Mathematics, 19.12.2020 07:10 lizzieee04

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

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Answers

Answer from: Emiann222

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

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: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

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]: $x=\frac{20\pm\sqrt{(-20)^2-4(1)(-289)} }{2(1)}$ Exponents: $x=\frac{20\pm\sqrt{400-4(1)(-289)} }{2(1)}$ Multiply: $x=\frac{20\pm\sqrt{400+1156} }{2}$ Add: $x=\frac{20\pm\sqrt{1556} }{2}$ Simplify: $x=\frac{20\pm 2\sqrt{389} }{2}$ Factor GCF: $x=\frac{2(10\pm \sqrt{389} )}{2}$ Divide: $x=10\pm \sqrt{389}$

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

Answer from: Quest

What class is this? i have no idea and i'm not going to give you the wrong answer. do you have a graph that goes with all the questions
Ineed on number 41-45 i have to leave for class at 11

Ineed on number 41-45 i have to leave for class at 11

Answer from: Quest

seems like d

step-by-step explanation:

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