Answer:
x = 6
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
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients/Degrees
- Expand by FOIL (First Outside Inside Last)
- Factoring
- Multiple Roots
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse
Step-by-step explanation:
<u>Step 1: Identify</u>
<em>a</em> = x + 3
<em>b</em> = x
<em>c</em> = √117
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [PT]: (x + 3)² + x² = (√117)²
- Expand [FOIL]: x² + 6x + 9 + x² = (√117)²
- Combine like terms: 2x² + 6x + 9 = (√117)²
- Exponents: 2x² + 6x + 9 = 117
- [SPE] Subtract 117 on both sides: 2x² + 6x - 108 = 0
- Factor out GCF: 2(x² + 3x - 54) = 0
- [DPE] Divide 2 on both sides: x² + 3x - 54 = 0
- Factor Quadratic: (x - 6)(x + 9) = 0
- Solve roots/solve <em>x</em>: x = -9, 6
Since we are dealing with positive values, we can disregard the negative root.
∴ x = 6
Answer:
B
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4.2%/100 = 0.042 per year,
then, solving our equation
I = 16500 × 0.042 × 5 = 3465
I = $ 3,465.00
The simple interest accumulated
on a principal of $ 16,500.00
at a rate of 4.2% per year
for 5 years is $ 3,465.00.
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Answer:
15 units
Step-by-step explanation:
ΔABC is right with ∠C = 90° and AB the hypotenuse
using Pythagoras' identity on the triangle
AB² = AC² + BC² , hence
BC² = AB² - AC² = 17² - 8² = 289 - 64 = 225
⇒BC = 
= 15 units
