True, vertical angles are always congruent.
Add 3 to both sides, so you will have
x^2 - 8x + 13 + 3 = 3
x^2 -8x + 16 = 3
And now the left side is a perfect square trinolmial: (x-4)^2.
Answer:
<u>Yes, the outdoor ice skating rink should be installed.</u>
Step-by-step explanation:
We can reach this conclusion after simulating the profit for each possible scenario made by The US weather service estimates:
<u>For 80-day suitable weather per year:</u>
- total invested capital =<u> </u>$950,000 + $200,000 (total operating and maintaining cost) = $1,150,000
- per day revenue= 500 x $20 = $10,000
- total revenue per season = $10,000 x 80 days = $800,000
- total operating and maintaining cost = $2,500 x 80 = $200,000
- total profit (returns) in a season = $800,000-$200,000<u> = $600,000</u>
- per year rate of return before taxes = 52% (total profit / total invested capital *100; $600,000/$1,1150,000 *100 = 52%
<u>For 100 days suitable weather per year:</u>
- total invested capital =<u> </u>$950,000 + $200,000 (total operating and maintaining cost) = $1,150,000
- per day revenue= 400 x $20 = $8,000
- total revenue per season = $8,000 x 100 days = $800,000
- total operating and maintaining cost = $2,500 x 100 = $250,000
- total profit (returns) in a season = $800,000-$250,000<u> = $550,000</u>
- per year rate of return before taxes = 52% (total profit / total invested capital *100; $550,000/$1,1150,000 *100 = 47%
<u>For 120 days suitable weather per year:</u>
- total invested capital =<u> </u>$950,000 + $200,000 (total operating and maintaining cost) = $1,150,000
- per day revenue= 300 x $20 = $6,000
- total revenue per season = $6,000 x 120 days = $720,000
- total operating and maintaining cost = $2,500 x 120 = $300,000
- total profit (returns) in a season = $800,000-$250,000<u> = $420,000</u>
- per year rate of return before taxes = 52% (total profit / total invested capital *100; $420,000/$1,1150,000 *100 = 58%
Threfore, we notice that the 22% per year rate of return before taxes criteria was met in each of the possible scenarios, making the endeavor worthwhile.
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Answer:
x²=5-x
x²+x-5=0
1x²+1x²-5=0
[ax²+bx²+c=0]
∆=b²-4ac
∆=1²-4(-5)(1)=1+20=21
x=(-b±√∆)/2a
x=(-1±√21)/2
meaning:
x=(-1+√21)/2 or x=(-1-√21)/2
