Use the following example to answer the question. Sarah buys t-shirts and hats. She pays a set rate per t-shirt and a different set rate per hat, with the rate for t-shirts being higher. Her total spending can be modeled by the expression 50x + 30y. Which of the statements correctly interprets a part of the expression?

Question

Statement #1: Sarah spends $50.00 per t-shirt.
Statement #2: Sarah spends $30.00 per t-shirt.
Statement #3: Sarah spends $50.00 in total for t-shirts.

Answer 1

The correct interpretation from the provided statements is:

Statement #1: Sarah spends $50.00 per t-shirt.

In the expression 50x + 30y, the coefficient 50 represents the cost per t-shirt (where x is the number of t-shirts), and the coefficient 30 represents the cost per hat (where y is the number of hats). Thus, Statement #1 accurately reflects the cost per t-shirt.

Statement #2 is incorrect because it describes the cost per hat instead of per t-shirt. Statement #3 is also incorrect because the expression represents total spending, not just the total for t-shirts.

Answer 2

Use the following example to answer the question. Sarah buys t-shirts and hats. She pays a set rate per t-shirt and a different set rate per hat, with the rate for t-shirts being higher. Her total spending can be modeled by the expression 50x + 30y. Which of the statements correctly interprets a part of the expression?

Statement #1: Sarah spends $50.00 per t-shirt.
Statement #2: Sarah spends $30.00 per t-shirt.
Statement #3: Sarah spends $50.00 in total for t-shirts.

Answer 3

The correct interpretation of the expression \(50x + 30y\) is:

Statement #1: Sarah spends $50.00 per t-shirt.

This is correct because the coefficient \(50\) corresponds to the cost per t-shirt (where \(x\) is the number of t-shirts).

Statement #2: Sarah spends $30.00 per t-shirt. This is incorrect because it mistakenly assigns the cost of hats to t-shirts; the $30 corresponds to the cost per hat (where \(y\) is the number of hats).

Statement #3: Sarah spends $50.00 in total for t-shirts. This is also incorrect because the expression represents the total spending across all items, not just the total for t-shirts.

Therefore, only Statement #1 accurately interprets a part of the expression.

Answer 4

Consider the expression
(18 -10)^2 + 4(9+13)^2/(3+2)^2. What is the simplified numerator?

Answer 5

To find the simplified numerator of the expression

\[ (18 - 10)^2 + 4(9 + 13)^2 \]

we first simplify each part step by step.

1. Calculate \( 18 - 10 \): \[ 18 - 10 = 8 \] Therefore, \[ (18 - 10)^2 = 8^2 = 64. \]

2. Calculate \( 9 + 13 \): \[ 9 + 13 = 22 \] Therefore, \[ (9 + 13)^2 = 22^2 = 484. \]

3. Multiply the squared result by 4: \[ 4(9 + 13)^2 = 4 \times 484 = 1936. \]

4. Add the two parts together: Now, we combine the results from steps 1 and 3: \[ 64 + 1936 = 2000. \]

Thus, the simplified numerator is

\[ \boxed{2000}. \]

Answer 6

Use the Commutative Property of Multiplication to rewrite the algebraic expression:
p22q14.

Answer 7

The Commutative Property of Multiplication states that the order of factors can be changed without affecting the product. For your expression \( p^{22}q^{14} \), we can rewrite it by switching the order of the variables.

Using the Commutative Property, we can rewrite the expression as:

\[ q^{14}p^{22} \]

Thus, the rewritten expression is

\[ \boxed{q^{14}p^{22}}. \]

Answer 8

Use the Commutative Property of Multiplication to rewrite the algebraic expression:
p^22 x q^14

Answer 9

Using the Commutative Property of Multiplication, which states that the order of factors can be changed while maintaining the same product, we can rewrite the expression \( p^{22} \times q^{14} \).

By switching the order of the factors, we can express the original expression as:

\[ q^{14} \times p^{22} \]

So, the rewritten expression is

\[ \boxed{q^{14} \times p^{22}}. \]