Answer:
x = 21
Step-by-step explanation:
<u>Step 1: Make an expression</u>
Since they are supplements, that means that they add up to 180 degrees.
3x + 6 + 5x + 6 = 180
<u>Step 2: Combine like terms</u>
3x + 6 + 5x + 6 = 180
(3x + 5x) + (6 + 6) = 180
8x + 12 = 180
<u>Step 3: Subtract 12 from both sides</u>
8x + 12 - 12 = 180 - 12
8x = 168
<u>Step 4: Divide both sides by 8</u>
8x / 8 = 168 / 8
x = 21
Answer: x = 21
The value of the card was $13 when he originally purchased it.
Answer:
Step-by-step explanation:
x = 0.8 + 0.2y
Equations:
2x+105=-3x+130
<em>subtract</em><em> </em><em>2x</em><em> </em><em>from</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em>
<em>105</em><em>=</em><em> </em><em>-5x</em><em>+</em><em>130</em>
<em>Subtract</em><em> </em><em>130</em><em> </em><em>from</em><em> </em><em>both</em><em> </em><em>sides</em>
<em>-5x</em><em>=</em><em> </em><em>-25</em>
<em>isolate</em><em> </em><em>the</em><em> </em><em>variable</em>
<em>x</em><em>=</em><em>5</em><em> </em>
<u>Plug</u><u> </u><u>back</u><u> </u><u>in</u>
<u>2</u><u>(</u><u>5</u><u>)</u><u>+</u><u>105</u><u>=</u><u> </u><u>-3</u><u>(</u><u>5</u><u>)</u><u>+</u><u>130</u>
<u>115</u><u>=</u><u> </u><u> </u><u>115</u>
Answer:
x = √53
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use PT to solve for the missing length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 6
Leg <em>b</em> = <em>x</em>
Hypotenuse <em>c</em> = √89
<u>Step 3: Solve for </u><em><u>x</u></em>
- Set up equation: 6² + x² = (√89)²
- Isolate <em>x</em> term: x² = (√89)² - 6²
- Exponents: x² = 89 - 36
- Subtract: x² = 53
- Isolate <em>x</em>: x = √53
