Answer:
θ = 49.4584°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cosθ = adjacent over hypotenuse
- Inverse Trig
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
Angle θ = ?
Adjacent Leg = 13
Hypotenuse = 20
<u>Step 2: Find Angle</u>
- Substitute in variables [cosine]: cosθ = 13/20
- Inverse Trig: θ = cos⁻¹(13/20)
- Evaluate: θ = 49.4584°
The probability is 3/14. There are 2 multiples of 4 in 14, which is 8 and 12. There is only 1 multiple of 6 in 14 which is 12. 1+2=3. It is possible outcomes over total outcomes so 3/14.
<h3>Answer:</h3>
none of these has "no solution"
<h3>Explanation:</h3>
A. The solution is (8/3, 3)
B. The second equation is -1/2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.
C. The solution is (-4, -2)
D. The solution is (4, -2)
E. The second equation is 2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.
_____
A system of equations will have "no solution" when it describes parallel lines—lines that do not intersect. In standard form, such equations are recognizable by their different constants. For example,
- 3x -4y = -4
- 3x -4y = 20 . . . . . . 20 is different from -4
have different constants, so the equations describe parallel lines.
We could multiply one of these by -2 and the system would still be "inconsistent"—having no solution.
Answer: 
Step-by-step explanation:
Move all terms to one side
Simplify 
Split the second term
Factor out common terms in the first two terms, then in the last two terms.
Factor out the common term 
