Answer:c
Step-by-step explanation:
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:
a. 26 units²
Step-by-step explanation:
The x-axis conveniently divides the figure into a triangle (above the x-axis) and a trapezoid (below the x-axis).
The top triangle has a base of 4 and a height of 3, so its area is ...
triangle area = (1/2)(4 units)(3 units) = 6 units²
The bottom trapezoid has a top base of 4, a bottom base of 6, and a height of 4 units. Its area is ...
trapezoid area = (1/2)(b1 +b2)h = (1/2)(4 units + 6 units)(4 units) = 20 units²
The total area of the figure is ...
area = triangle area + trapezoid area = 6 units² + 20 units² = 26 units²
Answer:
the third one
Step-by-step explanation:
Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x.
<span>Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. </span>
<span>We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. </span>
<span>x + y = 120 </span>
<span>1.35(x) + (1.05)y = 138 </span>
<span>We can rewrite the first as </span>
<span>x = -y + 120 </span>
<span>Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. </span>
<span>1.35(x) + 1.05(y) = 138 </span>
<span>1.35(-y + 120) + 1.05y = 138 </span>
<span>-1.35y + 162 + 1.05y = 138 </span>
<span>-0.3y + 162 = 138 </span>
<span>-0.3y = -24 </span>
<span>y = 80 </span>
<span>And since x + y = 120, that means x = 40. </span>
<span>Check: </span>
<span>40 pounds of x at $1.35 costs 40 * 1.35, or $54. </span>
<span>80 pounds of y at $1.05 costs 80 * 1.05, or $84. </span>
<span>Do those add up to our target total, according to the question, of 120 * 1.15 = $138? </span>
