Answer:
The answer is rotation 270° about the origin
Step-by-step explanation:
If (x , y) is a point in xy-coordinates
If the point rotate about the origin ⇒ (The positive direction is anti-clockwise)
1- 90°
Its image is (-y , x)
2- 180°
Its image is (-x , -y)
3- 270°
Its image is (y , -x)
If we assume A is (1 , 7)
1- ⇒ (-7 , 1) ⇒ rotation 90° about the origin
2- ⇒ (-1 , -7) ⇒ rotation 180° about the origin
3- ⇒ (7 , -1) ⇒ rotation 270° about the origin
∵ x-coordinate of point A small and +ve and y-coordinate large and +ve
∵ x-coordinate of point A' large and +ve and y-coordinate small and -ve
∴ The answer is rotation 270° about the origin
∴ The answer is rotation 270° about the origin
I’ll do an example problem, and I challenge you to do this on your own!
4x+6y=23
7y-8x=5
Solving for y in 4x+6y=23, we can separate the y by subtracting both sides by 4x (addition property of equality), resulting in 6y=23-4x. To make the y separate from everything else, we divide by 6, resulting in (23-4x)/6=y. To solve for x, we can do something similar - subtract 6y from both sides to get 23-6y=4x. Next, divide both sides by 4 to get (23-6y)/4=x.
Since we know that (23-4x)/6=y, we can plug that into 7y-8x=5, resulting in
7*(23-4x)/6-8x=5
= (161-28x)/6-8x
Multiplying both sides by 6, we get 161-28x-48x=30
= 161-76x
Subtracting 161 from both sides, we get -131=-76x. Next, we can divide both sides by -76 to separate the x and get x=131/76. Plugging that into 4x+6y=23, we get 4(131/76)+6y=23. Subtracting 4(131/76) from both sides, we get
6y=23-524/76. Lastly, we can divide both sides by 6 to get y=(23-524/76)/6
Good luck, and feel free to ask any questions!
Answer:
- 6
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [ 2, 6 ] , then
f(b) = f(6) = - 6² + 2(6) + 2 = - 36 + 12 + 2 = - 22
f(a) = f(2) = - 2² + 2(2) + 2 = - 4 + 4 + 2 = 2 , then
average rate of change = 
= 
= - 6
Answer:
i) 45km/hr
ii)29 min
Step-by-step explanation:
average speed = distanced travelled / time elapsed
It took 36min and need to convert to hr
36min x 
= 
= 
hours
distanced travelled is 27 km;
average speed = 27km / (9/15hr) = 45 km/hr
Add 36min to 0837 becomes 0913, the train will arrive at 0942 and the wait will be the difference of 0942 - 0913 = 29 min
Answer: 12,045 boxes
Step-by-step explanation:
120,450 divided by 10
= 12,045
