9514 1404 393
Eexplanation:
16. Suppose the roots are α and kα. Then we can write the equation as ...
a(x -α)(x -kα) = 0
ax² -ax(α +kα) +akα² = 0
Comparing to the original equation, we can equate coefficients to get ...
Solving the first for α gives ...
α = -b/(a(1+k)
Substituting into the second, we have ...
c = ak(-b/(a(1+k)))²
Multiplying by a(1+k)², we get ...
(1+k)²ac = kb²
Using k=2 gives ...
9ac = 2b² . . . . . as required
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17. Using the previous result with k=1 (equal roots), we have ...
(1+k)²ac = kb²
4ac = b² . . . . . for k=1
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<em>Additional comment</em>
We observed that the problems were similar, but had different factors relating the roots. So, we elected to solve the general case, then fill in the specific values for the two problems.
Answer : 76
Step by Step Explanation:
Substitute for "r" and solve for "t":
5(4t+8) + 2t = 414
22t + 40 = 414
22t = 374
t = 17 (# of tulips sold)
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r = 4*17+8 = 76 (# of roses sold)
Answer:
pay attention in class next time, love
Answer: Reflection over the x-axis
Supplementary angles sum to 180 degree
Let one angle be x
Then the other angle is x+80
Summing the 2 angle gives
x+x+80=180
2x+80=180
2x=180-80
X=50
Thus the angles are 50 degree and 50+80= 130 degree
