Answer:
x = -20
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
Step-by-step explanation:
<u>Step 1: Define</u>
2x - 12 = -52
<u>Step 2: Solve for </u><em><u>x</u></em>
- Add 12 on both sides: 2x = -40
- Divide 2 on both sides: x = -20
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 2(-20) - 12 = -52
- Multiply: -40 - 12 = -52
- Subtract: -52 = -52
Here we see that -52 does indeed equal -52.
∴ x = -20 is the solution to the equation.
<h3>One less than the product of four and a number is 11. What is that number ?</h3>
Answer: The number is 3
Step-by-step explanation:
We will call X the number, then 4X - 1 = 11
4X = 11 + 1 =12
X = 12/4 =3
This is the number = 3
Although the number of new wildflowers is decreasing, the total number of flowers is increasing every year (assuming flowers aren't dying or otherwise being removed). Every year, 25% of the number of new flowers from the previous year are added.
The sigma notation would be:
∑ (from n=1 to ∞) 4800 * (1/4)ⁿ , where n is the year.
Remember that this notation should give us the sum of all new flowers from year 1 to infinite, and the values of new flowers for each year should match those given in the table for years 1, 2, and 3
This means the total number of flowers equals:
Year 1: 4800 * 1/4 = 1200 ]
+
Year 2: 4800 * (1/4)² = 300
+
Year 3: 4800 * (1/4)³ = 75
+
Year 4: 4800 * (1/4)⁴ = 18.75 = ~19 (we can't have a part of a flower)
+
Year 5: 4800 * (1/4)⁵ = 4.68 = ~ 5
+
Year 6: 4800 * (1/4)⁶ = 1.17 = ~1
And so on. As you can see, it in the years that follow the number of flowers added approaches zero. Thus, we can approximate the infinite sum of new flowers using just Years 1-6:
1200 + 300 + 75 + 19 + 5 + 1 = 1,600
