Answer:
The length of the resulting segment is 500.
Step-by-step explanation:
Vectorially speaking, the dilation is defined by following operation:
![P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BP%28x%2Cy%29-O%28x%2Cy%29%5D)
(1)
Where:
- Center of dilation.
- Original point.
- Scale factor.
- Dilated point.
First, we proceed to determine the coordinates of the dilated segment:
(
, 
, 
, 
)
![P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2810%2C40%29-%280%2C0%29%5D)
![Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]](https://tex.z-dn.net/?f=Q%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BQ%28x%2Cy%29-O%28x%2Cy%29%5D)
![Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]](https://tex.z-dn.net/?f=Q%27%20%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2870%2C120%29-%280%2C0%29%5D)
Then, the length of the resulting segment is determined by following Pythagorean identity:
The length of the resulting segment is 500.
Answer:
4 miles per hour is the speed
Answer:
Step-by-step explanation:
Question 3
5 (k + 4) - 2k
Use distributive property of multiplication.
5k + 20 -2k
Combine like terms to get your answer.
3k +20
Question 4
2 (3 + d - 1)
Simplify the expression in the parenthesis.
2 (2 + d)
Use distributive property of multiplication.
4 + 2d
If you wanted it to be accepted at higher levels, switch the terms around.
2d + 4
Answer:
b > 250/9 and w ≥ 0
Step-by-step explanation:
7/9 (b - 27) > 49/81
First, simplify both sides of the inequality:
7/9b - 21 > 49/81
Add 21 to both sides
7/9b - 21 +21 > 49/81 +21
Multiply both sides by 9/7
9/7 x 7/9b > 49/81 x 9/7
b > 1750/81
Simplify
b > 250/9
11w - 8w ≥ 14w
Simplify both sides once again
3w ≥ 14w
Subtract 14w from both sides
3w - 14w ≥ 14w - 14w
-11w ≥ 0
Divide both sides by -11w
w ≥ 0
Answer:
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Step-by-step explanation:
