Question

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 1

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 2

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

Answer 3

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

Answer 4

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

Answer 5

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 6

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 7

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 8

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 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

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