A transformation is rigid if the original shape remains the same shape and size after the transformation.
Flipping a pancake:
After it is flipped, the pancake should stay the same size and shape, so it is a rigid motion and it is a rotation.
Deflating an air mattress:
Deflating a mattress changes its size, so the transformation is not rigid. This is called a dilation.
Moving a clock's minute hand:
Moving the minute hand does not change the hand's size or shape so the transformation is rigid. This transformation is a combination of a translation and a rotation. The translation is what moves the hand around the center of the clock, and the rotation is what changes the direction of the hand.
Enlarging a photo:
Enlarging a photo changes the photo's size, so this transformation is not rigid. This is called dilation.
Putting a golf ball:
Putting does not change the size or shape of a golf ball, so this transformation is rigid. Putting a golf ball both rotates and moves the ball, so the transformation is rotation and translation.
Looking in a car's rear view mirror:
Assuming the car is moving relative to something behind it(because otherwise there would be no transformation), As things come closer to the back of the car, they would appear larger in the mirror, and as things move away from the back of the car, they would appear smaller in the mirror. Because the size changes when looking at the mirror, this is not a rigid transformation and is called dilation.
Answer:
You must survey 784 air passengers.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The margin of error is:
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
Assume that nothing is known about the percentage of passengers who prefer aisle seats.
This means that 
, which is when the largest sample size will be needed.
Within 3.5 percentage points of the true population percentage.
We have to find n for which M = 0.035. So
You must survey 784 air passengers.
Answer: Substitution
Step-by-step explanation:
GIVEN:
y=3x
2x+4y=12
Then, 2x+4(3x)=12
-----------------------------------------
Substitution: replacing one variable in terms of another variable.
As we can see from the given aspects, y=3x, and the conclusion expression has no y instead of 3x. This means it represented y in terms of x, which fits the definition of substitution that replaces one variable.
Hope this helps!! :)
-x + 5y = 8
multiply this equation by 3
-3x + 15y = 24
now add it to the other equation ( elimination)
-3x + 15y = 24
3x + 7y = -2
-----------------------
0x + 22 y = 22
divide each side by 22
y =1
substitute into -x + 5y =8 to find x
-x + 5(1) = 8
-x + 5 = 8
-x =3
divide by -1
x =-3
Answer (-3,1)
Choice A
