Line segment and ray are defined terms
Point, line, and plane are undefined terms because they have not thickness or width
classical approach, relative-frequency approach,
subjective approach.
Answer:
yes
Step-by-step explanation:
There are several ways to go at this.
My first choice is to use a graphing calculator. It shows the function has a zero at x=5, so x-5 is a factor.
Another good choice is to use synthetic division (2nd attachment). If the remainder is zero, then x-5 is a factor. It is and it is.
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You can also evaluate the function at x=5. The remainder theorem tells you that if the value is zero, then x-5 is a factor. Evaluating the polynomial written in Horner form is a lot like synthetic division.
(((x -4)x -15)x +58)x -40 for x=5 is ... (-10·5 +58)5 -40 = 40-40 = 0
The value of h(5) is zero, so x-5 is a factor of h(x).
Answer:
x = 6
a = 18 ft
b = 36 ft
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Factoring/Expanding
- Solving quadratics
<u>Trigonometry</u>
- Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
Given: Right triangle
a = 3x
b = 6x
c = 40
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: (3x)² + (6x)² = 40²
- Evaluate: 9x² + 36x² = 1600
- Combine like terms: 45x² = 1600
- Isolate <em>x </em>term: x² = 320/9
- Isolate <em>x</em>: x = (±8√5)/3
- Evaluate: x = ±5.96285
Since it is not a quadrant triangle, we must use the positive value for <em>x</em>.
<u>Step 3: Find legs</u>
Leg a
- Define: 3x
- Substitute: 3(5.96285)
- Multiply: 17.8885
- Round: 18
Leg b
- Define: 6x
- Substitute: 6(5.96285)
- Multiply: 35.7771
- Round: 36