The positive numbers x and a-x have a sum of a. What is x in terms of a if the product x*(a-x) is a maximum? Choose 1 answer: (A) (a)/(2) (B) sqrt((a)/(2)) (C) sqrta (D) a (E) There is no x that would produce a maximum product

Equation Simplification: We know that x + (a - x) = a. This simplifies to a = a, which is always true, so we don't get information about x from this equation.Maximizing Product: To maximize the product x*(a-x), we can use the idea that for a fixed sum, the product of two numbers is maximized when the numbers are equal. So, we set x = a - x.Solving for x: Solving x = a - x gives us 2x = a, so x = a/2.Final Answer: Therefore, the value of x that maximizes the product x*(a-x) is a/2, which corresponds to answer choice (A).

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The positive numbers
x and
a-x have a sum of
a. What is
x in terms of
a if the product
x*(a-x) is a maximum?
Choose 1 answer:
(A)
(a)/(2)
(B)
sqrt((a)/(2))
(C)
sqrta
(D)
a
(E) There is no
x that would produce a maximum product

The positive numbers $x$ and $a-x$ have a sum of $a$ . What is $x$ in terms of $a$ if the product $x \cdot(a-x)$ is a maximum? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{a}{2}$ $\newline$ (B) $\sqrt{\frac{a}{2}}$ $\newline$ (C) $\sqrt{a}$ $\newline$ (D) $a$ $\newline$ (E) There is no $x$ that would produce a maximum product

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The positive numbers

x

and

a-x

have a sum of

a

. What is

x

in terms of

a

if the product

x \cdot(a-x)

is a maximum?

\newline

Choose

1

answer:

\newline

(A)

\frac{a}{2}

\newline

(B)

\sqrt{\frac{a}{2}}

\newline

(C)

\sqrt{a}

\newline

(D)

a

\newline

(E) There is no

x

that would produce a maximum product

Equation Simplification: We know that $x + (a - x) = a$ . This simplifies to $a = a$ , which is always true, so we don't get information about $x$ from this equation.
Maximizing Product: To maximize the product $x(a-x)$ , we can use the idea that for a fixed sum, the product of two numbers is maximized when the numbers are equal. So, we set $x = a - x$ .
Solving for $x$ : Solving $x = a - x$ gives us $2x = a$ , so $x = \frac{a}{2}$ .
Final Answer: Therefore, the value of $x$ that maximizes the product $x*(a-x)$ is $\frac{a}{2}$ , which corresponds to answer choice (A).