The correct representation of 6 + 2n > 12 (n > 3) is (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation::
6 + 2n > 12
Subtracting 6 from both sides:
6 + 2n - 6 > 12 - 6
2n > 6
Dividing by 2:
n > 3
The correct representation of 6 + 2n > 12 (n > 3) is (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.
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Answer:
3 < c < 13
Step-by-step explanation:
A triangle is known to have 3 sides: Side a, Side b and Side c.
For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).
To solve the above question, we would be using the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.
Side a + Side b > Side c
Side a + Side c > Side b
Side b + Side c > Side a
For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,
side (a) = 5
side (b) = 8
Let's represent the third side as c
To solve for the above question,we would be having the following Inequality.
= b - a < c < b + a
= 8 - 5 < c < 8 + 5
= 3 < c < 13
Answer:
B. x = -1 ± i
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Factoring
- Quadratic Formula:
<u>Algebra II</u>
- Imaginary Numbers: √-1 = i
Step-by-step explanation:
<u>Step 1: Define</u>
x² + 2x = -2
<u>Step 2: Identify Variables</u>
- Rewrite Quadratic in Standard Form [Addition Property of Equality]: x² + 2x + 2 = 0
- Break up Quadratic: a = 1, b = 2, c = 2
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute in variables [Quadratic Formula]:
- [√Radical] Evaluate exponents:
- Multiply:
- [√Radical] Subtract:
- [√Radical] Factor:
- [√Radicals] Simplify:
- Factor:
- Divide:
Answer:
Option : A
Step-by-step explanation:
Hope it helps you!