the product of two numbers and the difference them are 289 and 20 respectively. find the numbers

Answers

Answer 1

Answer:

x = 10 + √389, y = -10 + √389 // x = 29.7231, y = 9.72308

or

x = 10 - √389, y = -10 - √389 // x = -9.72308, y = -29.7231

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/eliminationStandard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define Systems

xy = 289

x - y = 20

Step 2: Rewrite Systems

x - y = 20

Subtract x on both sides:                   -y = 20 - xDivide -1 on both sides:                      y = x - 20

Step 3: Redefine Systems

xy = 289

y = x - 20

Step 4: Solve for x

Substitution

Substitute in y:                    x(x - 20) = 289Distribute x:                         x² - 20x = 289Rewrite [SF]:                        x² - 20x - 289 = 0Define variables:                 a = 1, b = -20, c = -289Substitute [QF]:                   [tex]x=\frac{20\pm\sqrt{(-20)^2-4(1)(-289)} }{2(1)}[/tex]Exponents:                          [tex]x=\frac{20\pm\sqrt{400-4(1)(-289)} }{2(1)}[/tex]Multiply:                               [tex]x=\frac{20\pm\sqrt{400+1156} }{2}[/tex]Add:                                     [tex]x=\frac{20\pm\sqrt{1556} }{2}[/tex]Simplify:                               [tex]x=\frac{20\pm 2\sqrt{389} }{2}[/tex]Factor GCF:                         [tex]x=\frac{2(10\pm \sqrt{389} )}{2}[/tex]Divide:                                 [tex]x=10\pm \sqrt{389}[/tex]

Step 5: Solve for y

Possibility 1: x = 10 + √389

Define equation:                    x - y = 20Substitute in x:                       (10 + √389) - y = 20Isolate y term:                        -y = 20 - (10 + √389)Isolate y:                                 y = (10 + √389) - 20Combine like terms:              y = -10 + √389Evaluate:                                y = 9.72308

Possibility 2: x = 10 - √389

Define equation:                    x - y = 20Substitute in x:                       (10 - √389) - y = 20Isolate y term:                        -y = 20 - (10 - √389)Isolate y:                                 y = (10 - √389) - 20Combine like terms:              y = -10 - √389Evaluate:                                y = -29.7231

Step 6: Identify Solutions

Possibility 1:

x = 10 + √389, y = -10 + √389

x = 29.7231, y = 9.72308

Possibility 2:

x = 10 - √389, y = -10 - √389

x = -9.72308, y = -29.7231


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Step-by-step explanation:

In point 1:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

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Step-by-step explanation:

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PLEASE HELP ME WITH THIS SOMEONE




Answers

Answer:

try d

Step-by-step explanation:

because if you look at what point a is it you get 9 and if you look at where point b is at you get 9,3 but pint b says 2 so im thinking it was publish error on that one so the answer will be 9,3 have a good day and stay safe

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Answer:

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Answer:

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Answers

Answer:

Line D

Step-by-step explanation:

Line D is the only one that starts at -3

The Equation of Line D in the graph represents the equation y = x - 3.  Option D is correct.

What is the intercept in the equation?

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
We have given the equation y = x - 3, and have to determine which line in the graph is represented by the given equation,
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Answers

Answer:

18 pieces

Step-by-step explanation:

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