A student collects data during an investigation about inertia and acceleration. If the force acting on the objects is constant, which statement about inertia and acceleration is supported by the data? (1 point) Responses An object with a higher mass has more inertia which causes it to speed up less quickly. An object with a higher mass has more inertia which causes it to speed up less quickly. An object with less mass has more inertia which causes it to speed up more quickly. An object with less mass has more inertia which causes it to speed up more quickly. An object with less mass has less inertia which causes it to speed up less quickly. An object with less mass has less inertia which causes it to speed up less quickly. An object with a higher mass has less inertia which causes it to speed up more quickly.
An object with a higher mass has more inertia which causes it to speed up less quickly.
The picture shows a physics lab set up. Why does the disc fall straight down into the glass when we quickly pull the index card away from the glass in a horizontal direction? (1 point) Responses equilibrium equilibrium static friction static friction inertia inertia kinetic friction
The correct answer is inertia. When the index card is quickly pulled away in a horizontal direction, the disc tends to remain at rest due to its inertia. As a result, the disc falls straight down into the glass as it resists the change in its state of motion.
A student is riding the school bus. The bus stops as the driver applies the brakes. Which of these statements best describes this situation?(1 point) Responses There is no force acting on the bus so it stops moving. There is no force acting on the bus so it stops moving. The school bus does not lose or gain kinetic energy. The school bus does not lose or gain kinetic energy. A force is changing the motion of the bus. A force is changing the motion of the bus. The bus is gaining energy because of friction. The bus is gaining energy because of friction.
A force is changing the motion of the bus.
A pitcher throws a baseball to the catcher. The ball's path begins as a straight line, and then its patch curves toward the ground. Which two forces are acting on the baseball?(1 point) Responses
electricity and friction
gravity and friction
inertia and magnetism
nuclear and inertia
Gravity and friction are the two forces acting on the baseball.
Two people are in a rowboat on a river. The current of the river water carries them at a speed of five meters per second even when they are not rowing. What will happen to the boat's motion of no other forces act on the boat?(1 point)
The boat's speed will increase.
The boat's speed will decrease.
The boat's speed will stay the same.
The boat will change direction.
The boat's speed will stay the same.
Inertia is
the resistance of an object to change its motion.
an object's motion.
a moving object's speed and direction.
a force that acts on a resting object.
The resistance of an object to change its motion.
You are sitting in a stopped bus. When the bus starts moving forward, you appear to move backward relative to the bus. Which statement best explains this observation?
The force of inertia on you balances the force from the motion of the bus.
Inertia prevents the force of the bus from acting on you.
The bus moves forward, while inertia keep you in place.
The motion of the bus creates an unbalanced backward force on you.
Which statement best explains why a paper airplane eventually falls to the ground?
The force from throwing the airplane loses strength as the airplane moves.
Inertia creates the new forces acting on the airplane to keep it up.
Inertia acts as a balanced force that slows the airplane and pulls it down.
The unbalanced forces of air resistance and gravity slow the airplane and pull it down.
The unbalanced forces of air resistance and gravity slow the airplane and pull it down.
Solve the system of equations. x=6y−3 2x+7y=13 (1 point)
To solve the system of equations:
x = 6y - 3
2x + 7y = 13
We can start by substituting the value of x from the first equation into the second equation:
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
Now, we isolate y by adding 6 to both sides of the equation:
19y = 19
Dividing both sides of the equation by 19, we get:
y = 1
Now that we have the value of y, we can substitute it back into the first equation to solve for x:
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
Solve the system of equations. 8x−3y= −22 y=10+4x (1 point)
To solve the system of equations:
8x - 3y = -22
y = 10 + 4x
We can substitute the value of y from the second equation into the first equation:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
Combine like terms:
-4x - 30 = -22
Add 30 to both sides of the equation:
-4x = 8
Divide both sides of the equation by -4:
x = -2
Now, substitute the value of x back into the second equation to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
Solve the system of equations. 5x+2y=14 x−6y=22 (1 point)
To solve the system of equations:
5x + 2y = 14
x - 6y = 22
We can start by solving one of the equations for one variable and substitute it into the other equation.
Let's solve the second equation for x:
x = 22 + 6y
Now, substitute this value of x into the first equation:
5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
Combine like terms:
32y + 110 = 14
Subtract 110 from both sides of the equation:
32y = -96
Divide both sides of the equation by 32:
y = -3
Now substitute this value of y back into the second equation to solve for x:
x - 6(-3) = 22
x + 18 = 22
Subtract 18 from both sides of the equation:
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -3.
Solve the system of equations. –9x+y=12 2x+4y= −28 (1 point)
To solve the system of equations:
-9x + y = 12
2x + 4y = -28
We can solve this system of equations by using the method of substitution or elimination. I will use the method of elimination.
Multiply the first equation by 4 to get rid of the y-term:
-36x + 4y = 48
Now, we can subtract the new equation from the second equation:
(2x + 4y) - (-36x + 4y) = -28 - 48
Simplify:
2x + 4y + 36x - 4y = -76
Combine like terms:
38x = -76
Divide both sides of the equation by 38:
x = -2
Now substitute the value of x back into the first equation to solve for y:
-9(-2) + y = 12
18 + y = 12
Subtract 18 from both sides of the equation:
y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
How many solutions does the system of equations have? 6x+2y=−18 3x+y=24 (1 point)
To determine the number of solutions the system of equations has, we can examine whether the lines represented by the equations are parallel, coincident, or intersecting.
Given the system of equations:
6x + 2y = -18
3x + y = 24
We can rewrite the second equation in terms of y:
y = 24 - 3x
By comparing coefficients, we can see that the slopes of the two lines are not equal. The slope of the first line is -3, while the slope of the second line is -2/3. Since the slopes are not equal, the lines are not parallel.
To determine if the lines are coincident or intersecting, we can compare the y-intercepts.
For the first equation, when x = 0, we have:
6(0) + 2y = -18
2y = -18
y = -9
For the second equation, when x = 0, we have:
3(0) + y = 24
y = 24
Since the y-intercepts are not equal, the lines are not coincident.
Therefore, since the lines are not parallel or coincident, they must intersect at a single point.
Therefore, the system of equations has one solution.
are you sure?
I apologize for the mistake. Let's double-check the calculations.
The system of equations is:
6x + 2y = -18
3x + y = 24
To solve this system, we can use the method of substitution or elimination.
Using the second equation, we can solve for y:
y = 24 - 3x
Now, substitute this value of y into the first equation:
6x + 2(24 - 3x) = -18
Simplify:
6x + 48 - 6x = -18
Combine like terms:
48 = -18
This is a contradiction. The equation is not true for any value of x or y.
Therefore, the system of equations has no solution.
I apologize for the confusion caused by the previous incorrect response.
Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point) Responses (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (−2, −4) left parenthesis negative 2 comma negative 4 right parenthesis (2, 10) left parenthesis 2 comma 10 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis
To solve the system of equations using substitution:
y = 2 + 3x
4x - 3y = -16
Step 1: Solve the first equation for y:
y = 2 + 3x
Step 2: Substitute the expression for y in the second equation:
4x - 3(2 + 3x) = -16
Step 3: Simplify and solve for x:
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
Step 4: Substitute the value of x back into the first equation to solve for y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8).
Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point) Responses (−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (5.25, 1.25) left parenthesis 5.25 comma 1.25 right parenthesis (−6, −1) left parenthesis negative 6 comma negative 1 right parenthesis (4, 1)
To solve the system of equations:
2x + 6y = -18
x = 5y - 1
We can substitute the value of x from the second equation into the first equation:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
Combine like terms:
16y - 2 = -18
Add 2 to both sides of the equation:
16y = -16
Divide both sides of the equation by 16:
y = -1
Now substitute this value of y back into the second equation to solve for x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is x = -6 and y = -1.
Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses
(2, −4)
(−2, 8)
(12, 12)
(2,-2)
To solve the system of equations:
3x + y = 2
7x - 4y = 30
We can solve this system of equations by using the method of substitution.
Let's solve the first equation for y:
y = 2 - 3x
Now, substitute this value of y into the second equation:
7x - 4(2 - 3x) = 30
Simplify:
7x - 8 + 12x = 30
19x - 8 = 30
Add 8 to both sides of the equation:
19x = 38
Divide both sides of the equation by 19:
x = 2
Now substitute the value of x back into the first equation to solve for y:
3(2) + y = 2
6 + y = 2
Subtract 6 from both sides of the equation:
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
The correct response is (2, -4).
Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point) Responses (−35, −3) left parenthesis negative 35 comma negative 3 right parenthesis (−5, 3) left parenthesis negative 5 comma 3 right parenthesis (35, −3) left parenthesis 35 comma negative 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis
To solve the system of equations:
-4x + 6y = 38
x - 5y = -20
We can use the method of elimination to solve this system.
Multiply the second equation by 4 to simplify the coefficients of x:
4(x - 5y) = 4(-20)
4x - 20y = -80
Now, we can add the two equations together:
-4x + 6y + (4x - 20y) = 38 + (-80)
Simplify:
-14y = -42
Divide both sides of the equation by -14:
y = 3
Now substitute this value of y back into the second equation to solve for x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3.
The correct response is (-5, 3).
How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36
To determine the number of solutions the system of equations has, we can examine whether the lines represented by the equations are parallel, coincident, or intersecting.
Given the system of equations:
-5x + y = -18
10x - 2y = 36
Let's rearrange the second equation to simplify it:
10x - 2y = 36
5x - y = 18
We can see that the coefficients of x and y are proportional in the two equations, but the constant terms are not equal. This means that the lines represented by the equations are parallel and will never intersect.
Therefore, the system of equations has no solution.
In other words, the lines represented by the equations do not intersect, so there are no values of x and y that simultaneously satisfy both equations.
are you sure?
Apologies for the confusion in my previous response. Allow me to recalculate and provide the correct answer.
To solve the system of equations:
-5x + y = -18
10x - 2y = 36
We can try to eliminate one variable by multiplying one or both equations by a constant to make the coefficients of one variable the same but opposite in sign.
In this case, let's multiply the first equation by 2:
-10x + 2y = -36
10x - 2y = 36
Now, we can add the two equations:
(-10x + 2y) + (10x - 2y) = -36 + 36
Simplifying, we get:
0 = 0
This means the two equations are equivalent and represent the same line.
Therefore, the system of equations has infinitely many solutions.
In other words, any point that satisfies one equation will automatically satisfy the other equation as well.
are.you.sure???
I apologize for the confusion caused by my previous incorrect response.
Let's recalculate and provide the correct answer.
To solve the system of equations:
-5x + y = -18
10x - 2y = 36
We can use the method of elimination to solve this system.
Multiply the first equation by 2 to simplify the coefficients of y:
2(-5x + y) = 2(-18)
-10x + 2y = -36
Now, we can eliminate the y variable by adding the two equations together:
(-10x + 2y) + (10x - 2y) = -36 + 36
Simplifying, we get:
0 = 0
This equation is always true, indicating that the two equations represent the same line and have infinitely many solutions.
Therefore, the system of equations has