Given that th<span>e coordinates of the vertices of △DEF are D(2, −1) , E(7, −1) , and F(2, −3) and the coordinates of the vertices of △D′E′F′ are D′(0, −1) , E′(−5, −1) , and F′(0, −3) .
Notice that the y-coordinates of the pre-image and that of the image are the same, which means that there is a reflection across the y-axis.
A refrection across the y-axis results in the change in sign of the x-coordinates of the pre-image and the image while the y-coordinate of the image remains the same as that of the pre-image.
A refrection across the y-axis of </span>△DEF with vertices D(2, −1) , E(7, −1) , and F(2, −3)
will result in and image with vertices (-2, -1), (-7, -1) and (-2, -3) respectively.
Notice that the x-coordinate of the final image △D′E′F′ with vertices <span>D′(0, −1) , E′(−5, −1) , and F′(0, −3) is 2 units greater than the vertices of the result of recting the pre-image across the y-axis.
This means that the result of refrecting the pre-image was shifted two places to the right.
Therefore, </span>the sequence of transformations that maps △DEF to △D′E′F′ are reflection across the y-axis and translation 2 units right.
The unknown digit is 4 because you must have a number (in the space) that is less than five and more than four because looking at a number like
10 9 8 7 6 5 4 3 2 1 the only while number in between 5 and 3 is 4.
Step-by-step explanation:
Given that,
- Length of the one portion of the board = x feet
- Length of the another portion = (7x – 9) feet
According to the question,
Total length = Sum of the length of the two pieces
Total length = {x + (7x – 9)} feet
Total length = {x + 7x – 9} feet
<u>Total length = (8x – 9) feet</u>
Therefore, the total length of the board as a simplified expression in x is (8x – 9) feet.
<h3>Answer:</h3><h3>T
wo possible smallest and largest angles are 11.78° and 78.22°.</h3>
Step-by-step explanation:
Minigolf ball will follow a trajectory to get into the hole.
Since range of a trajectory is calculated by the formula,
Where u = initial speed of the ball
θ = angle between the hole and direction in which the ball has been projected
g = gravitational pull
Now we plug in the values in the formula,
sin2θ = 
2θ = 
2θ = 23.57° or 156.43°
θ = 11.78° or 78.22°
Hence two possible smallest and largest angles are 11.78° and 78.22°.
