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Antoine goes to the mall to buy new shoes and jerseys. He pays a set rate per pair of shoes and a set rate per jersey, and he pays more per jersey than he pays per pair of shoes. His total spending can be modeled by the equation 35x+55y

. Which of the statements correctly interprets a part of the expression?

Statement #1: Antoine spends $35.00 per pair of shoes.

Statement #2: Antoine spends $55.00 per pair of shoes.

Statement #3: Antoine spends $35.00 in total for shoes.

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

11 answers

Statement #1: Antoine spends $35.00 per pair of shoes.

This statement correctly interprets a part of the expression \(35x + 55y\), where \(x\) represents the number of pairs of shoes Antoine buys at a price of $35 each.

So the correct choice is Statement #1.

Consider the expression (16−12)^2+5(8+2^2)/5^3−(1+4)^2
. What is the simplified numerator?(1 point)
Responses

4^2+60
4 squared plus 60

100
100

76
76

54

To simplify the expression \((16 - 12)^2 + 5(8 + 2^2)\), we can break it down step by step.

  1. Calculate \(16 - 12\): \[ 16 - 12 = 4 \]

  2. Calculate \((16 - 12)^2\): \[ (4)^2 = 16 \]

  3. Calculate \(2^2\): \[ 2^2 = 4 \]

  4. Calculate \(8 + 2^2\): \[ 8 + 4 = 12 \]

  5. Now calculate \(5(8 + 2^2)\): \[ 5 \times 12 = 60 \]

  6. Now combine the results: \[ (16 - 12)^2 + 5(8 + 2^2) = 16 + 60 = 76 \]

So, the simplified numerator of the expression is:

76

The correct response is 76.

Use the Commutative Property of Multiplication to rewrite the algebraic expression: k^17⋅z^33
.(1 point)

The Commutative Property of Multiplication states that the order in which we multiply numbers or variables does not affect the product. Therefore, we can rewrite the expression \( k^{17} \cdot z^{33} \) by switching the order of the factors.

Using the Commutative Property of Multiplication, we can rewrite it as:

\[ z^{33} \cdot k^{17} \]

So the expression \( k^{17} \cdot z^{33} \) can be rewritten as \( z^{33} \cdot k^{17} \).

Which expression correctly demonstrates the Commutative Property of Multiplication?(1 point)
Responses

15(x+4)=15(x⋅4)
15 left parenthesis x plus 4 right parenthesis equals 15 left parenthesis x times 4 right parenthesis

15⋅(x)⋅4=4⋅15⋅(x)
15 times left parenthesis x right parenthesis times 4 equals 4 times 15 times left parenthesis x right parenthesis

x+4+15=15+4+x
x plus 4 plus 15 equals 15 plus 4 plus x

15⋅x⋅4=4+15+x

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. Among the options provided, the expression that correctly demonstrates this property is:

15 ⋅ (x) ⋅ 4 = 4 ⋅ 15 ⋅ (x)

This shows that the multiplication of \(15\), \(x\), and \(4\) can be rearranged without changing the result, which is the essence of the Commutative Property of Multiplication.

The correct response is:

15⋅(x)⋅4 = 4⋅15⋅(x)

Write an equivalent expression to (a⋅b)⋅c
using the Associative Property of Multiplication.(1 point

The Associative Property of Multiplication states that the way in which factors are grouped does not affect the product. To use this property to rewrite the expression \((a \cdot b) \cdot c\), you can regroup the factors:

Using the Associative Property, you can rewrite it as:

\[ a \cdot (b \cdot c) \]

So, an equivalent expression to \((a \cdot b) \cdot c\) using the Associative Property of Multiplication is:

\(a \cdot (b \cdot c)\).

Which expression is equivalent to −3x−5
?(1 point)
Responses

(x−7)+(2−4x)
left parenthesis x minus 7 right parenthesis plus left parenthesis 2 minus 4 x right parenthesis

(−4x−6)+(2+5x)
left parenthesis negative 4 x minus 6 right parenthesis plus left parenthesis 2 plus 5 x right parenthesis

−1+3x−(2x+6)
negative 1 plus 3 x minus left parenthesis 2 x plus 6 right parenthesis

−1+(x−4x)+6

To determine which expression is equivalent to \(-3x - 5\), let's simplify each of the given options.

  1. \((x - 7) + (2 - 4x)\): \[ = x - 7 + 2 - 4x = x - 4x - 7 + 2 = -3x - 5 \]

  2. \((-4x - 6) + (2 + 5x)\): \[ = -4x - 6 + 2 + 5x = (-4x + 5x) + (-6 + 2) = 1x - 4 = x - 4 \]

  3. \(-1 + 3x - (2x + 6)\): \[ = -1 + 3x - 2x - 6 = 3x - 2x - 1 - 6 = x - 7 \]

  4. \(-1 + (x - 4x) + 6\): \[ = -1 + x - 4x + 6 = -1 + (1x - 4x) + 6 = -1 - 3x + 6 = -3x + 5 \]

After simplifying, we find that the only option that equals \(-3x - 5\) is:

\((x - 7) + (2 - 4x)\).

Thus, the correct response is:

\((x - 7) + (2 - 4x)\).