Question

The sum of two numbers is 23, and the product of the same two numbers is 130. Which formula best represents how to determine the two numbers?(1 point)
Responses

y=m2 +23m+130
y=m2 +23m+130
- no response given

y=m2 +23m−130
y=m2 +23m−130
- incorrect

y=−m2 +23m−130
y=−m2 +23m−130
- no response given

y=−m2 +23m+130
y=−m2 +23m+130
- no response given

Answer 1

To determine the two numbers based on the given conditions, we can set up a system of equations. Let the two numbers be \( x \) and \( y \).

From the problem statement, we have:

1. The sum of the two numbers:
\[
x + y = 23
\]

2. The product of the two numbers:
\[
xy = 130
\]

We can express \( y \) in terms of \( x \) using the first equation:
\[
y = 23 - x
\]

Substituting this expression for \( y \) into the second equation gives us:
\[
x(23 - x) = 130
\]

Expanding this leads to:
\[
23x - x^2 = 130
\]

Rearranging it gives:
\[
x^2 - 23x + 130 = 0
\]

This is a standard quadratic equation in the form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \)
- \( b = -23 \)
- \( c = -130 \)

To find a formula based on the letters used in the options you provided, we can rewrite this in the format:
\[
y = -x^2 + 23x - 130
\]

This is similar to one of your options, specifically:
- \( y = -m^2 + 23m - 130 \) (where \( m \) is used instead of \( x \))

Therefore, the best representation of the two numbers based on the provided options is:
\[
y = -m^2 + 23m - 130
\]

(Please disregard the fact that in your options the variable \( m \) is used instead of \( x \); it’s the same representation.)