Answer:
![\displaystyle PQ \approx 5.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20PQ%20%5Capprox%205.2)
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
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cosθ = adjacent over hypotenuse
Step-by-step explanation:
<u>Step 1: Identify</u>
Angle θ = 55°
Adjacent Leg = PQ
Hypotenuse = 9
<u>Step 2: Solve</u>
- Substitute in variables [cosine]:
![\displaystyle cos55^\circ = \frac{PQ}{9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos55%5E%5Ccirc%20%3D%20%5Cfrac%7BPQ%7D%7B9%7D)
- [Multiplication Property of Equality] Isolate PQ:
![\displaystyle 9cos55^\circ = PQ](https://tex.z-dn.net/?f=%5Cdisplaystyle%209cos55%5E%5Ccirc%20%3D%20PQ)
- Evaluate:
![\displaystyle 5.16219 = PQ](https://tex.z-dn.net/?f=%5Cdisplaystyle%205.16219%20%3D%20PQ)
- Rewrite:
![\displaystyle PQ = 5.16219](https://tex.z-dn.net/?f=%5Cdisplaystyle%20PQ%20%3D%205.16219)
- Round:
![\displaystyle PQ \approx 5.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20PQ%20%5Capprox%205.2)
Answer:
The Final Investment Value is
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Answer:5
Step-by-step explanation:
Simplifying
8x + -20 = 3x + 5
Reorder the terms:
-20 + 8x = 3x + 5
Reorder the terms:
-20 + 8x = 5 + 3x
Solving
-20 + 8x = 5 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-20 + 8x + -3x = 5 + 3x + -3x
Combine like terms: 8x + -3x = 5x
-20 + 5x = 5 + 3x + -3x
Combine like terms: 3x + -3x = 0
-20 + 5x = 5 + 0
-20 + 5x = 5
Add '20' to each side of the equation.
-20 + 20 + 5x = 5 + 20
Combine like terms: -20 + 20 = 0
0 + 5x = 5 + 20
5x = 5 + 20
Combine like terms: 5 + 20 = 25
5x = 25
Divide each side by '5'.
x = 5
Simplifying
x = 5