Let's break down the questions one by one:
**Question 1 A)** Identify the correct list of coefficients for the quadratic expression: \(7x^2 - 4x + 12\).
- The coefficients in the expression \(7x^2 - 4x + 12\) are:
- Coefficient of \(x^2\): 7
- Coefficient of \(x\): -4
- Constant term: 12
So, the correct response is: **7, −4, 12**.
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**Question 2 A)** Identify the constant in the cubic expression: \(6x^3 + 3x^2 - 2x + 7\).
- The constant in this expression is the term without \(x\), which is 7.
So, the correct response is: **7**.
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**Question 3 A)** Identify the following as an expression or an equation.
- \(2x - 5 = 4\) is an equation (because it has an equals sign).
- \(−3x^3 = 8\) is also an equation (with an equals sign).
- \(21 \cdot -3x\) is an expression (no equals sign).
- \(5x^2 - 8x + 2\) is an expression (no equals sign).
So the answers are:
- \(2x - 5 = 4\): **Equation**
- \(−3x^3 = 8\): **Equation**
- \(21 \cdot -3x\): **Expression**
- \(5x^2 - 8x + 2\): **Expression**
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**Question 4 A)** Joseph is selling cellphone data plans. He plans to charge $55 per month for unlimited data, as well as a one-time startup fee of $21. Fill in the expression with the correct numbers to represent the given scenario.
Let's let \(m\) represent the number of months. The total cost can be expressed as:
- The total cost for \(m\) months: \(55m + 21\)
To find the total cost for 6 months:
- Total cost for 6 months = \(55(6) + 21 = 330 + 21 = 351\)
So:
- Fill in the expression: **55m + 21**
- The total cost for 6 months is: **351**
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**Question 5 A)** Select the quadratic equation that is equivalent to: the product of negative six and a number squared, plus the product of five and the same number is thirty-one.
- The expression can be formed as:
\[-6x^2 + 5x = 31\]
The equation indicates that the product of negative six and \(x^2\) plus the product of five and \(x\) equals thirty-one.
So the correct response is: **−6x^2 + 5x = 31**.