Answer:
angle: 71
x = -3
Step-by-step explanation:
step 1: 180-(55+54) = 71
step 2: x+74=71 (subtract 74 from both sides)
step 3: x=-3
step 4: -3+74=71
Answer:
a. 96 square units
Step-by-step explanation:
The figure is a rectangle with width AB = (20-12) = 8 units and height BC = (20-8) = 12 units.
The area of the rectangle is (8 units)×(12 units) = 96 square units.
Answer:
n = 22
Step-by-step explanation:
Since they are vertical angles they are the same.
Therefore you can put together this equation:
2n - 8 = 36
Add 8 to both sides
2n = 44
Divide by 2
n = 22
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
