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:
12
Step-by-step explanation:
15/10=1.5
8 times 1.5=12
$18.00 if you move the decimal one place to the left 10% tip would be $1.80,
multiply $1.80 x 2 = $3.60 which is 20% for the tip.
$18.00 + $3.60 = $21.60 divide by 4 people = $5.40 per person
When ur looking at the graph of ur inequality, u will see a shaded region.....all the points in the shaded region are ur possible solutions. So when u plot ur ordered pair, if it falls in the shaded region, it is a solution...if it does not fall in the shaded area, it is not a solution.
Answer:
{ x | -3 <= x < +1 }
Step-by-step explanation:
We note that the graph occupies from x=-3 to x=+1, while -3 is a value included (endpoint is solid), and +1 is excluded (endpoint hollow).
Thus the domain is { x | -3 <= x < +1 }
