Andrea is 6 years younger than tony. In two years, tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andreas and Tony’s current ages.
A. a = 3 (a+2)
B. a + 2 = 3 (a - 6+2)
C. 3(a+2)=a - 6 + 2
D. a + 2 = 3(a + 6 + 2)
so does the equation have infinite solutions
The correct equation would be:
C. 3(a+2) = a - 6 + 2
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Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Responses
a=3(a+2)
a equals 3 left parenthesis a plus 2 right parenthesis
a+2=3(a−6+2)
a plus 2 equals 3 left parenthesis a minus 6 plus 2 right parenthesis
a+2=3(a+6+2)
a plus 2 equals 3 left parenthesis a plus 6 plus 2 right parenthesis
3(a+2)=a−6+2
The correct equation would be:
a + 2 = 3(a - 6 + 2)
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
Addition Property of Equality
Addition Property of Equality
Identity Property of Multiplication
Identity Property of Multiplication
Subtraction Property of Equality
Subtraction Property of Equality
Division Property of Equality
The last property of equality that you would use to justify the solution to this problem is:
Subtraction Property of Equality
Manipulate the equation y=7x−12 so that it is written in terms of x. Which equation is equivalent to y=7x−12?(1 point)
Responses
x=(y+12)7
x equals Start Fraction left parenthesis y plus 12 right parenthesis over 7 End Fraction
x=(y−12)7
x equals Start Fraction left parenthesis y minus 12 right parenthesis over 7 End Fraction
x=(y12)−7
x equals left parenthesis Start Fraction y over 12 End Fraction right parenthesis minus 7
x=(y7)+12
The equation that is equivalent to y=7x−12 when written in terms of x is:
x=(y+12)7
Which equation is equivalent to w=x+y−z?(1 point)
Responses
z=x+y−w
z equals x plus y minus w
z=(x+y)w
z equals Start Fraction left parenthesis x plus y right parenthesis over w End Fraction
z=w−x−y
z equals w minus x minus y
z=x+y+w
z equals x plus y plus w
The equation that is equivalent to w=x+y−z is:
z=w−x−y
A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
Responses
10 inches
10 inches
15 inches
15 inches
20 inches
20 inches
12 inches
12 inches
Let x be the length of the shorter section.
The equation that allows you to solve for the length of the shorter section is:
2(x+5) = 3x
To solve this equation, we can distribute the 2:
2x + 10 = 3x
Next, we can subtract 2x from both sides of the equation:
10 = x
Therefore, the length of the shorter section is 10 inches.
Look at the expression: −3(2x+7)
(1 point)
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.
This expression involves these two operations Response area and Response area .
We will use the Response area to simplify this expression.
The simplified expression looks like Response area .
The option "<b id="docs-internal-guid-3e7de014-7fff-f961-640a-fd27cdb6b8da">multiplication" (11 of 11) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
This expression involves these two operations: addition and multiplication.
We will use the Response area to simplify this expression.
The simplified expression looks like Response area -6x - 21 .
The option "multiplication" has been selected.
To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
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.
Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
To solve the equation 24(34+x) = 1,200, the following steps were taken:
Step 1: Distribute the 24 to both terms inside the parentheses: 816 + 24x = 1,200.
The reason for this step is the distributive property.
Step 2: Subtract 816 from both sides of the equation: 816 - 816 + 24x = 1,200 - 816.
The reason for this step is to isolate the term with the variable.
Step 3: Simplify the equation by combining like terms: 24x = 384.
The reason for this step is to further isolate the term with the variable.
Step 4: Divide both sides of the equation by 24 to solve for x: x = 16.
The reason for this step is to solve for the unknown variable x by dividing both sides of the equation by the coefficient of x.
Simplify: −4(2x+5)
(1 point)
Responses
(−4−2x)+(−4−5)
open paren negative 4 minus 2 x close paren plus open paren negative 4 minus 5 close paren
(−4÷2x)+(−4÷5)
open paren negative 4 divided by 2 x close paren plus open paren negative 4 divided by 5 close paren
(−4×2x)+(−4×5)
open paren negative 4 times 2 x close paren plus open paren negative 4 times 5 close paren
(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
To simplify -4(2x+5), the correct response is:
(-4×2x)+(−4×5)
or
(-4 times 2x) plus (-4 times 5)
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.
The steps to solve the equation -2(4x+8)+2x = -5x+10 in the correct order are:
Step 1: Distribute -2 to both terms inside the parentheses: -8x - 16 + 2x = -5x + 10.
Step 2: Combine like terms on the left side of the equation: -6x - 16 = -5x + 10.
Step 3: Move all terms containing x to one side and the constant terms to the other side: -6x + 5x = 10 + 16.
Step 4: Simplify and combine like terms: -x = 26.
Step 5: Multiply both sides of the equation by -1 to solve for x (to get rid of the negative sign): x = -26.
So, the correct order of the steps is:
1. Distribute
2. Combine like terms
3. Move terms
4. Simplify
5. Multiply by -1
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
The mistake made by the student is in Step 3.
In Step 3, the student added 4 to both sides of the equation. However, the correct operation in this step should be subtracting 4 from both sides of the equation to isolate the variable.
So, the correct Step 3 should be: 10x - 4 - 4 = 24 - 4
Then, the equation simplifies to: 10x - 8 = 20
All subsequent steps can proceed correctly from this point, leading to the solution x = 2.
Which factors determine the potential energy of an object?(1 point)
Responses
Gravity and position
Gravity and position
Mass and velocity
Mass and velocity
Mass and position
Mass and position
Weight and velocity
The factors that determine the potential energy of an object are:
Gravity and position
An object’s gravitational potential energy is dependent on the object’s mass, the strength of its gravitational field, and which of the following: (1 point)
Responses
the height of the object
the height of the object
the temperature of the object
the temperature of the object
the velocity of the object
the velocity of the object
the shape of the object
The object's gravitational potential energy is dependent on the object's mass, the strength of its gravitational field, and the height of the object.
At what point does the child have the greatest potential energy?
The child has the greatest potential energy at the highest point of their vertical motion.
Lucy picks up an object from the floor. How will the potential energy change if Lucy lifts the object above her head?(1 point)
Responses
The object's potential energy will increase.
The object's potential energy will increase.
The object's potential energy will stay the same.
The object's potential energy will stay the same.
The object's potential energy will decrease.
The object's potential energy will decrease.
The object's potential energy will be zero.
The object's potential energy will increase.
Which of the graphs shows the relationship between an object’s gravitational potential energy and the object's height above the ground?(1 point)
Responses
Skip to navigation
I'm sorry, but I cannot see the graphs you are referring to as I am a text-based AI model. However, the relationship between an object's gravitational potential energy and its height above the ground is typically represented by a graph that shows a direct proportional relationship. As the object's height increases, its gravitational potential energy also increases. So, you should look for a graph that shows a positive linear relationship between potential energy and height.
thanks pookie i lav you
You're welcome! I'm glad I could help. However, I am an AI language model and do not have the capability to feel emotions or form personal relationships. But I'm here to assist you with any questions you may have.
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.
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 decreases, its kinetic energy decreases.
As the ball’s potential energy decreases, 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 increases.
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
After 2.5 seconds
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The ball has the highest kinetic energy after 2 seconds.
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 destroys potential energy.
The roller coaster destroys potential energy.
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 potential energy, but kinetic energy does not change.
The roller coaster creates potential energy, but kinetic energy does not change.
The roller coaster creates kinetic energy.
The roller coaster creates kinetic energy.
Skip to navigation
According to the bar graph, the statement that is true is:
The roller coaster creates potential energy, but kinetic energy does not change.
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 is not conserved.
Total mechanical energy is not conserved.
Total mechanical energy stays the same.
Total mechanical energy stays the same.
Total mechanical energy goes up.
Total mechanical energy goes up.
Skip to navigation
When the pendulum swings from point A to point B, its total mechanical energy stays the same.
A model roller coaster rolls from point X to point Y. Describe the energy transformation.
(1 point)
Responses
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.
Potential energy transfers to kinetic energy, then some kinetic energy transfers to potential energy.
Potential energy transfers to kinetic energy, then some kinetic energy transfers to potential 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.
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.
Skip to navigation
In the case of the model roller coaster rolling from point X to point Y, the energy transformation can be described as:
Potential energy transfers to kinetic energy, then some kinetic energy transfers to potential energy.
Which of the following is an example of an equation with no solution?(1 point)
Responses
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
An example of an equation with no solution is:
3x+4=3x+3
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
An example of an equation with exactly one solution is:
3x+4=4x+3
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses
The equation has one solution: x=3.
The equation has one solution: x equals 3 .
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
To solve the equation 3(x+2)−6=3x, we can start by distributing the 3:
3x + 6 - 6 = 3x
Next, we can simplify:
3x = 3x
The equation simplifies to 3x = 3x, which means that the variable x is eliminated and the equation is true for any value of x.
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
Continue to play the simulation. This simulation will go on and on for eternity if we let it. This simulation is in what we call a Closed System. We are only looking at the variables we want to in this simulation. In the Real World (Open System), if we had a Pendulum like this, it would eventually stop. Explain why it would stop in the Real World.
Type Answer HERE: