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.
Statement #___ correctly interprets a part of the expression.
11 answers
Statement #1: Sarah spends $50.00 per t-shirt.
This statement correctly interprets a part of the expression because in the expression \(50x + 30y\), the term \(50x\) indicates that Sarah pays $50 for each t-shirt (where \(x\) represents the number of t-shirts).
Therefore, the correct answer is:
Statement #1 correctly interprets a part of the expression.
To simplify the numerator of the expression \((18-10)^2 + 4(9+13)^2\), we will follow these steps:
Calculate \(18 - 10\): \[ 18 - 10 = 8 \]
Calculate \((18 - 10)^2\): \[ (8)^2 = 64 \]
Calculate \(9 + 13\): \[ 9 + 13 = 22 \]
Calculate \((9 + 13)^2\): \[ (22)^2 = 484 \]
Multiply \((9 + 13)^2\) by 4: \[ 4(484) = 1936 \]
Add the results from steps 2 and 5 together: \[ 64 + 1936 = 2000 \]
Thus, the simplified numerator is: \[ \boxed{2000} \]
The Commutative Property of Multiplication states that the order in which you multiply numbers does not change the product. Therefore, you can rearrange the terms in the expression \(p^{22} \cdot q^{14}\).
Using the Commutative Property, the expression can be rewritten as:
\[ q^{14} \cdot p^{22} \]
So, the rewritten expression is:
\[ \boxed{q^{14} \cdot p^{22}} \]
Let's analyze each expression to determine whether they demonstrate the Commutative Property of Multiplication. The Commutative Property states that changing the order of the factors does not change the product, which can be mathematically expressed as \(a \cdot b = b \cdot a\).
For the expression \(7 \times 3 = 3 \times 7\):
For the expression \(4y \times 2 = 2 \times 4y\):
For the expression \(5z \times 6 = 6 \times 5z\):
Since all statements are valid representations of the Commutative Property of Multiplication, we can conclude that:
All of the above correctly demonstrates the Commutative Property of Multiplication.
Therefore, the answer is:
\[ \boxed{\text{All of the above}} \]
The Associative Property of Multiplication states that the way in which factors are grouped in a multiplication problem does not affect the product. In other words, \((a \cdot b) \cdot c = a \cdot (b \cdot c)\).
To use the Associative Property to rewrite the expression \((b \cdot c) \cdot d\), we can regroup the factors to obtain an equivalent expression.
You can write:
\[ b \cdot (c \cdot d) \]
Thus, using the Associative Property of Multiplication, the expression \((b \cdot c) \cdot d\) can be equivalently written as:
\[ \boxed{b \cdot (c \cdot d)} \]
To determine which expression is equivalent to \(-4x - 6\), let's simplify each of the given options one by one.
Option 1: \(-2(2x + 3)\)
Distributing \(-2\):
\[
-2(2x) - 2(3) = -4x - 6
\]
This expression is equivalent to \(-4x - 6\).
Option 2: \(3(-x + 2)\)
Distributing \(3\):
\[
3(-x) + 3(2) = -3x + 6
\]
This expression is not equivalent to \(-4x - 6\).
Option 3: \(8x - 6 - 4x\)
Combining like terms:
\[
(8x - 4x) - 6 = 4x - 6
\]
This expression is not equivalent to \(-4x - 6\).
Option 4: \(-4x + 3(-3x - 2)\)
Distributing \(3\):
\[
-4x + 3(-3x) + 3(-2) = -4x - 9x - 6
\]
Combining like terms:
\[
-4x - 9x - 6 = -13x - 6
\]
This expression is not equivalent to \(-4x - 6\).
From this analysis, the only option that is equivalent to \(-4x - 6\) is:
\[ \boxed{-2(2x + 3)} \]
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