Answer:
17 ± sqrt(337)
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2
Step-by-step explanation:
Let a = shorter leg
b= longer leg = a+7
c = hypotenuse = 2a-5
We can use the Pythagorean theorem
a^2+b^2 = c^2
a^2 + (a+7)^2 = (2a-5)^2
(a+7)^2 = a^2 +7a +7a+49 = a^2 +14a +49
(2a-5)^2 = 2a*2a -10a -10a +25 = 4a^2 -20a +25
Substituting these into the equation
a^2 + (a^2 +14a +49) = (4a^2 -20a +25)
Combine like terms
2a^2 +14a +49 = 4a^2 -20a +25
Subtracting 2a^2 from each side
2a^2 -2a^2 +14a +49 = 4a^2-2a^2 -20a +25
+14a +49 = 2a^2 -20a +25
Subtract 14a from each side
-14a+14a +49 = 2a^2 -20a -14a+25
+49 = 2a^2 -34a +25
Subtract 49 from each side
49-49 = 2a^2 -34a +25-49
0 = 2a^2 -34a -24
Divide each side by 2
0/2 = 2/2a^2 -34/2a -24/2
0 = a^2 -17a -12
Using the quadratic formula
a=1 b= -17 c = -12
17 ±sqrt( (-17)^2 - 4(1)(-12))
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2(1)
17 ± sqrt(337)
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2
Answer:
Step-by-step explanation:
sin^-1 (21/67) = 18.27 degrees
√(67)^2 - (21)^2 = 63.62
Answer:
12 coins
Step-by-step explanation:
Points scored by collecting 7 coins = 581
Number of coins required to collect 996 points
Let Number of coins = c
7 coins = 581 points
c coins = 996 points
Cross multiply :
581 * c = 996 * 7
581c = 6972
Divide both sides by 581
581c / 581 = 6972 / 581
c = 12
Hence, number of coins required to collect 996 points is 12
Answer:
Tina is first
Tony is first
Theo is first
Step-by-step explanation:
Events with greater probability are more likely.
Let's put the probabilities in decimal form.
P(Tina is first) = 0.05
P(Theo is first) = %85 = 0.85
P(Tony is first) = 1/10 = 0.1
0.05 < 0.1 < 0.85
The events are listed below from least to most likely.
Tina is first, Tony is first, Theo is first
hope it helps
870 since 71 is closest to 70
