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
__
17. Using the previous result with k=1 (equal roots), we have ...
(1+k)²ac = kb²
4ac = b² . . . . . for k=1
______
<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:
39 cents per donut
Step-by-step explanation:
2.36 / 6 = 0.39333333333
Round cents to the nearest hundredth
Hope this helps
-IronWolfX
Answer:
13 is the distance
Step-by-step explanation:
The answer to this is 3.083
Answer:
33 students
Step-by-step explanation:
Since there aren’t going to be fractions of people, you can just count up using the whole numbers in the ratio (4 on the left, 7 on the right) and then check if the sum is between 24 and 40.
4:7 = 11 students (not enough)
8:14 = 22 students (not enough)
12:21 = 33 students (fits criteria)
12 boys, 21 girls, for a total of 33 students.
