Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point)
Responses
Division Property of Equality
Division Property of Equality
Addition Property of Equality
Addition Property of Equality
Identity Property of Multiplication
Identity Property of Multiplication
Subtraction Property of Equality
Subtraction Property of Equality
Bot GPT 3.5 is incorrect, the right answer for this question is: "Division property of equality"
Apologies for the incorrect response. You are correct, the last property of equality used to justify the solution to this problem is the Division Property of Equality.
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The population of moose in a forest is 200, and it is decreasing by 15 moose each year. In the same forest, there are 150 mountain goats. The number of mountain goats is decreasing by 5 mountain goats each year. Let n be the number of years. Supply the numbers to complete the linear equation that can be used to find the number of years it will take for the populations of these two animals to be equal. Then, solve the equation.(2 points)
200−
n=150−
n
It will take
years for the population of moose and mountain goats to be equal.
Sure, let's solve the equation:
"Four times the sum of a number and four" can be represented as 4(x + 4).
"Two multiplied by two less than three times the number" can be represented as 2(3x - 2).
The equation can be written as:
4(x + 4) = 2(3x - 2).
Expanding the equation, we get:
4x + 16 = 6x - 4.
To solve for x, we'll first isolate the variable terms by subtracting 4x from both sides:
4x - 4x + 16 = 6x - 4 - 4x,
16 = 2x - 4.
Next, we'll isolate the constant term by adding 4 to both sides:
16 + 4 = 2x - 4 + 4,
20 = 2x.
Finally, we'll divide both sides by 2 to solve for x:
20 / 2 = 2x / 2,
10 = x.
So, the solution to the problem is x = 10.
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When using the most efficient method to solve the following problem, what step is performed first? Enter 1 for Distributive Property or 2 for Subtraction Property of Equality.
2(x+3)=5x−2
(1 point)
When using the most efficient method to solve the equation 2(x+3) = 5x - 2, the step performed first is the Distributive Property. Therefore, the correct answer is 1 for the Distributive Property.
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Arthur writes the equation a=10b−7. He wants to rewrite it in terms of b. In Arthur’s first step, what value should he add to both sides of the equation?(1 point)
To rewrite the equation a = 10b - 7 in terms of b, Arthur should add 7 to both sides of the equation.
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Tilda writes the equation 5y=20x+8. She wants to rewrite the equation in terms of x. After subtracting 8 from both sides of the equation, what number should she divide both sides of the equation by in order to accomplish this goal?(1 point)
To rewrite the equation 5y = 20x + 8 in terms of x, Tilda should first subtract 8 from both sides of the equation:
5y - 8 = 20x.
To isolate x, she should then divide both sides of the equation by 20. Therefore, the number Tilda should divide both sides of the equation by is 20.
Bot GPT 3.5 You are amazing, you were right with every answer
Thank you for the kind words! I'm here to help you with any questions you have. If you need any further assistance, feel free to ask!
Bot GPT 3.5 was incorrect on 2 answers, i got a 4/6 :(
To complete the equation, we need to supply the missing numbers:
200 - 15n = 150 - 5n.
To solve the equation, we'll first combine like terms by subtracting 150 from both sides:
200 - 150 - 15n = 150 - 150 - 5n,
50 - 15n = -5n.
Next, we'll add 5n to both sides to isolate the variable:
50 - 15n + 5n = -5n + 5n,
50 - 10n = 0.
Now, we'll subtract 50 from both sides:
50 - 50 - 10n = 0 - 50,
-10n = -50.
Finally, we'll divide both sides by -10 to solve for n:
(-10n) / -10 = (-50) / -10,
n = 5.
Therefore, it will take 5 years for the population of moose and mountain goats to be equal.
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Four times the sum of a number and four is the same as two multiplied by two less than three times the number. What is the solution to this problem?(1 point)
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Complete the following statements with the correct words.(1 point)
An object that is stationary has
energy. When the object is pushed, that energy transfers to
energy. Throughout this energy transfer, the object's total energy
.
An object that is stationary has potential energy. When the object is pushed, that energy transfers to kinetic energy. Throughout this energy transfer, the object's total energy remains constant.
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When a baseball is at rest and then is thrown, what is the relationship between the ball’s potential and kinetic energy?(1 point)
Responses
As the ball’s potential energy decreases, its kinetic energy increases.
As the ball’s potential energy decreases, its kinetic energy increases.
As the ball’s potential energy increases, its kinetic energy increases.
As the ball’s potential energy increases, its kinetic energy increases.
As the ball’s potential energy increases, its kinetic energy decreases.
As the ball’s potential energy increases, its kinetic energy decreases.
As the ball’s potential energy decreases, its kinetic energy decrease
As the ball's potential energy decreases, its kinetic energy increases.
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A student drops a ball from a height of 60 meters. The table below shows the ball’s speed and height as time passes.
At what point in time does the ball have the highest kinetic energy?
(1 point)
Responses
At the start (0 seconds)
At the start (0 seconds)
After 0.5 seconds
After 0.5 seconds
After 2 seconds
After 2 seconds
After 2.5 seconds
The point in time when the ball has the highest kinetic energy is after 2.5 seconds.
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A student observes a roller coaster at locations A, B, C, and D on the track.
Which statement is true according to the bar graph?
(1 point)
Responses
The roller coaster creates potential energy, but kinetic energy does not change.
The roller coaster creates potential energy, but kinetic energy does not change.
Both potential and kinetic energy change, but total energy does not change.
Both potential and kinetic energy change, but total energy does not change.
The roller coaster creates kinetic energy.
The roller coaster creates kinetic energy.
The roller coaster destroys potential energy.
The correct statement according to the bar graph is: "Both potential and kinetic energy change, but total energy does not change."
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When the pendulum shown below swings from point A to point B, what happens to its total mechanical energy (ignoring friction)?
(1 point)
Responses
Total mechanical energy goes down.
Total mechanical energy goes down.
Total mechanical energy goes up.
Total mechanical energy goes up.
Total mechanical energy is not conserved.
Total mechanical energy is not conserved.
Total mechanical energy stays the same.
When the pendulum swings from point A to point B, ignoring friction, the total mechanical energy stays the same.
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A model roller coaster rolls from point X to point Y. Describe the energy transformation.
(1 point)
Responses
Kinetic energy transfers to potential energy, then some potential energy transfers to kinetic energy.
Kinetic energy transfers to potential energy, then some potential energy transfers to kinetic energy.
Thermal energy transfers to potential energy, then some potential energy transfers to thermal energy.
Thermal energy transfers to potential energy, then some potential energy transfers to thermal energy.
Kinetic energy transfers to potential energy, then some potential transfers to thermal energy.
Kinetic energy transfers to potential energy, then some potential transfers to thermal energy.
Potential energy transfers to kinetic energy, then some kinetic energy transfers to potential energy.