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. 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. (1 point) Statement # correctly interprets a part of the expression.

Answer 1

To analyze the expression \(5.00x + 7.50y\), let's break it down:

• \(x\) represents the number of student tickets sold.
• \(y\) represents the number of adult tickets sold.
• The term \(5.00x\) represents the total revenue generated from student ticket sales (where each ticket is priced at $5.00).
• The term \(7.50y\) represents the total revenue generated from adult ticket sales (where each ticket is priced at $7.50).

Now, let's evaluate the statements:

• Statement 1: "The school will make about $121.50 after all tickets are bought."
  This statement is not correct as the total earnings from the play will depend on the specific values of \(x\) and \(y\), and cannot be determined from the expression alone without knowing those quantities.

• Statement 2: "Student tickets are $5.00 each."
  This statement is correct because the coefficient of \(x\) in the expression \(5.00x\) indicates that each student ticket costs $5.00.

• Statement 3: "Student tickets are $7.50 each."
  This statement is incorrect because, as identified earlier, student tickets are $5.00, not $7.50.

Thus, Statement 2 correctly interprets a part of the expression.

Answer 2

Use the Commutative Property of Multiplication to rewrite the algebraic expression: x10⋅y20 (1 point)

Answer 3

The Commutative Property of Multiplication states that the order in which we multiply numbers does not affect the product.

Applying this property to the algebraic expression \(x^{10} \cdot y^{20}\), we can rewrite it by swapping the order of the factors:

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

So, the expression \(x^{10} \cdot y^{20}\) can be rewritten as \(y^{20} \cdot x^{10}\).

Answer 4

Write an equivalent expression to 𝑥+(𝑦+𝑧), using the Associative Property of Addition. (1 point)

Answer 5

The Associative Property of Addition states that when adding three or more numbers, the way in which the numbers are grouped does not change the sum.

Given the expression \(x + (y + z)\), we can apply the Associative Property by regrouping the terms:

\[ (x + y) + z \]

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