Which sequence of transformations produces an image that is not congruent to the original figure?A. A translation of 3 units to the left followed by a reflection across the x-axis
B. A rotation of 90 clockwise followed by a translation of 6 units to the left
C. A translation of 5 units to the left followed by a dilation of a factor of 2
D. A reflection across the y-axis followed by a rotation of 180counterclockwise
Answers
Answer:
Option C
Step-by-step explanation:
Whenever transformation is done we have either reflection on a given line, or rotation about a fixed point or a dilation by a scale factor
Whenever transformations are reflections over a line, the original figure size will not be altered and hence we have congruent figures.
Similarly for rotations also original figures will not be altered
But whenever a dilaton by a scale factor other than 1 is done, we have either shrink or dilation of original figure.
So there is a chance of getting similar figure but not congruent figure.
So here we find option C is right answer
All the other options deal with transformatios that just move the figure without modifying their dimmenssions.
When you dilate a figure you increase the dimmenssions, so the result is a different figure.
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y = x2 + 12x + 30
8x − y = 10
(−4, −2) and (2, 5)
(−2, −4) and (2, 5)
(−2, −4) and (5, 2)
No Real Solutions
Answers
8 x-y=10 ⇒ y= 8 x-10
We will switch that in 1st equation:
8 x-10=x²+12 x+30, or:
x² + 4 x +40 = 0, a=1,B=4, c=40
Discriminant : D= b² - 4 ac= 16 - 160 = -144 and because it is negative there are no real solutions.
Answer: D)
y=x²+12x+30
y=8x-10
==>x²+12x+30=8x-10
==>x²+4x+40=0
Δ=16-4*40<0 ==> no real solutions.
Answers
Hope it right! and it helps u out!
Answers
Answer:
Step-by-step explanation:
We need to first find the volume of the cube, then subtract from it the volume of the sphere. This is what we are being asked to find. First, the volume of the cube is length times width times height. Since this is a cube, all of the sides are the same length, making the volume
V = 18³ so
V = 5832 inches cubed. Now for the sphere.
The formula for the volume of a sphere is
and we will use 3.1415 for π.
which gives us
V = 3053.538
Subtracting the volume of the sphere from the volume of the cube:
V = 5832 - 3053.538
V = 2778.462 inches cubed
Answer:
2,778 in³
Step-by-step explanation:
Volume cube
v = 18³
v = 5,832
Volume sphere
v = (4/3)π9³
v = 3,053.6280592893
Volume space
v = 5,832 - 3,053.6280592893
v = 2,778.3719407107
2,778 in³
Answers