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Snowcat [4.5K]
3 years ago
15

The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the

first.
Mathematics
1 answer:
Agata [3.3K]3 years ago
6 0

Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

  • a +b +c = 26
  • 2a -b = c -2
  • -3a +b = c

Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

... -a = 2c -2 . . . . simplify

... -6 = 2c . . . . . . add 2, substitute for a

... -3 = c . . . . . . . . divide by 2

Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

... b = 21 . . . . . . . . .add 24

The numbers are 8, 21, -3.

_____

The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

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3 years ago
What are the zeros of f(x) = x2 - 8x+16?
Stels [109]

Answer:

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Step-by-step explanation:

f(x) = x^2 - 8x+16

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3 years ago
Simplify the expression below. Then classify the resulting expression
evablogger [386]

Answer:

Simplified = 5

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Step-by-step explanation:

<h2>PART I: Simplify the expression</h2>

<u>Given expression:</u>

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<u>Expand parenthesis by distributive property:</u>

= 3x² + 6x + 5 - 3x (2) - 3x (x)

= 3x² +6x + 5 - 6x - 3x²

<u>Put like terms together:</u>

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<h2>PART II: Classify polynomial</h2>

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Polynomial is classified by the number of terms a polynomial has.

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  • Binomial: a polynomial with two terms
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<u>Classify the given expression:</u>

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Hope this helps!! :)

Please let me know if you have any questions

3 0
2 years ago
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Answer:

Step-by-step explanation:

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