Answer: Rotations, reflections, translations (A, C, and E)
Imagine you had a camera aimed at a triangular figure on a piece of paper. If you rotate the camera, then the image of the triangle appears to rotate. In reality it's the other way around. What this means is that the triangle is not changing at all. It keeps the same size, shape, area, perimeter, etc. This applies to when the camera pans left or right, ie shifts from side to side. The triangle will translate but again the triangle isn't changing at all. It's merely an illusion. Reflections are the same way. Imagine having a piece of glass or a mirror that reflects the image which is an identical copy; although everything is flipped.
Dilations are not isometries because the image is a different size then the pre-image. The same shape is maintained though. Note: the scale factor must be some number other than 1.
another note: "isometry" breaks down into "iso+metry" with "iso" meaning "same" or "equal", and "metry" meaning "measure". So if you had 2 identical yard sticks, then they are isometrical or equal in length.
Your answer is x=1 , y=3........
Answer:
The slopes of line m and p will be the same: 1/25 (I think thats what that says)
Step-by-step explanation:
when two lines are parallel it means they will never touch, and so they must have the same slope. If their slopes were different (even by 1 decimal), they would touch and so would no longer be parallel.
Answer:
$2355.06
Step-by-step explanation:
Use the compound interest formula, filling in the numbers you know. Then solve for the number you don't know.
A = P(1 +r/n)^(nt)
where A is the account balance, P is the amount invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
4000 = P(1 +.053/52)^(52·10) = P(1.6984738)
P = 4000/1.6984738 ≈ 2355.06
You would need to deposit $2355.06 in order to have $4000 in 10 years.
Answer:
a). N = 2
b). N = 16
c). t = 624 minutes
Step-by-step explanation:
Exponential model that shows the rumor spread through a group is
Where N = Number of teenagers who have heard the rumors
t = Duration after the rumor first started
(a). At the time t = 0
N = 2
Therefore, 2 teenagers started the rumor.
(b). At t = 5 hours
N = 
N = 15.96
N ≈ 16
16 teenagers heard the rumors after 5 hours.
(c). If N = 150
150 = 
75 = 
log(75) = 0.7t(log1.81)
1.87506 = 0.7t(0.25767)
t = 
t = 10.395 hours
t ≈ 624 minutes
Therefore, after 624 minutes or rumor will be heard by 150 teenagers.
