Answer:
39 degrees
Step-by-step explanation:
The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP. Take 180-141 to get 39 degrees for <PMN
<span>Every term in a sequence is denoted by a1 being the first one, a2 the second one, a3 the third one and so on. So in your case, a3 means, which one is the third term? So 100 would be your answer. </span>
Answer:
180
Step-by-step explanation:
Answer:
Step-by-step explanation:
The given triangle is:
C) acute
E) right
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