The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 m^2, what is the length and the width?
(3 points)
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An expression for the length of the rectangle in terms of the width would be Response area
The formula for the area of a rectangle is Response area
Using trial and error, if the area is 96 m^2, then the length and width are
The expression for the length of the rectangle in terms of the width would be 2w - 4.
The formula for the area of a rectangle is length * width.
Using trial and error, if the area is 96 m^2, then the length and width are 12 m and 8 m, respectively.
Match the equation with its solution(s).(5 points)
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3(2i+7)=6i+21
3i+5=2i−7
3i+2i−7=18
3(2i−7)=15
3i+5=3i+7
The equations with their corresponding solutions are:
1. 3(2i+7)=6i+21 - i = 14/3
2. 3i+5=2i−7 - i = -12
3. 3i+2i−7=18 - i = 25/5
4. 3(2i−7)=15 - i = 36/3
5. 3i+5=3i+7 - No solution
WRONG
I apologize for the incorrect response. Here are the correct matches:
1. 3(2i+7)=6i+21 - i = 0
2. 3i+5=2i−7 - i = -12
3. 3i+2i−7=18 - i = 5
4. 3(2i−7)=15 - No solution
5. 3i+5=3i+7 - No solution
1 4 and 5 are wrong
My apologies for the mistakes. Here are the correct matches:
1. 3(2i+7)=6i+21 - i = -2
2. 3i+5=2i−7 - i = -12
3. 3i+2i−7=18 - i = 8
4. 3(2i−7)=15 - No solution
5. 3i+5=3i+7 - No solution
WRONG those are not in the answer choices
I apologize for the confusion. Here are the correct matches according to the given answer choices:
1. 3(2i+7)=6i+21 - i = -2
2. 3i+5=2i−7 - i = -12
3. 3i+2i−7=18 - No solution
4. 3(2i−7)=15 - i = 3
5. 3i+5=3i+7 - No solution
Discussion Protocols Quick Check
2 of 42 of 4 Items
Question
Which type of question creates an effective discussion?(1 point)
Responses
leading
leading
vague
vague
clarification
clarification
close-ended
Discussion Protocols Quick Check
2 of 42 of 4 Items
Question
Which type of question creates an effective discussion?(1 point)
Responses
leading
leading
vague
vague
clarification
clarification
close-ended
The correct answer is "clarification."
3(2i+7)=6i+21
To solve the equation 3(2i+7) = 6i+21, we can start by distributing the 3 to the terms inside the parentheses:
6i + 21 = 6i + 21
At this point, we can see that both sides of the equation are equal. Since they are the same, the solution to the equation is all real numbers.
is it infinite solutions or no solutions or one soulition
Apologies for the mistake in my previous response. Let's re-evaluate the equation:
3(2i+7) = 6i+21
Expanding the left side of the equation, we get:
6i + 21 = 6i + 21
We notice that the variables are eliminated, and the equation simplifies to:
21 = 21
This equation is always true, regardless of the value of i. Therefore, the equation has infinite solutions.
4. Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8
(5 points)
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Step 1: Property to get
simplified equation
Step 2: Property to get Response area simplified equation
For this equation, there is/are
Step 1: Distributive property to simplify the equation:
2(x+8) = 2x + 16
Step 2: Simplifying the right side of the equation:
2x + 16 = 2x + 8
For this equation, there is only one solution, which is x = any real number.
4. Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8
(5 points)
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Step 1: _______Property to get
simplified equation ______________
Step 2: __________Property to get __________ simplified equation
For this equation, there is ___________
Step 1: Distributive property to simplify the equation:
2(x+8) = 2x + 16
Step 2: Simplifying the right side of the equation:
2x + 16 = 2x + 8
For this equation, there is one solution, which is x = 0.
what property was used for step two
Apologies for the confusion. Step 2 does not involve any specific property. It is the result of simplifying both sides of the equation by combining like terms.
. The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 m^2, what is the length and the width?
(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.
An expression for the length of the rectangle in terms of the width would be
The formula for the area of a rectangle is
Using trial and error, if the area is 96 m^2, then the length and width are Response area
An expression for the length of the rectangle in terms of the width would be 2w - 4.
The formula for the area of a rectangle is length * width.
Using trial and error, if the area is 96 m^2, then the length and width are 12 m and 8 m, respectively.
Match the description of the one variable equation with the number of solutions it will have.(4 points)
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x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3
The descriptions of the one-variable equations with the number of solutions they will have are as follows:
1. x-7=7-x - One solution
2. 3(x+5)=3x+5 - Infinite solutions
3. 10-x=25 - One solution
4. 2(x+4)=2x+5+3 - No solution
Explain your answer.
Certainly! Let's go through each equation and explain the number of solutions it will have:
1. x-7=7-x
This equation can be simplified to 2x = 14, and then further simplified to x = 7. Therefore, there is one solution for this equation.
2. 3(x+5)=3x+5
When we distribute the 3 to the terms in the parentheses, the equation becomes 3x + 15 = 3x + 5. Notice that the variable "x" cancels out when subtracting 3x from both sides of the equation. We then have 15 = 5. This implies that the equation is always true, regardless of the value of x. Therefore, there are infinite solutions for this equation.
3. 10-x=25
By subtracting 10 from both sides of the equation, we obtain -x = 15. Multiplying both sides by -1, we find x = -15. Hence, there is one solution for this equation.
4. 2(x+4)=2x+5+3
After distributing the 2 to the terms in the parentheses, we have 2x + 8 = 2x + 8. Notice that the variable "x" cancels out when subtracting 2x from both sides of the equation. We then have 8 = 8. Similar to the second equation, this equation is always true regardless of the value of x. Therefore, there are infinite solutions for this equation.
wrong
Apologies for the previous incorrect response. Here is the correct explanation for each equation:
1. x-7=7-x
By simplifying the equation, we get 2x = 14, which further simplifies to x = 7. Therefore, there is one solution for this equation.
2. 3(x+5)=3x+5
After distributing the 3 to the terms inside the parentheses, the equation becomes 3x + 15 = 3x + 5. Notice that when we subtract 3x from both sides, we are left with 15 = 5, which is not true. This means that there are no solutions for this equation.
3. 10-x=25
By subtracting 10 from both sides, the equation simplifies to -x = 15. When we multiply both sides by -1, we get x = -15. Therefore, there is one solution for this equation.
4. 2(x+4)=2x+5+3
After distributing the 2 to the terms inside the parentheses, the equation becomes 2x + 8 = 2x + 8. Notice that when we subtract 2x from both sides, we are left with 8 = 8, which is always true. This means that there are infinitely many solutions for this equation.
thank youu
You're welcome! If you have any more questions, feel free to ask.
6. A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
Responses
37>2n+24
37 is greater than 2 n plus 24
37≥2n+24
37 is greater than or equal to 2 n plus 24
37<2n+24
37<2n+24
24n+2≥37
The inequality that describes this scenario is:
37 ≥ 2n + 24
explain
Certainly! Let's break down the scenario to determine the correct inequality:
The student wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let's assume the student buys n notebooks. The cost of the notebooks will be n * $2.
The student also wants to buy a calculator that costs $24.
To represent the total cost of the notebooks and the calculator combined, we can write the expression: 2n + 24.
Since the student only has $37 to spend, we can create an inequality to represent this situation. The total cost (2n+24) should not exceed $37.
Therefore, the correct inequality is:
37 ≥ 2n + 24
This inequality states that 37 is greater than or equal to the total cost of the notebooks and the calculator.
7. Solve for b in the following equation: A=12(a+b)
(1 point)
Responses
b=12A−a
b is equal to 1 half cap A minus A
b=2A+a
b is equal to 2 cap A plus A
b=12A+a
b is equal to 1 half cap A plus A
b=2A−a
To solve for b in the equation A = 12(a+b), we can start by isolating b on one side of the equation.
A = 12(a+b)
Let's distribute the 12 to the terms inside the parentheses:
A = 12a + 12b
Next, subtract 12a from both sides to move all the terms involving b to one side:
A - 12a = 12b
Now, divide both sides by 12:
(A - 12a)/12 = b
Simplifying further, we get:
b = (A - 12a)/12
Therefore, the correct response is:
b = (A - 12a)/12
7. Solve for b in the following equation: A=1/2(a+b)
(1 point)
Responses
b=1/2A−a
b is equal to 1 half cap A minus A
b=2A+a
b is equal to 2 cap A plus A
b=1/2A+a
b is equal to 1 half cap A plus A
b=2A−a
To solve for b in the equation A = 1/2(a+b), we can start by isolating b on one side of the equation.
A = 1/2(a+b)
Let's multiply both sides of the equation by 2 to eliminate the fraction:
2A = a + b
Next, subtract 'a' from both sides:
2A - a = b
Therefore, the correct response is:
b = 2A - a
8. Graph the solutions for the inequality: −3x+1≤−47
(2 points)
Responses
To graph the solutions for the inequality -3x + 1 ≤ -47, we can start by treating it as an equation and finding the solution.
-3x + 1 = -47
First, let's subtract 1 from both sides of the equation:
-3x = -48
Next, divide both sides by -3 to solve for x:
x = 16
Since the original inequality is less than or equal to, the solution includes x = 16 and all values less than 16.
To graph this solution, we can plot a closed circle at x = 16 (since it is included in the solution) and shade the region to the left of the vertical line passing through x = 16.
Here is an approximate graph representation:
```plaintext
|
|
|
|
|
----+------------------------
-3 -2 -1 0 1 2 3 x-axis
```
The shaded region would be to the left of the vertical line passing through x = 16.
Please note that the graph is only an approximation and not to scale.
9. A student claims that graph below represents the solutions to the inequality: −4<x
What was the student's mistake?
(1 point)
The student's mistake is that the graph represents the solutions to the inequality -4 < x incorrectly. The student's graph shows a shaded region to the right of the vertical line passing through x = -4, which implies that x is greater than -4. However, the correct solution to the inequality -4 < x is a shaded region to the right of the vertical line passing through x = -4, including x = -4.
Therefore, the student's mistake is not including x = -4 in the shaded region on the graph.
9. A student claims that graph below represents the solutions to the inequality: −4<x
What was the student's mistake?
(1 point)
Responses
The student did not make a mistake; this is the correct graph of the inequality
The student did not make a mistake; this is the correct graph of the inequality
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student should have filled in the point at -4 to show the solution x could be equal to -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student's mistake is:
The student did x is less than -4 when the variable is on the other side; -4 is
12. Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate, how many minutes will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:
Solution:
Meaning of the solution in words: