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3 years ago

Analyze the diagram below and complete the instructions that follow.

Mathematics

1 answer:

valentinak56 [21]3 years ago

4 0

Answer:

x = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Terms/Coefficients/Degrees
Expand by FOIL (First Outside Inside Last)
Factoring
Multiple Roots

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Identify

a = x + 3

b = x

c = √117

Step 2: Solve for x

Substitute [PT]: (x + 3)² + x² = (√117)²
Expand [FOIL]: x² + 6x + 9 + x² = (√117)²
Combine like terms: 2x² + 6x + 9 = (√117)²
Exponents: 2x² + 6x + 9 = 117
[SPE] Subtract 117 on both sides: 2x² + 6x - 108 = 0
Factor out GCF: 2(x² + 3x - 54) = 0
[DPE] Divide 2 on both sides: x² + 3x - 54 = 0
Factor Quadratic: (x - 6)(x + 9) = 0
Solve roots/solve x: x = -9, 6

Since we are dealing with positive values, we can disregard the negative root.

∴ x = 6

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Tell whether the ordered pair is a solution to the system of linear equations. 1 point

viktelen [127]

Answer:

(5,-6) is a solution

Step-by-step explanation:

Given

$6x + 3y = 12$

$4x + y = 14$

Required

Tell whether (5,-6) is a solution

In (5,-6): x = 5 and y = -6.

Substitute these values in the given equations

$6x + 3y = 12$ becomes

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$12 = 12$

$4x + y = 14$ becomes

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$20 - 6 = 14$

$14 = 14$

Because both solutions are true, then (5,-6) is a solution

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