So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!
No because to get a proportional relationship you have to add the same number to all x to get y
Answer:
Answer: (B) 3
Step-by-step explanation:
20x + 15(2x) + 10(3x) = 40
20x + 30x + 30x = 40
80x = 40
x = 40/80
x = 1/2
Find the amount of lobster
Lobster = x = 1/2 pound
Find the amount of crab:
Crab = 2x = 2(1/2) = 1 pound
Find the amount of Shrimp:
Shrimp = 3x = 3(1/2) = 3/2 pounds
Find the total pounds of seafood:
Total = 1/2 + 1 + 3/2 = 3 pounds
Answer: (B) 3
Answer:
x = 4 or x = (-3)/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 - 5 x - 12 = 0
x = (5 ± sqrt((-5)^2 - 4×2 (-12)))/(2×2) = (5 ± sqrt(25 + 96))/4 = (5 ± sqrt(121))/4:
x = (5 + sqrt(121))/4 or x = (5 - sqrt(121))/4
sqrt(121) = sqrt(11^2) = 11:
x = (5 + 11)/4 or x = (5 - 11)/4
(5 + 11)/4 = 16/4 = 4:
x = 4 or x = (5 - 11)/4
(5 - 11)/4 = -6/4 = -3/2:
Answer: x = 4 or x = (-3)/2
Answer:
z = 1.28 < a - 200/20
And if we solve for a we got
a = 200 + 1.28 * 20 = 225.6
So the value of height that separates the bottom 90% of data from the top 10% is 225.6.
Step-by-step explanation:
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
X ~ N (200,20)
For u = 200 and o = 20
For this case we can use the z score in order to solve this problem, given by this formula:
Z = x-u/o
For this part we want to find a value a, such that we satisfy this condition:
P (X > a) = 0.1 (a)
P (X < a) = 0.9 (b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
P ( X < a) = P (X-u/o < a - u/o) = 0.9
P (z < a-u/o) = 0.9
But we know which value of z satisfy the previous equation so then we can do this:
z = 1.28 < a - 200/20
And if we solve for a we got
a = 200 + 1.28 * 20 = 225.6
So the value of height that separates the bottom 90% of data from the top 10% is 225.6.
