If a segment has endpoints (0, 4) and (3, 4) , how long will the segment be after it is rotated 270° clockwise?
To find the length of the segment after rotating it 270° clockwise, we can use the distance formula.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Applying the formula to the given endpoints, we have:
d = sqrt((3 - 0)^2 + (4 - 4)^2)
= sqrt(9 + 0)
= sqrt(9)
= 3
Therefore, the length of the segment after rotating it 270° clockwise is 3 units.
A square with sides 6 units in length is reflected across the x -axis. How long are the sides in the reflected figure?
When a figure is reflected across the x-axis, the y-coordinates of its vertices change sign while the x-coordinates remain the same.
In the case of the square with sides of 6 units in length, if we reflect it across the x-axis, the y-coordinate of each vertex will change sign.
The vertices of the original square are as follows:
(0,0), (6,0), (6,6), (0,6)
After reflecting across the x-axis, the y-coordinates change sign:
(0,0) remains the same
(6,0) becomes (6,-0) or simply (6,0) after dropping the negative sign
(6,6) becomes (6,-6)
(0,6) remains the same
The vertices of the reflected square are therefore:
(0,0), (6,0), (6,-6), (0,6)
The length of the sides in the reflected figure remains unchanged. Therefore, the sides of the reflected square are also 6 units in length.
A triangle with an area of 25 square units is rotated 180° clockwise. What is the area of the rotated figure?
When a figure is rotated by 180° clockwise, the shape remains the same but is flipped upside down.
Therefore, rotating a triangle by 180° clockwise doesn't change the area.
So, the area of the rotated figure would still be 25 square units.
Pure water and pure salt are poor conductors of electricity. When salt is dissolved in water, the resulting solution conducts electricity well. Which statement explains why this occurs with these substances?(1 point)
Responses
The process of dissolving frees the electrons in the solution to move.
The process of dissolving frees the electrons in the solution to move.
The process of dissolving more closely binds the electrons in the solution.
The process of dissolving more closely binds the electrons in the solution.
The process of dissolving closely binds the ions in the solution.
The process of dissolving closely binds the ions in the solution.
The process of dissolving frees the atoms in the solution to move.
The correct answer is: The process of dissolving closely binds the ions in the solution.
When salt (sodium chloride) is dissolved in water, it dissociates into positive sodium ions (Na+) and negative chloride ions (Cl-). These ions are then dispersed throughout the water, allowing them to freely move and conduct electricity. Therefore, the process of dissolving closely binds the ions in the solution and enables the flow of electric current.
Pure water and pure salt are poor conductors of electricity. When salt is dissolved in water, the resulting solution conducts electricity well. Which statement explains why this occurs with these substances?
The process of dissolving frees the electrons in the solution to move.
The process of dissolving more closely binds the electrons in the solution.
The process of dissolving closely binds the ions in the solution.
The process of dissolving frees the atoms in the solution to move.
I apologize for the incorrect response in my previous answer. The correct statement that explains why a saltwater solution is a good conductor of electricity is:
The process of dissolving closely binds the ions in the solution.
When salt (sodium chloride) is dissolved in water, it dissociates into positive sodium (Na+) and negative chloride (Cl-) ions. These ions are surrounded by water molecules, which form a solvation shell around each ion. This process closely binds the ions in the solution, allowing them to move freely and carry electric charge, thereby enabling the solution to conduct electricity.
Which statement correctly describes the conductivity of the specified material?(1 point)
Responses
Aluminum has a low conductivity.
Plastics have high conductivity.
Copper has low conductivity.
Gold has high conductivity