Answer:
76
2 real solutions
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Standard Form: ax² + bx + c = 0
Discriminant: b² - 4ac
- Positive - 2 solutions
- Equal to 0 - 1 solution
- Negative - No solutions/Imaginary
Step-by-step explanation:
<u>Step 1: Define</u>
x² - 6x - 10 = 0
<u>Step 2: Identify Variables</u>
<em>Compare quadratic.</em>
x² - 6x - 10 = 0 ↔ ax² + bx + c = 0
a = 1, b = -6, c = -10
<u>Step 3: Find Discriminant</u>
- Substitute in variables [Discriminant]: (-6)² - 4(1)(-10)
- [Discriminant] Evaluate exponents: 36 - 4(1)(-10)
- [Discriminant] Multiply: 36 + 40
- [Discriminant] Add: 76
This tells us that our quadratic has 2 real solutions.
Multiply by 60/5280 which is how many seconds per minute over the amount of feet per mile
Answer:
W ≈ 5.2 cm
Step-by-step explanation:
Represent the length and width by L and W respectively.
Then L * W = 81 cm^2, and L = 3W.
Substituting 3W for L in the first equation, we get:
3W * W - 81 = 0, or 3W^2 - 81 = 0.
To make it easier to find the final answer, rewrite 3W^2 - 81 = 0 as
81
W^2 = ------- = 27
3
Then W (the width) is the positive square root of 27, or W ≈ 5.2 cm