TNCA is having a play. The student tickets will cost less than the adult tickets. The total earnings from the play can be modeled by the following expression: 5.00𝑥+7.50𝑦.

Question

Which statement correctly interprets a part of that expression.
Statement 1: The school will make about $121.50 after all tickets are bought.
Statement 2: Student tickets are $5.00 each.
Statement 3: Student tickets are $7.50 each.
Statement # correctly interprets a part of the expression.

Answer 1

To analyze the expression \( 5.00x + 7.50y \), where \( x \) represents the number of student tickets sold and \( y \) represents the number of adult tickets sold, we can interpret the components of the expression:

• The \( 5.00x \) term represents the total earnings from student tickets, where each student ticket costs $5.00.
• The \( 7.50y \) term represents the total earnings from adult tickets, where each adult ticket costs $7.50.

Now, let's look at the statements:

• Statement 1: "The school will make about $121.50 after all tickets are bought."
  This statement is not an accurate interpretation of any part of the expression. The expression represents the total earnings based on the number of tickets sold, but it doesn't reflect a specific total amount.

• Statement 2: "Student tickets are $5.00 each."
  This statement is a correct interpretation of the coefficient \( 5.00 \) in the expression \( 5.00x + 7.50y \). It correctly identifies the price of a student ticket.

• Statement 3: "Student tickets are $7.50 each."
  This statement is incorrect. It confuses the price of student tickets with adult tickets.

Given the above evaluations, Statement 2 correctly interprets a part of the expression.

Thus, the answer is Statement 2: Student tickets are $5.00 each.

Answer 2

Use the Commutative Property of Multiplication to rewrite the algebraic expression: x^10⋅y^20

Answer 3

The Commutative Property of Multiplication states that the order of multiplication does not affect the product. That is, for any numbers \( a \) and \( b \),

\[ a \cdot b = b \cdot a. \]

Using this property, you can rewrite the algebraic expression \( x^{10} \cdot y^{20} \) in a different order.

So, applying the Commutative Property, you can rewrite the expression as:

\[ y^{20} \cdot x^{10}. \]

Both \( x^{10} \cdot y^{20} \) and \( y^{20} \cdot x^{10} \) are equivalent due to the commutative property.

Answer 4

Write an equivalent expression to 𝑥+(𝑦+𝑧), using the Associative Property of Addition.

Answer 5

The Associative Property of Addition states that the way in which numbers are grouped in an addition problem does not change their sum. In mathematical terms, for any numbers \( a \), \( b \), and \( c \):

\[ a + (b + c) = (a + b) + c. \]

Given the expression \( x + (y + z) \), you can apply the Associative Property to rewrite it by changing the grouping of the terms.

Using the property, you can rewrite the expression as:

\[ (x + y) + z. \]

So, an equivalent expression to \( x + (y + z) \) using the Associative Property of Addition is:

\[ (x + y) + z. \]

Answer 6

Multiply the polynomials (5x−2)(6x+3)

Answer 7

To multiply the polynomials \( (5x - 2)(6x + 3) \), we can use the distributive property (also known as the FOIL method for binomials, which stands for First, Outside, Inside, Last).

1. First: Multiply the first terms: \[ 5x \cdot 6x = 30x^2 \]

2. Outside: Multiply the outer terms: \[ 5x \cdot 3 = 15x \]

3. Inside: Multiply the inner terms: \[ -2 \cdot 6x = -12x \]

4. Last: Multiply the last terms: \[ -2 \cdot 3 = -6 \]

Now, combine all these results together: \[ 30x^2 + 15x - 12x - 6 \]

Combine the like terms \( 15x \) and \( -12x \): \[ 30x^2 + (15x - 12x) - 6 = 30x^2 + 3x - 6 \]

So, the final result of multiplying the polynomials \( (5x - 2)(6x + 3) \) is: \[ \boxed{30x^2 + 3x - 6} \]