Answer:
![\displaystyle cos\theta = \frac{2\sqrt{13}}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B2%5Csqrt%7B13%7D%7D%7B13%7D)
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>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse
[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
<em>a</em> = 8
<em>b</em> = 12
<em>c</em>
<u>Step 2: Solve for </u><em><u>c</u></em>
- Substitute in variables [Pythagorean Theorem]: 8² + 12² = c²
- Evaluate exponents: 64 + 144 = c²
- Add: 208 = c²
- [Equality Property] Square root both sides: √208 = c
- Rewrite: c = √208
- Simplify: c = 4√13
<u>Step 3: Define Pt. 2</u>
<em>Identify variables</em>
Angle θ
Adjacent leg = 8
Hypotenuse = 4√13
<u>Step 4: Find</u>
- Substitute in variables [Cosine]:
![\displaystyle cos\theta = \frac{8}{4\sqrt{13}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B8%7D%7B4%5Csqrt%7B13%7D%7D)
- Rationalize:
![\displaystyle cos\theta = \frac{2\sqrt{13}}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%20%3D%20%5Cfrac%7B2%5Csqrt%7B13%7D%7D%7B13%7D)
Answer:
See below in bold.
Step-by-step explanation:
(A) 20 -4x=12 -x+8-3x
-4x + x + 3x = 12 + 8 - 20
0 = 0 This is an Identity.
Infinite solutions.
B). 5x+4x-3=24+8x
9x - 8x = 24 + 3
x = 27. One solution.
C. 5x+6=2x+6+3x-15
5x - 2x - 3x = -15 + 6 - 6
0 = -15
No solution.
Answer:
x=2, x=-2
Step-by-step explanation:
3x²-3+4x²-12=13
7x²=13+12+3
7x²=28
x²=4
x=-2
x=2
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