Gavin drove 85 miles on 10 gallons of gas.How many miles can gavin drive on 25 gallons of gas?
1 answer:
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Answer:
147.5 km and 64.4 km
Step-by-step explanation:
a=120 km
b=70 km
β=28 degrees ( ∘)
b^2=(a^2)+(c^2)−2ac*cosβ
70^2 =(120^2 )+(c^2)−2⋅ 120⋅ c⋅ cos(28∘ )
(c^2 ) −211.907c+9500=0
note p, q, and r are replacement variables in the Pythagorean theorem since a, b, and c are already in use
p=1;q=−211.907;r=9500
D=(q^2 ) −4pr=(211.907^2 )−4⋅1⋅9500=6904.75561996
D>0
=
(−q±
)/2p=(211.91±
)/2
=105.95371114±41.5474295834
(−147.501140726)(
−64.4062815596)=0
=147.501140726
=64.4062815596
Answer:
Empirical probability
Step-by-step explanation:
Empirical probability is data collected from experiment and real-life situation.
The "empirical probability" of an outcome is obtained by dividing the frequency of occurrence of an event by the number of trails of the experiment.
- <u>Therefore, the correct answer is empirical probability.</u>
I hope this helps you! Let me know if my answer is wrong or not.
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
Division
2 = tan B · tan C
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C
