3.12 can you help me with my last question please
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>
Answer:
-18
Step-by-step explanation:
![f(x) = 4x+14\\g(x) = 3x^{2} + 5x -6\\f(g(x)) = 4(3x^{2} + 5x -6)+14 \\f(g(-1)) = 4(3(-1 ^{2}) + 5(-1) -6) +14 \\\\= 4(3 - 5 - 6) + 14\\= 4 (-8) + 14\\= - 32 + 14 \\= -18](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%2B14%5C%5Cg%28x%29%20%3D%203x%5E%7B2%7D%20%2B%205x%20-6%5C%5Cf%28g%28x%29%29%20%3D%204%283x%5E%7B2%7D%20%2B%205x%20-6%29%2B14%20%5C%5Cf%28g%28-1%29%29%20%3D%204%283%28-1%20%5E%7B2%7D%29%20%2B%205%28-1%29%20-6%29%20%2B14%20%20%5C%5C%5C%5C%3D%204%283%20-%205%20-%206%29%20%2B%2014%5C%5C%3D%204%20%28-8%29%20%2B%2014%5C%5C%3D%20-%2032%20%2B%2014%20%5C%5C%3D%20-18)
Answer:
A
Step-by-step explanation: