∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 . What is the value of x?
2 answers:
Answer: 11
Step-by-step explanation:
We are given that ∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .
We know that vertical angles are congruent, then their measures must be equal.
i.e. if ∠E and ∠F are vertical angles.
⇒ m∠E=m∠F
[Substitute the measures of ∠E and ∠F]
Subtract 5x from both sides , we get
Add 12 on both sides , we get
Divide both sides by 2 , we get
or x=11
Hence, the value of x= 11
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Answer:
i) $500 at 5% simple interest for two years. Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years.
Interest = 530.88 - 500 = $30.88
Step-by-step explanation:
i) $500 at 5% simple interest for two years.
Initial amount, P = $ 500
Rate of interest, r = 0.05
Time in years, t = 2
Therefore Final amount A = P(1 + rt) = 500(1 + (0.05 2) ) = $550
Therefore Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years
Initial or Principal Amount, P = $500
Rate of interest, r =0.03
number of conversions, m = 12
Time in years, t = 3
Therefore final amount, = $530.88
Therefore Interest = 530.88 - 500 = $30.88