Answer:
1. (x,y)→(y,-x)
2. (x,y)→(-y,x)
3. (x,y)→(-x,-y)
Step-by-step explanation:
1. Rotation 90° clockwise (or 270° counterclockwise) about the origin changes x into y and y into -x, so it has the rule
(x,y)→(y,-x)
2. Rotation 90° counterclockwise (or 270° clockwise) about the origin changes x into -y and y into x, so it has the rule
(x,y)→(-y,x)
3. Rotation 180° clockwise about the origin changes x into y and y into -x, so it has the rule
(x,y)→(-x,-y)
Here you can apply rotation by 90° clockwise twice, so
(x,y)→(-y,x)→(-x,-y)
Answer:
(4, -2) (see attached)
Step-by-step explanation:
Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.
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<h3>vector components</h3>
The components of the vectors are ...
u = (1, -2)
v = (-6, -6)
Then the components of the vector sum are ...
2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)
2u -1/3v = (4, -2)
<h3>graphically</h3>
The sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.
One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.
The resultant is in red in the attachment.
Answer:
Total percent of the room did she paint green = 60%
Step-by-step explanation:
Given - Cheryl painted her living room walls with two different colors. She painted part of the room yellow and another part green. If the surface area of the walls in her room is 720 ft² and she painted 288 ft² yellow.
To find - What percent of the room did she paint green ?
Proof -
Given that,
The surface area of the walls in her room = 720 ft²
Total area painted in yellow color = 288 ft²
So,
Total area painted in green color would be = 720 - 288 = 432 ft²
Now,
Let the total percent green color painted = x
So,
720 × x% = 432
⇒
⇒ x =
= 60
∴ we get
Total percent of the room did she paint green = 60%
Wanda's graph is incorrect because Claudia needs to earn $80 or more and Wanda's graph shows $80 or less.
Answer:16
Step-by-step explanation: