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)

Question

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.)