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Zarrin [17]
2 years ago
6

What two numbers can be added to get a sum of 16, and multiplied to get a product of 30?

Mathematics
1 answer:
alexdok [17]2 years ago
3 0

9514 1404 393

Answer:

  8 ± √34 ≈ {2.169, 13.831}

Step-by-step explanation:

Let x represent one of the numbers. Then the other is 16 -x and their product is ...

  x(16 -x) = 30

  x^2 -16x = -30 . . . . . eliminate parentheses, multiply by -1

  x^2 -16x +64 = 34 . . . . add 64 to complete the square

  (x -8)^2 = 34 . . . . . . . . rewrite

  x -8 = ±√34 . . . . . . . .square root

  x = 8 ± √34 . . . . . . add 8

  x ≈ {2.169, 13.831}

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==============================================

Explanation:

The recursive rule

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----------------

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

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f(n) = f(n+1)+3

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Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

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