Answer:
The answer to the question is B.
Wait, I'm sorry, correction: a = 15, b = 7, c = 5, d = 10, e = 12.
Step-by-step explanation:
1.
Answer D. (75%)
2.
A > 1 so answers B and D. (1.3 and 3.33)
3.
Answer B. (1.04)
4.
This one is strange but answer C (128 players).
5.
Answer D. (13.7%)
Amount = P
P is the amount you invested.
r is the interest rate in decimal form (so 6% = 0.06)
n is the number of times a year you are paid interest (semiannually = 2)
nt is the number of payment times you expected (4 years, twice a year = 8 times)
<span>The line of symmetry of the triangle bisects the right angle and the diagonal of the square.
The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
</span>Let CG be a distance x from the vertex of the right angle in the triangle.
Remaining distance = 5√2 - x.
<span>
(1)(x) = (2)(5√2 - x)</span>
x = 10√2 - 2x
<span>3x = 10√2 </span>
<span>x = (10/3)√2.
</span>
Using Pythagorean theorem,
x^2 + y^2 = c^2
<span>c = (10/3)√2,
and x = y,
so 2x^2 = 200/9
x = √(100/9) = 10/3 = y.
</span>
<span>x = y = 3.333</span>
Answer:
x = -8
m∠BDC = 68°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry</u>
- Definition of a Line: A line is 180°
Step-by-step explanation:
<u>Step 1: Set up Equation</u>
m∠BDC + m∠CDA = 180°
(-7x + 12)° + (-8x + 48)° = 180°
<u>Step 2: Solve for </u><em><u>x</u></em>
- Combine like terms: -15x + 60 = 180
- Isolate <em>x</em> term: -15x = 120
- Isolate <em>x</em>: x = -8
<u>Step 3: Find m∠BDC</u>
- Define: m∠BDC = (-7x + 12)°
- Substitute in <em>x</em>: m∠BDC = (-7(-8) + 12)°
- Multiply: m∠BDC = (56 + 12)°
- Add: m∠BDC = 68°
