C.
because a, b, and d aren't porportional
but c x is divided by 2
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
1. (-4 , 3) : substitute way .
2. (10 , -1) : elimination way.
3. (26/7 , -26/7 ) : elimination way.
4. ( 1 , 1) : elimination way.
Answer:
Step-by-step explanation:
The length is 46.10 cm.
Since ∠BCA = 50.5°, ∠ACD = 180-50.5 =129.5°. This means that ∠CAD = 180-(129.5+35.8) = 14.7°. We can now use the law of sines;
sin 14.7/20 = sin 35.8/x
Cross multiply:
x*sin 14.7 = 20*sin 35.8
Divide both sides by sin 14.7:
x = (20*sin 35.8)/(sin 14.7) = 46.10
