1) RED will be rotated 90° counterclockwise around the origin.
2) The coordinates of R'E'D' will be R'(2, 2); E'(0, 4) and F'(0, 0). The rule for a 90° counterclockwise rotation about the origin is that the coordinates (x, y) are mapped to (-y, x).
3) An isometric transformation is one in which the angles between sides and the distances of each side are preserved between the pre-image and the image. This means the angle measures and side lengths will be the same. Therefore the image will be similar to the pre-image, as the angle measures will be the same and the side lengths will be proportional.
Answer:
F(4) = 97
Step-by-step explanation:
F(x)= x³+2x²+1
when x = 4
F(4)= 4³+2(4²)+1
= 4³+2(4²)+1
= 64 + 2(16) + 1
= 64 + 32 + 1
= 97
Answer:
90 m
Step-by-step explanation:
The piece on the right side fits perfectly in the left side so you can move the triangle to the left in order to make a square. After that, you can do 10 times 9 because 5+4=9 to get 90m as the area.
Answer:
7033 / 10 000
Step-by-step explanation:
x = .70330
10 000 x = 7033.0 divide both sides by 10 000
x = 7033 / 10 000
Answer:
The ship is located at (3,5)
Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III
Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II
To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.
Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9
We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3
Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5
Based on the above, the position of the ship is (3,5).
Hope this helps :)
