Question
Which of the following mathematical expressions is equivalent to the verbal expression "A number, x,
squared is 39 more than the product of 10 and x" ?
F. 2x = 39 + 10x
G. 2x = 39х + 10x
H. 1=39 - 10x
J. *7=39 + 1°
K. *7=39 + 10x
squared is 39 more than the product of 10 and x" ?
F. 2x = 39 + 10x
G. 2x = 39х + 10x
H. 1=39 - 10x
J. *7=39 + 1°
K. *7=39 + 10x
Answers
GPT-4o mini
To translate the verbal expression "A number, \( x \), squared is 39 more than the product of 10 and \( x \)" into a mathematical equation, let's break it down:
1. "A number, \( x \), squared" translates to \( x^2 \).
2. "is" translates to \( = \).
3. "39 more than" translates to \( + 39 \).
4. "the product of 10 and \( x \)" translates to \( 10x \).
Putting this together, we have:
\[
x^2 = 10x + 39
\]
Now, we can rearrange this equation to bring all terms to one side:
\[
x^2 - 10x - 39 = 0
\]
Now, let's check which of the answer choices given matches this expression:
F. \( 2x = 39 + 10x \) (Not equivalent)
G. \( 2x = 39x + 10x \) (Not equivalent)
H. \( 1 = 39 - 10x \) (Not equivalent)
J. \( 7 = 39 + 1° \) (Not a valid expression)
K. \( 7 = 39 + 10x \) (Not equivalent)
None of the choices exactly match \( x^2 = 10x + 39 \), and none follow the rearranged form.
If you were looking for an option that could be rearranged to reflect this equation, there may be a typographical error in the answer choices or they may need to include an additional option to present the polynomial format correctly.
If you have specific selections for the answer choices that can be further clarified, feel free to share! Otherwise, \( x^2 = 10x + 39 \) or its rearranged form is the correct mathematical representation.
1. "A number, \( x \), squared" translates to \( x^2 \).
2. "is" translates to \( = \).
3. "39 more than" translates to \( + 39 \).
4. "the product of 10 and \( x \)" translates to \( 10x \).
Putting this together, we have:
\[
x^2 = 10x + 39
\]
Now, we can rearrange this equation to bring all terms to one side:
\[
x^2 - 10x - 39 = 0
\]
Now, let's check which of the answer choices given matches this expression:
F. \( 2x = 39 + 10x \) (Not equivalent)
G. \( 2x = 39x + 10x \) (Not equivalent)
H. \( 1 = 39 - 10x \) (Not equivalent)
J. \( 7 = 39 + 1° \) (Not a valid expression)
K. \( 7 = 39 + 10x \) (Not equivalent)
None of the choices exactly match \( x^2 = 10x + 39 \), and none follow the rearranged form.
If you were looking for an option that could be rearranged to reflect this equation, there may be a typographical error in the answer choices or they may need to include an additional option to present the polynomial format correctly.
If you have specific selections for the answer choices that can be further clarified, feel free to share! Otherwise, \( x^2 = 10x + 39 \) or its rearranged form is the correct mathematical representation.