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3 years ago

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Twelve more than a number is the product of -3 and 6. Translate using n

1 answer:

sergiy2304 [10]3 years ago

7 0

Answer: n + 12 = -18 or n + 12= -3(6)

Step-by-step explanation:

12 more than a number means 12 is added to the number so the expression will be n + 12 and the product of -3 and 6 is the same as -3 times 6 which is -18 . n + 12 has to equal -18 .

n + 12 = -18 now subtract 12 from both sides

-12 -12

n= -30

So the number is -30

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What is the solution of x=2+ square root x-2?

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So I'm going to assume that this question is asking for <u>non extraneous solutions</u>, or solutions that are found in the equation <em>and</em> are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

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Next, square both sides:

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Next, subtract x and add 2 to both sides of the equation:

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Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

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Next, factor x^2 - 2x and -3x + 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$x(x-2)-3(x-2)=0$

Now you can rewrite the equation as $(x-3)(x-2)=0$

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Now, it may appear that the answer is C, however we need to plug the numbers back into the original equation to see if they are true as such:

$2=2+\sqrt{2-2}\\2=2+\sqrt{0}\\2=2+0\\2=2\ \textsf{true}\\\\3=2+\sqrt{3-2}\\3=2+\sqrt{1}\\3=2+1\\3=3\ \textsf{true}$

Since both solutions hold true when x = 2 and x = 3, <u>your answer is C. x = 2 or x = 3.</u>

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