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:
![\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
<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]:
![\displaystyle x=\frac{-2 \pm \sqrt{2^2-4(1)(2)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B2%5E2-4%281%29%282%29%7D%7D%7B2%281%29%7D)
- [√Radical] Evaluate exponents:
![\displaystyle x=\frac{-2 \pm \sqrt{4-4(1)(2)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B4-4%281%29%282%29%7D%7D%7B2%281%29%7D)
- Multiply:
![\displaystyle x=\frac{-2 \pm \sqrt{4-8}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B4-8%7D%7D%7B2%7D)
- [√Radical] Subtract:
![\displaystyle x=\frac{-2 \pm \sqrt{-4}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B-4%7D%7D%7B2%7D)
- [√Radical] Factor:
![\displaystyle x=\frac{-2 \pm \sqrt{-1}\sqrt{4}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B-1%7D%5Csqrt%7B4%7D%7D%7B2%7D)
- [√Radicals] Simplify:
![\displaystyle x=\frac{-2 \pm 2i}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-2%20%5Cpm%202i%7D%7B2%7D)
- Factor:
![\displaystyle x=\frac{2(-1 \pm i)}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%28-1%20%5Cpm%20i%29%7D%7B2%7D)
- Divide:
![\displaystyle x = -1 \pm i](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%20-1%20%5Cpm%20i)
Answer:
Your calculation is correct, but I'd answer 33.0 in.
Step-by-step explanation:
You are correct. Good job.
You are given two points on a line, and told that the function is "direct variation." You can save a lot of time by recognizing that the y-intercept here is zero (0). Thus, the line passes through the origin.
A line through (2,14) and (4,38) is NOT direct variation, because the line connecting those two points does NOT pass through the origin, and thus has a vertical intercept.
Step-by-step explanation:
5×16+4×9=116
(4+6×2)-12=4
Answer:
x = 5
Step-by-step explanation:
By remote exterior angle theorem:
![(6 + 25x) \degree = (18x - 3)\degree + 44\degree \\ 6 + 25x = 18x - 3 + 44 \\ 25x - 18x = 41 - 6 \\ 7x = 35 \\ x = \frac{35}{7} \\ \huge \red{ \boxed{ x = 5}}](https://tex.z-dn.net/?f=%286%20%2B%2025x%29%20%5Cdegree%20%3D%20%2818x%20-%203%29%5Cdegree%20%20%2B%2044%5Cdegree%20%20%5C%5C%206%20%2B%2025x%20%3D%2018x%20-%203%20%2B%2044%20%5C%5C%2025x%20-%2018x%20%3D%2041%20-%206%20%5C%5C%207x%20%3D%2035%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B35%7D%7B7%7D%20%20%5C%5C%20%5Chuge%20%5Cred%7B%20%5Cboxed%7B%20x%20%3D%205%7D%7D)