In Triangle DEF, if angle D is congruent to angle E, DE= x + 4, EF= 4x - 8, and DF= 7X - 35 find X and the measure of each side
1 answer:
If angle D is congruent to angle E, then the triangle DFE is an isosceles triangle (look at the picture).
Therefore DF ≅ EF.
DE = x + 4, EF = 4x - 8, DF = 7x - 35
The equation:
7x - 35 = 4x - 8 <em>add 35 to both sides</em>
7x = 4x + 27 <em>subtract 4x from both sides</em>
3x = 27 <em>divide both sides by 3</em>
x = 9
DE = x + 4 → DE = 9 + 4 = 13
EF = 4x - 8 → EF = 4(9) - 8 = 36 - 8 = 28
DF = 7x - 35 → DF = 7(9) - 35 = 63 - 35 = 28
<h3>Answer:</h3><h3>x = 9, DE = 13, EF = 28, DF = 28.</h3>
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<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>Step-by-step explanation:
Given the function j(x) = 11.6 and k(x) =
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j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
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k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
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From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) =
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