Answer:
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Answers
If the temperature decreasing in New York leads to the number of people wearing sweaters increasing, this is Negative correlation.
There are several types of correlation:
Positive correlation - An increase in one variable leads to an increase in another variable and vice versa Negative correlation - An increase in one variable leads to a decrease in another variable and vice versa Zero correlation - Variables don't change in relation to one anotherIn this scenario we notice that when temperatures decreased, people wearing sweaters increased. This is therefore negative correlation as the variables moved in opposite directions.
In conclusion, what was observed is negative correlation.
Find out more at https://brainly.com/question/10099551.