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Helga [31]
3 years ago
15

Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each

of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80. How many more cookies will Jessica have Martha? If x represents the number of cookies Jessica started with, complete the statements below.
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
8 0

Answer:

x^2 - 30 + 224 ≥ 0  

the amount of cookies Jessica has more than Martha is at least two

Step-by-step explanation:

J + M = 30

x - 12 < 80

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If y= 3x + 6, what is the minimum value of (x^3)(y)?
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Answer:

Given the statement: if y =3x+6.

Find the minimum value of (x^3)(y)

Let f(x) = (x^3)(y)

Substitute the value of y ;

f(x)=(x^3)(3x+6)

Distribute the terms;

f(x)= 3x^4 + 6x^3

The derivative value of f(x) with respect to x.

\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)

Using \frac{d}{dx}(x^n) = nx^{n-1}

we have;

\frac{df}{dx} =(12x^3+18x^2)

Set \frac{df}{dx} = 0

then;

(12x^3+18x^2) =0

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By zero product property;

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⇒ x=0 and x = -\frac{3}{2} = -1.5

then;

at x = 0

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x = -1.5

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Hence the minimum value of (x^3)(y) is, -5.0625






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