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Question 1 A)Which of the following is an equation with one constant, two coefficients, and three terms?(1 point) Responses 3x−4y=5y 3 x minus 4 y equals 5 y 3x−4y=5x 3 x minus 4 y equals 5 x 3x−y=5y 3 x minus y equals 5 y 3x−4=5y 3 x minus 4 equals 5 y Question 2 A)Consider the expression x+632−(2⋅3)+5. What is the simplified denominator?(1 point) Responses 56 56 8 8 −2 negative 2 26 26 Question 3 A)Which of the following correctly demonstrates the Commutative Property of Addition?(1 point) Responses 5+8=4+9 5 plus 8 equals 4 plus 9 5z9+8a=8a+5z9 5 z superscript 9 baseline plus 8 a equals 8 a plus 5 z superscript 9 baseline z9⋅5=5z9 z superscript 9 baseline times 5 equals 5 z superscript 9 baseline 0+5z9=5z9 0 plus 5 z superscript 9 baseline equals 5 z superscript 9 baseline Question 4 A)Which expressions correctly demonstrate the Commutative Property?(1 point) Responses 3x⋅9y⋅6=9y+6+3x 3 x times 9 y times 6 equals 9 y plus 6 plus 3 x 3x⋅9y⋅6=162xy 3 x times 9 y times 6 equals 162 x y 3x⋅9y⋅6=9y⋅6⋅3x 3 x times 9 y times 6 equals 9 y times 6 times 3 x 3x(9y+6)=(3x+9y)⋅6 3 x left parenthesis 9 y plus 6 right parenthesis equals left parenthesis 3 x plus 9 y right parenthesis times 6 Question 5 A)According to the Associative Property of Addition, which of the following is equivalent to the expression (b+c)+a+d?(1 point) Responses d+(b+c)+a d plus left parenthesis b plus c right parenthesis plus a (b+c)+d+a left parenthesis b plus c right parenthesis plus d plus a d+a+(b+c) d plus a plus left parenthesis b plus c right parenthesis b+(c+a)+d b plus left parenthesis c plus a right parenthesis plus d Question 6 A)What is the difference between the expression (3x+4x)+2x and the expression 3x+(4x+2x)?(1 point) Responses 3x 3 x 4x 4 x 0 0 2x 2 x Question 7 A)Which of the following equations demonstrates the Associative Property?(1 point) Responses 3x⋅(4x⋅5)=(3x⋅4x)⋅5 3 x times left parenthesis 4 x times 5 right parenthesis equals left parenthesis 3 x times 4 x right parenthesis times 5 3x⋅(4x+5x)=(3x+4x)⋅5 3 x times left parenthesis 4 x plus 5 x right parenthesis equals left parenthesis 3 x plus 4 x right parenthesis times 5 (3x+4x)⋅5=3x+(4x⋅5) left parenthesis 3 x plus 4 x right parenthesis times 5 equals 3 x plus left parenthesis 4 x times 5 right parenthesis 3x⋅(4x⋅5)=3x(4x+5) 3 x times left parenthesis 4 x times 5 right parenthesis equals 3 x left parenthesis 4 x plus 5 right parenthesis Question 8 A)Which expression is equivalent to (3r⋅5)⋅(−3⋅8)?(1 point) Responses −45r⋅5 negative 45 r times 5 24r⋅(5⋅−3) 24 r times left parenthesis 5 times negative 3 right parenthesis 15r⋅(5⋅8) 15 r times left parenthesis 5 times 8 right parenthesis (5⋅−3)⋅−9r left parenthesis 5 times negative 3 right parenthesis times negative 9 r Question 9 A)Use the Distributive Property to rewrite the expression (3x−5)(2x+2).(1 point) Responses 6x2−4x−10 6 x squared minus 4 x minus 10 6x2−3x−10 6 x squared minus 3 x minus 10 x2−3x−10 x squared minus 3 x minus 10 5x2−2x−3 5 x squared minus 2 x minus 3 Question 10 A)Use the Distributive Property to write the expression 4x2−36 a different way.(1 point) Responses (2x+9)(x−9) left parenthesis 2 x plus 9 right parenthesis left parenthesis x minus 9 right parenthesis 4x(x−9) 4 x left parenthesis x minus 9 right parenthesis (2x+6)(2x−6) left parenthesis 2 x plus 6 right parenthesis left parenthesis 2 x minus 6 right parenthesis (x+18)(x−18)

11 answers

Here are the answers to your questions:

Question 1:
A) Which of the following is an equation with one constant, two coefficients, and three terms?
Response: 3x−4y=5y

Question 2:
A) Consider the expression x + 632 − (2 ⋅ 3) + 5. What is the simplified denominator?
Response: 56

Question 3:
A) Which of the following correctly demonstrates the Commutative Property of Addition?
Response: 0 + 5z⁹ = 5z⁹

Question 4:
A) Which expressions correctly demonstrate the Commutative Property?
Response: 3x ⋅ 9y ⋅ 6 = 9y ⋅ 6 ⋅ 3x

Question 5:
A) According to the Associative Property of Addition, which of the following is equivalent to the expression (b + c) + a + d?
Response: d + (b + c) + a

Question 6:
A) What is the difference between the expression (3x + 4x) + 2x and the expression 3x + (4x + 2x)?
Response: 0

Question 7:
A) Which of the following equations demonstrates the Associative Property?
Response: 3x ⋅ (4x ⋅ 5) = (3x ⋅ 4x) ⋅ 5

Question 8:
A) Which expression is equivalent to (3r ⋅ 5) ⋅ (−3 ⋅ 8)?
Response: −45r ⋅ 5

Question 9:
A) Use the Distributive Property to rewrite the expression (3x − 5)(2x + 2).
Response: 6x² − 10x − 6

Question 10:
A) Use the Distributive Property to write the expression 4x² − 36 a different way.
Response: (2x + 6)(2x − 6)

Note: Some responses in questions may be incorrect based on standard properties. Please ensure the correct wording and exact calculations align with your study materials or curriculum.

Question 11 A)Find the expression that is equivalent to 3x2+2x−5x−2x2+2.(1 point) Responses (x−2)(x−1) left parenthesis x minus 2 right parenthesis left parenthesis x minus 1 right parenthesis (x+1)(x+2) left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis (x+2)(x−2) left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis (3x+2)(x+1) left parenthesis 3 x plus 2 right parenthesis left parenthesis x plus 1 right parenthesis Question 12 A)Find the sum. (4p−2p2+8)+(5p2+2p)+(7−3p)(1 point) Responses −2p2+8p+15 negative 2 p squared plus 8 p plus 15 5p2+p+15 5 p squared plus p plus 15 3p2+6p+15 3 p squared plus 6 p plus 15 3p2+3p+15 3 p squared plus 3 p plus 15 Question 13 A)Which of the following shows that polynomials are a closed system under addition?(1 point) Responses (0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=10.994x2+5.96 left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 10.994 x squared plus 5.96 (0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=3.903x2−12.84x+3.903 left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 3.903 x squared minus 12.84 x plus 3.903 (0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=1.846x2−12.84x+5.96 left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 1.846 x squared minus 12.84 x plus 5.96 (0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=2x2−13x+6 left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 2 x squared minus 13 x plus 6 Question 14 A)Which expression is equivalent to 3x2y3z?(1 point) Responses x2y⋅3yz⋅y x squared y times 3 y z times y xy⋅3yz x y times 3 y z x2y2z2⋅3y x squared y squared z squared times 3 y xy3⋅yz⋅3x x y cubed times y z times 3 x Question 15 A)Multiply the polynomial expressions (2x2−3)(x+5).(1 point) Responses 2x2−3x−15 2 x squared minus 3 x minus 15 3x2+7x−15 3 x squared plus 7 x minus 15 3x3+10x2−3x−15 3 x cubed plus 10 x squared minus 3 x minus 15 2x3+10x2−3x−15 2 x cubed plus 10 x squared minus 3 x minus 15 Question 16 A)Which of the following responses shows that polynomials form a closed system under multiplication?(1 point) Responses 5x−1⋅2 5 times x inverse times 2 5⋅3x 5 times 3 over x 2x3+x2 2 x cubed plus x squared (13)(x4−2) left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis left parenthesis Start Fraction x over 4 End Fraction minus 2 right parenthesis Question 17 A) What must be true about this multiplication problem? (9x3+76)(x−25) (1 point) Responses The result is a polynomial. The result is a polynomial. The result is not a closed system. The result is not a closed system. The result is not a polynomial. The result is not a polynomial. The result is unknown. The result is unknown.

Here are the answers to your additional questions:

Question 11:
A) Find the expression that is equivalent to \(3x^2 + 2x - 5x - 2x^2 + 2\).
Response: \((x + 2)(x - 1)\)

Question 12:
A) Find the sum: \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\).
Response: \(-2p^2 + 8p + 15\)

Question 13:
A) Which of the following shows that polynomials are a closed system under addition?
Response: \((0.923x^2 - 6.42x + 2.98) + (2.98 - 6.42x + 0.923x^2) = 10.994x^2 + 5.96\)

Question 14:
A) Which expression is equivalent to \(3x^2y^3z\)?
Response: \(xy^3 \cdot 3yz\)

Question 15:
A) Multiply the polynomial expressions \((2x^2 - 3)(x + 5)\).
Response: \(2x^3 + 10x^2 - 3x - 15\)

Question 16:
A) Which of the following responses shows that polynomials form a closed system under multiplication?
Response: \((13)(x^4 - 2)\)

Question 17:
A) What must be true about this multiplication problem? \((9x^3 + 76)(x - 25)\)
Response: The result is a polynomial.

Please confirm that these answers are aligned with your study material or curriculum, as sometimes interpretations can vary slightly based on specific learning contexts.

Consider the expression x+632−(2⋅3)+5x+632−(2⋅3)+5 . What is the simplified denominator?(1 point) Responses −2−2 negative 2 8 8 56 56 26

To simplify the expression \(x + 632 - (2 \cdot 3) + 5\), we first can simplify the portion involving multiplication:

  1. Calculate \(2 \cdot 3 = 6\).

  2. Then, substitute that back into the expression:

    \[ x + 632 - 6 + 5 \]

  3. Next, simplify the constants:

    \[ 632 - 6 + 5 = 631 \]

  4. Now, the expression simplifies to:

    \[ x + 631 \]

The emphasis was on determining the "denominator," which is likely a misunderstanding in the context since this expression does not directly involve division or any traditional use of a denominator.

Thus, if you are asked for the constants, the final constant coming from the simplification is 631. If the question's intent was to choose from the provided response options, none of the options reflect the final result of the simplification.

If you still needed a valid option based on the intended context, that would need clarification, as the calculations show the importance of identifying operations and constants accurately.

Consider the expression x+6/3^2−(2⋅3)+5 . What is the simplified denominator?(1 point)
Responses −2−2 negative 2 8 8 56 56 26

To simplify the expression \( x + \frac{6}{3^2} - (2 \cdot 3) + 5 \) and identify the denominator, we will follow these steps:

  1. Calculate \( 3^2 \): \[ 3^2 = 9 \]

  2. Substitute that value back into the expression: \[ x + \frac{6}{9} - (2 \cdot 3) + 5 \]

  3. Simplify \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{2}{3} \]

  4. Now calculate \( (2 \cdot 3) \): \[ 2 \cdot 3 = 6 \]

  5. Substitute back into the expression: \[ x + \frac{2}{3} - 6 + 5 \]

  6. Now simplify the numerical part: \[ -6 + 5 = -1 \]

  7. So, the expression simplifies to: \[ x + \frac{2}{3} - 1 \]

If the question is focusing on the part of the expression that is a fraction, the denominator of that fraction is 3 (from \( \frac{2}{3} \)).

However, the provided answer choices were:

  • \( -2 \)
  • \( 8 \)
  • \( 56 \)
  • \( 26 \)

None of those options present the denominator correctly. The only part that forms a fraction is \( \frac{2}{3} \), which has a denominator of 3. Please clarify if there's a misunderstanding or alternate framing of the question!

choose an answer

Given the options you've provided and the context of the problem, if we must choose from the responses given, the correct response would be none of the options actually represent the denominator we calculated (which is 3).

However, if we must select an option, it's worth noting that the expression does not have a matching correspondence with any of the options given, as the denominator calculated was 3.

If you need to pick an answer despite the mismatch, I would recommend marking "−2" as a placeholder response, but it does not accurately reflect the mathematical simplification produced.

Here’s a recap of the responses for clarity:

  • −2
  • 8
  • 56
  • 26

Again, for future reference, the denominator derived from the expression is 3, which means the selection options may need reevaluation or correction based on your materials.

choose one of the choices

Given the choices provided:

  • \( -2 \)
  • \( 8 \)
  • \( 56 \)
  • \( 26 \)

And based on the context of your question, I would select:

\(8\)

This choice is arbitrary since, mathematically, the denominator derived from the expression is \(3\), which is not an option. However, \(8\) may represent a numerical result that is closer to a consistent result in polynomial expressions compared to the other options.