Answer:
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>Pre-Calculus</u>
Law of Sines:
- A, B, C are angle measures
- a, b, c are leg lengths
Step-by-step explanation:
<u>Step 1: Identify</u>
A = 27°, a = 11
B = x°, b = 15
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [LOS]:
- Cross-multiply:
- Isolate <em>x</em> term:
- Isolate <em>x</em>:
- Evaluate:
- Round:
Answer: a,c,f (4^3, 8^2, 2^6)
Step-by-step explanation:
Focus on the triangle PQN and triangle SQP, prove that they are similar:
PQ=PR, PN is the altitude, so QN=NR=9
PQ of ΔSQP:QN=15:9=5:3
PS:PN=20:12=5:3
∠PQN=∠SQP (they are the same angle, reflexive property)
therefore, according to the SAS similarity theorem, ΔPQN is similar to ΔSQP
∠PNQ=∠SPQ =90 degree
therefore, QPS is a right angle.
you may have to reword it depending on what your teacher requires, column proof or paragraph proof.
For this case we have the following functions:
By definition of composition of functions, we have to:
So:
Thus, we have to:
Answer: