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Question 1 A) Two classmates are working on multiplying the binomials (2x-5)(x+12). Their work is below: Joey Erin (2x−5)(x+12)(2x−5)(x+12) (2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12) 2x+24x−5x−602x+24x−5x−60 21x−6021x−60 (2x−5)(x+12)(2x−5)(x+12) (2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12) 2x2+24x−5x−602x2+24x−5x−60 2x2+19x−602x2+19x−60 Which classmate completed the problem correctly? (1 point) Explain what mistake the other classmate made. Use complete sentences to receive credit. (2 points) (3 points) BoldItalicUnderlineBullet listNumbered list 0 / 10000 Word Limit Question 2 A) Here is an example of a linear expression word problem: Matt is starting a dog walking business. He charges a one-time meeting fee of $10 and $14 per 30-minute walk. Write the mathematical expression that models this scenario (2 points) What is the total cost of 6 walks? Show all work to receive credit. (3 points) (5 points) BoldItalicUnderlineBullet listNumbered list 0 / 10000 Word Limit Question 3 A) (2x3−12x2+5x−3)−(7x3+10x2−3x+20)(2x3−12x2+5x−3)−(7x3+10x2−3x+20) What is the first step in simplifying this difference? (1 point) Responses Combine like terms. Combine like terms. Distribute the negative to the second set of parenthesis. Distribute the negative to the second set of parenthesis. Make the parenthesis one term. Make the parenthesis one term. Put the expression in descending order. Put the expression in descending order. Distribute the negative to every term in the first and second set of parenthesis. Distribute the negative to every term in the first and second set of parenthesis. Question 4 A)(7 points) You are simplifying the following: (6x3+2x2−5x−14)−(−5x3+7x2+2x−1)(6x3+2x2−5x−14)−(−5x3+7x2+2x−1) Below is Step 1. Fill in the blanks with the correct sign. 6x36x3 2x22x2 5x5x 1414 5x35x3 7x27x2 2x2x 11 Question 5 A) The perimeter of the shape below is 21x2−5x + 421x2−5x + 4. Find the length of the missing side. (1 point) Responses 4x2+54x2+54 x squared plus 5 −14x2+12x−8−14x2+12x−8negative 14 x squared plus 12 x minus 8 14x2−12x+814x2−12x+814 x squared minus 12 x plus 8 4x2−84x2−84 x squared minus 8 Question 6 A) Which line shows the correct and complete distribution for the problem below? (2x+3)(3x−1)(2x+3)(3x−1)(1 point) Responses 2x⋅3x +3⋅3x2x⋅3x +3⋅3x2x⋅3x +3⋅3x2x⋅3x +3⋅3x 2x⋅3+3x⋅−12x⋅3+3x⋅−12 x times 3 plus 3 x times negative 1 2x⋅3x+2x⋅−1+3⋅3x+3⋅−12x⋅3x+2x⋅−1+3⋅3x+3⋅−12 x times 3 x plus 2 x times negative 1 plus 3 times 3 x plus 3 times negative 1 2x⋅3x−2x⋅−1−3⋅3x−3⋅−12x⋅3x−2x⋅−1−3⋅3x−3⋅−12 x times 3 x minus 2 x times negative 1 minus 3 times 3 x minus 3 times negative 1 Question 7 A)A new app charges a joining fee of $2 and a monthly subscription cost of $5 each month. Choose the expression below that represents the cost of the app for m months?(1 point) Responses 5+2m=c5+2m=c5 plus 2 m is equal to c 2+5m2+5m2 plus 5 m 5+2m5+2m5 plus 2 m 2+5m=c2+5m=c2 plus 5 m is equal to c Question 8 A) Identify the correct list of coefficients for the quadratic expression: 3x2+5x−123x2+5x−12(1 point) Responses 3x2, 5x, −123x2, 5x, −123x2, 5x, −123x2, 5x, −12 3x2, 5x3x2, 5x3x2, 5x3x2, 5x 3, 5 3, 5 3, 5, −123, 5, −123, 5, −123, 5, −12 Question 9 A)Identify the constant in the cubic expression: 2x3−8x2−10x+12x3−8x2−10x+1.(1 point) Responses 1 1 -10 -10 2 2 -8 -8 Question 10 A)Identify the following as an expression or an equation(4 points) Expression Equation 2x3−4x22x3−4x2 x=3x2−4x=3x2−4 5x=255x=25 3x+2π3x+2π

3 answers

Question 1

A) Incorrect Work by Classmates

Joey: \[ (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12) \Rightarrow 2x^2 + 24x - 5x - 60 \] Final result: \(2x^2 + 19x - 60\)

Erin: Correctly calculated individual products: \[ (2x)(x) = 2x^2 \] \[ (2x)(12) = 24x \] \[ (-5)(x) = -5x \] \[ (-5)(12) = -60 \] Final result: \(2x^2 + 19x - 60\)

Incorrect Classmate

Both classmates initially followed the process correctly but made a mistake in simplification. Joey simplified \(24x - 5x\) to \(19x\), which is correct, but didn't show the intermediate steps clearly. Erin made no apparent mistakes in the calculations.

Conclusion: Erin completed the problem correctly, while Joey followed the process correctly but did not emphasize clarity in combining like terms. Erin's presentation and clarity in showing steps made it easier to follow.

Question 2

A) Cost Modeling Expressed

Matt's total cost, including the one-time meeting fee and the cost per walk, can be modeled as: \[ C = 10 + 14w \] Where \(C\) is total cost and \(w\) is the number of walks.

Total Cost for 6 Walks

Total cost for 6 walks: \[ C = 10 + 14(6) \] Calculating: \[ C = 10 + 84 = 94 \] Thus, the total cost for 6 walks is $94.

Question 3

A) First Step in Simplification

To simplify the expression \((2x^3 - 12x^2 + 5x - 3) - (7x^3 + 10x^2 - 3x + 20)\), the first step is: Distribute the negative to the second set of parentheses.

Question 4

A) Simplification Fill-in

Expression: \[ (6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1) \]

After distributing the negative, it becomes: \[ 6x^3 + 2x^2 - 5x - 14 + 5x^3 - 7x^2 - 2x + 1 \]

Fill in the blanks showing signs: 6x³, +, 2x², -, 5x, -, 14, +, 5x³, -, 7x², -, 2x, +, 1

Question 5

A) Length of the Missing Side

Given perimeter: \[ 21x^2 - 5x + 4 \] Let \(S\) be the total length of the sides that are known. If you know that: \[ P = S + \text{(missing side)} \] The missing side can be found by subtracting the known perimeter from \(P\).

Assuming known sides are \(S\), then the length of missing side would be expressed as: \[ \text{missing side} = 21x^2 - 5x + 4 - S \]

Exact length can’t be determined without knowing \(S\) or the lengths of other sides.

Question 6

A) Correct Distribution

For the expression \((2x + 3)(3x - 1)\), the correct and complete distribution should include all terms: \[ 2x \cdot 3x + 2x \cdot -1 + 3 \cdot 3x + 3 \cdot -1 \]

Correct response: \(2x \cdot 3x + 2x \cdot -1 + 3 \cdot 3x + 3 \cdot -1\)

Question 7

A) Cost Expression

The cost of the app for \(m\) months is expressed as: \[ C = 2 + 5m \]

The correct response: \(2 + 5m = c\)

Question 8

A) Coefficients Identification

For the expression \(3x^2 + 5x - 12\), the coefficients are: 3, 5, -12

Question 9

A) Constant Identification

In the expression \(2x^3 - 8x^2 - 10x + 1\), the constant is: 1

Question 10

A) Expression or Equation Classification

  1. \(2x^3 - 4x^2\) - Expression
  2. \(x = 3\) - Equation
  3. \(5x = 25\) - Equation
  4. \(3x + 2\pi\) - Expression
The perimeter of the shape below is 21x2−5x + 421x2−5x + 4. Find the length of the missing side.

To find the length of the missing side of a shape when given the perimeter, we need to know the lengths of all the other sides.

  1. Given Perimeter: \[ P = 21x^2 - 5x + 4 \]

  2. Known Lengths: Suppose the lengths of the known sides are \(S_1\), \(S_2\), etc. Let’s say for this example, we are given the lengths of 2 sides: \(S_1\) and \(S_2\).

  3. Finding the Missing Side: The formula for the perimeter of a polygon is the sum of all sides. So, if \(L\) represents the missing side, then: \[ P = S_1 + S_2 + L \] Rearranging this gives: \[ L = P - (S_1 + S_2) \]

  4. Example Calculation: If you had been given specific lengths for \(S_1\) and \(S_2\), you would plug those into the formula: \[ L = (21x^2 - 5x + 4) - (S_1 + S_2) \]

Since we don't have the specific lengths of the other side(s) given in the question, we can’t calculate a numerical or algebraic answer for \(L\) without that information.

Request for Additional Information

Please provide the lengths of the other sides in order to determine the length of the missing side.