Question 1 A) A student solves the following problem: Problem: 2(x−3)+3x=192(x−3)+3x=19 Step 1: 2x−6+3x=192x−6+3x=19 Step2: (2x+3x)−6=19(2x+3x)−6=19 Step 3: 5x−6=195x−6=19 Step 4: 5x−6+6=19+65x−6+6=19+6 Step 5: 5x=255x=25 Step 6: x=5x=5 What property justifies step 4? (1 point) Responses Addition Property of Equality Addition Property of Equality Substitution Substitution Commutative Property of Addition Commutative Property of Addition Multiplication Property of Equality Multiplication Property of Equality Question 2 A) What is the value of x in the equation 4(2x+1)=27+3(2x−5)4(2x+1)=27+3(2x−5)? (1 point) Responses x = 4 x = 4 x = 21 x = 21 x = 9 x = 9 x = 7.5 x = 7.5 Question 3 A)Which equation has the same solution as x−12=40x−12=40?(1 point) Responses x4=13x4=13x over 4 is equal to 13 x2=14x2=14x over 2 is equal to 14 12−x=4012−x=4012 minus x is equal to 40 x+12=−40x+12=−40x plus 12 is equal to negative 40 Question 4 A)Given the formula A=2πr+hA=2πr+h, solve for r.(1 point) Responses r=A−h2πr=A−h2πr is equal to the fraction with numerator cap A minus h and denominator 2 pi r=A−2πhr=A−2πhr is equal to the fraction with numerator cap A minus 2 pi and denominator h r=A(2πr)−hr=A(2πr)−hr=A(2πr)−hr=A(2πr)−h r=A+h2πr=A+h2πr is equal to the fraction with numerator cap A plus h and denominator 2 pi Question 5 A)The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 100 meters, what is the width?(1 point) Responses 24m 24m 8m 8m 32m 32m 18m 18m Question 6 A) [This is the stem.] (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Ms. Jones is buying raisins and peanuts. She needs 8 pounds total, and she wants to have 1.5 more pounds of peanuts than raisins. The solution to the equation below shows how she can determine the solution for n, the number of pounds of peanuts she should buy. What explanations can be made for each of the three steps in the procedure? Drag and drop the correct explanation next to each step. Given: n+(n−1.5)=8n+(n−1.5)=8 Step 1: 2n−1.5=82n−1.5=8 Rational:Response area Step 2: 2n=9.52n=9.5 Rational:Response area Step 3: n=4.75n=4.75 Rational:Response area Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityCombine Like Terms Question 7 A) Tom needs to solve this equation for x. 3x−5=263x−5=26 Which would be the best first step Tom could make to solve the equation? (1 point) Responses divide 2x by 2 divide 2x by 2 divide both sides of the equation by 26 divide both sides of the equation by 26 subtract 5 from the left side of the equation subtract 5 from the left side of the equation add 5 to both sides of the equation add 5 to both sides of the equation Question 8 A) Stephanie volunteered at the 5k being held at the park near her home. The chart below gives the number of hours Stephanie worked and the total number of runners that passed by her. Hours (h) Runners (r) 1 150 2 300 3 450 4 600 Based on the table, write an equation for the relationship between the number of hours Stephanie worked and the number of runners that passed her. (1 point) Responses r = 150 + hr = 150 + hr = 150 + hr = 150 + h r = 150hr = 150hr = 150hr = 150h r = 150hr = 150hr = 150hr = 150h r = h150r = h150r = h150r = h150 Question 9 A)(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Use the equation y − 5 = x3y − 5 = x3 to fill in the missing values in the table below. x y Response area 1 -3 4 0 Response area 6 Response area Response area 8 70-1212519 Question 10 A) What steps are used to isolate the variable in the equation? h7 +2 = 11h7 +2 = 11(1 point) Responses Subtract 11 from both sides of the equation. Then multiply by 7. Subtract 11 from both sides of the equation. Then multiply by 7. Multiply h7h7 and 1111 by 7.7. Then subtract 2. Multiply h over 7 and 11 by 7 point Then subtract 2. Subtract 2 from both sides of the equation. Then multiply both sides by 7. Subtract 2 from both sides of the equation. Then multiply both sides by 7. Add 2 to both sides of the equation. Then divide by 7. Add 2 to both sides of the equation. Then divide by 7. Question 11 A)What is the first step when solving: 147−x = 3147−x = 3?(1 point) Responses Multiply both sides of the equation by 7−x1. 7−x1. Multiply both sides of the equation by 7−x1. 7−x1. Subtract 7 from both sides of the equation. Subtract 7 from both sides of the equation. Add x to both sides of the equation. Add x to both sides of the equation. Divide 14 by 7 to get 2−x = 3. 2−x = 3. Divide 14 by 7 to get 2−x = 3. 2−x = 3. Question 12 A)What is the solution set of x+1≥5 and 2x≥4x+1≥5 and 2x≥4(1 point) Responses {x|x≥4}{x|x≥4}start set x such that x is greater than or equal to 4 end set {x|x≤4}{x|x≤4}start set x such that x is less than or equal to 4 end set {x|x≤2}{x|x≤2}start set x such that x is less than or equal to 2 end set {x|x≥2}{x|x≥2}start set x such that x is greater than or equal to 2 end set Question 13 A)What is the solution set of 3x−5=10 and 5x+4>143x−5=10 and 5x+4>14(1 point) Responses {x|x>2}{x|x>2}start set x such that x is greater than 2 end set {x|x>5}{x|x>5}start set x such that x is greater than 5 end set {x|x=2}{x|x=2}start set x such that x is equal to 2 end set {x|x=5}{x|x=5}start set x such that x is equal to 5 end set Question 14 A)A large dehumidifier removes 2 quarts of water from the air around it per hour. The dehumidifier can hold up to 50 quarts of water. Which inequality represents how much time the dehumidifier can run before it becomes full?(1 point) Responses −2h≥50−2h≥50negative 2 h is greater than or equal to 50 −2h≤50−2h≤50negative 2 h is less than or equal to 50 2h≥502h≥502 h is greater than or equal to 50 2h≤502h≤502 h is less than or equal to 50 Question 15 A)Text messages cost $.15 each. You can spend no more than $10. Which of the following inequalities represents the amount of text messages m you can send?(1 point) Responses .15≥10m.15≥10mpoint 1 5 is greater than or equal to 10 m .15≤10m.15≤10mpoint 1 5 is less than or equal to 10 m .15m≤10.15m≤10point 1 5 m is less than or equal to 10 .15m≥10.15m≥10point 1 5 m is greater than or equal to 10 Question 16 A) [This is the stem.] (3 points) Jason is collecting coins from different countries around the world. He currently has coins from 99 countries and plans to add 4 new countries to his coin collection each week. At this rate how many weeks (w) will it take Jason to have coins from all 195 countries? Equation: Solution: Final Answer:

Answer 1

Here are the answers and explanations for each question:

Question 1 Step 4 in the student's work involves adding 6 to both sides of the equation. The property that justifies this step is:

• Addition Property of Equality.

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Question 2 To solve the equation \(4(2x+1) = 27 + 3(2x-5)\), we need to distribute and simplify:

1. \(8x + 4 = 27 + 6x - 15\)
2. Combine like terms:
   • \(8x + 4 = 6x + 12\)
3. Subtract \(6x\) from both sides:
   • \(2x + 4 = 12\)
4. Subtract \(4\) from both sides:
   • \(2x = 8\)
5. Divide both sides by \(2\):
   • \(x = 4\).

So the value of \(x\) is:

• x = 4.

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Question 3 To find an equation that has the same solution as \(x - 12 = 40\):

• Solving this gives \(x = 52\). The equation that would yield this solution is:
• \(x + 12 = 52\) (not listed, but \(x + 12 = -40\) or \(12 - x = 40\) doesn't give the same solution).

Among the options given, the closest valid choice is:

• \(12 - x = 40\) (which results in \(x = -28\), but seems to be a different approach).

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Question 4 To solve the formula \(A = 2\pi r + h\) for \(r\), you would rearrange it:

1. Subtract \(h\) from both sides: \(A - h = 2\pi r\).
2. Divide by \(2\pi\):

• \(r = \frac{A - h}{2\pi}\).

So the answer is:

• \(r = \frac{A - h}{2\pi}\).

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Question 5 Let \(w\) be width. Then the length \(l = 2w - 4\). The formula for perimeter \(P = 2(l + w)\). Given that \(P = 100\):

• \(2((2w - 4) + w) = 100\)
• \(2(3w - 4) = 100\)
• \(3w - 4 = 50\)
• \(3w = 54\)
• \(w = 18\).

So the width is:

• 18m.

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Question 6 For \( n + (n - 1.5) = 8 \):

• Step 1: Combine like terms.

  • Rational: Combine Like Terms

• Step 2: Add \(1.5\) to both sides.

  • Rational: Addition Property of Equality

• Step 3: Divide by \(2\).

  • Rational: Division Property of Equality.

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Question 7 To solve \(3x - 5 = 26\), the best first step is:

• Add 5 to both sides of the equation.

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Question 8 Based on the chart provided, the relationship can be expressed as:

• \(r = 150h\) (indicating 150 runners for every hour worked).

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Question 9 Using the equation \(y - 5 = x^3\), the values can be filled in by substituting \(x\):

• For \(x = 1\), \(y = 1^3 + 5 = 6\).
• For \(x = 0\), \(y = 0^3 + 5 = 5\).
• So, based on patterns \(x = 2\), gives \(y = 2^3 + 5 = 13\); \(x = 3\), gives \(y = 27 + 5 = 32\); etc.

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Question 10 To isolate \(h\) in \(h/7 + 2 = 11\):

1. Subtract \(2\) from both sides: \(h/7 = 9\).
2. Multiply both sides by \(7\).

So, the correct steps are:

• Subtract 2 from both sides of the equation. Then multiply both sides by 7.

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Question 11 To solve \(14 - x = 3\), the first logical step is:

• Add \(x\) to both sides.

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Question 12 To solve \(x + 1 \geq 5\) and \(2x \geq 4\):

1. From \(x + 1 \geq 5\), we have \(x \geq 4\).
2. From \(2x \geq 4\), we have \(x \geq 2\). The more restrictive constraint is:

• {x | x ≥ 4}.

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Question 13 For \(3x - 5 = 10\) and \(5x + 4 > 14\):

1. From \(3x - 5 = 10\) → \(3x = 15\) → \(x = 5\).
2. From \(5x + 4 > 14\) → \(5x > 10\) → \(x > 2\).

Thus the solution set is:

• {x | x > 5}.

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Question 14 The dehumidifier removes water at a rate of \(2\) quarts/hour and has a maximum capacity of \(50\) quarts:

• Thus, the inequality representing the number of hours \(h\) is:
• \(2h \leq 50\).

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Question 15 Text messages cost $0.15 each, and you can spend up to $10:

• The inequality that represents maximum messages \(m\) is:
• \(0.15m \leq 10\).

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Question 16 Let "n" be the number of countries Jason needs:

• He has 99 and wants 195, so:
• \(99 + 4w = 195\).
• Rearranging gives \(4w = 96 \Rightarrow w = 24\).

Final Answer: Jason needs to work for 24 weeks.

Answer 2

Q6 step 3 says n=4,75 Rational
Multiplication property of Equality
Subtraction property of Equality
Combine like terms

Answer 3

In Question 6, let's clarify each step and their corresponding rationalizations:

• Given: \(n + (n - 1.5) = 8\)

1. Step 1: Combine the terms.

   • Equation: \(2n - 1.5 = 8\)
   • Rational: Combine Like Terms (This is the explanation for Step 1).

2. Step 2: Add \(1.5\) to both sides to isolate \(2n\).

   • Equation: \(2n = 9.5\)
   • Rational: Addition Property of Equality (This is the explanation for Step 2).

3. Step 3: Divide both sides by \(2\) to solve for \(n\).

   • Equation: \(n = 4.75\)
   • Rational: Division Property of Equality (This is the correct explanation for Step 3; it divides both sides by 2).

Summary for Step 3:

For Step 3, the proper justification should be:

• Rational: Division Property of Equality.

If you're looking for the correct rationalization for Step 3 as it relates to the final form \(n = 4.75\), ensure to use the Division Property of Equality. If you have other options available and need to select one for the Step 3 explanation, it would likely be "Division Property of Equality".

If you need to drag and drop:

• Insert Division Property of Equality next to Step 3.

Thank you for your patience, and let me know if there's anything else you'd like to clarify!

Answer 4

Q4 Use the equation y-5=x/3 to fill in the missing values in the table below.
Chart
x y
_ 1
-3 4
0 _
6 _
_ 8

Responses
5
12
7
9
-12
0
1

Answer 5

To fill in the missing values from the equation \(y - 5 = \frac{x}{3}\), we can isolate \(y\):

\[ y = \frac{x}{3} + 5 \]

Now, we can calculate the corresponding values of \(y\) for the given values of \(x\) and also find corresponding \(x\) values for the given \(y\) values.

Given table:

| x | y | |-------|-------| | _ | 1 | | -3 | 4 | | 0 | _ | | 6 | _ | | _ | 8 |

1. For \(y = 1\): \[ 1 = \frac{x}{3} + 5 \ -4 = \frac{x}{3} \ x = -12 \] So, the first row is \((-12, 1)\).

2. For \(x = -3\): \[ y = \frac{-3}{3} + 5 \ y = -1 + 5 \ y = 4 \] This row is already filled.

3. For \(x = 0\): \[ y = \frac{0}{3} + 5 \ y = 0 + 5 \ y = 5 \] So, the row for \(x = 0\) is \((0, 5)\).

4. For \(x = 6\): \[ y = \frac{6}{3} + 5 \ y = 2 + 5 \ y = 7 \] So, the row for \(x = 6\) is \((6, 7)\).

5. For \(y = 8\): \[ 8 = \frac{x}{3} + 5 \ 3 = \frac{x}{3} \ x = 9 \] So, the last row is \((9, 8)\).

Completed table:

| x | y | |-------|-------| | -12 | 1 | | -3 | 4 | | 0 | 5 | | 6 | 7 | | 9 | 8 |

Summary of answers for missing values:

• For \(x\) when \(y = 1\): -12
• For \(y\) when \(x = 0\): 5
• For \(y\) when \(x = 6\): 7
• For \(x\) when \(y = 8\): 9

The answers that fit from your response options are:

• -12 (for \(y = 1\))
• 5 (for \(x = 0\))
• 7 (for \(x = 6\))
• 9 (for \(y = 8\))

Answer 6

Q16 Final answer choices
Jason will need to collect 24 coins per week to get coins from all the countries
It will take Jason 24 weeks to have coins from all the countries.
It will take Jason 20 weeks to have coins from all the countries.
Jason will need to collect 20 coins per week to get coins from all the counties.

Answer 7

To solve the problem, let's summarize the information given about Jason's coin collection:

• Jason currently has coins from 99 countries.
• He wants to collect coins from a total of 195 countries.
• He plans to add 4 new countries to his collection each week.

Set Up the Equation

The total number of new countries Jason needs to collect is:

\[ 195 - 99 = 96 \text{ countries} \]

Next, since Jason collects coins from 4 new countries each week, the equation for the number of weeks \(w\) needed to collect these countries is:

\[ 4w = 96 \]

Solve for \(w\)

Now, we can solve for \(w\):

\[ w = \frac{96}{4} \ w = 24 \]

Conclusion

Thus, it will take Jason 24 weeks to collect coins from all the countries.

Final Answer Choices

Based on this calculation, the correct option is:

• It will take Jason 24 weeks to have coins from all the countries.