Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.
<h3>
Are the two rectangles similar?</h3>
We know that rectangle 1 has dimensions L and W.
And rectangle 2 is made by multiplying the dimensions of rectangle 1 by a factor k > 0.
Then, rectangle 2 is just a dilation of rectangle 1, this means that in fact, the two rectangles are similar by definition.
Then:
Dimensions of rectangle 1:
- Length = L
- Width = W.
- Perimeter = 2*(W + L)
- Area = W*L
For rectangle 2:
- Length = k*L
- Width = k*W
- Perimeter = 2*(k*L + k*W) = k*(2*(L + W))
- Area = (k*L)*(k*W) = k²(L*W)
Above we can see that the perimeter of rectangle 2 is k times the perimeter of rectangle 1, and the area of rectangle 2 is k squared times the area of the rectangle 1.
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A
substitute each point into the inequality and check validity of solution
A (4, 4)
4 ≤ 16 - 12 + 2 ⇒ 4 ≤ 6 → True hence valid solution
B (3, 3 )
3 ≤ 9 - 9 + 2 ⇒ 3 ≤ 2 → False hence not valid
C (1, 1 )
1 ≤ 1 - 3 + 2 ⇒ 1 ≤ 0 → False hence not valid
D (2, 2 )
2 ≤ 4 - 6 + 2 ⇒ 2 ≤ 0 → False hence not valid
Answer:
6(d - 5)
Step-by-step explanation:
Answer:
IQR is 3.5
Step-by-step explanation:
<u>Step 1: Organize the numbers in numerical order</u>
0,0,2,2,3,4,6,8
<u>Step 2: Break the set up into quartiles (4 parts)</u>
0 0 | 2 2 | 3 4 | 6 8
<u>Step 3: Find the average of each quartile</u>
0 | 2 | 3.5 | 7
<u>Step 4: Find the IQR (Q3-Q1)</u>
3.5-0=3.5
Therefore, the IQR is 3.5