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2 answers:
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Answer:
Step-by-step explanation
Given:
A figure of triangles.
To find:
Whether the triangles SPT and triangle QPR are similar.
Solution:
In triangle SPT and triangle QPR,
(Given)
(Common angle)
In triangles SPT and triangle QPR, two corresponding angles are congruent. So, by AA property of similarity both triangles are similar.
Therefore, yes, the triangle SPT and triangle QPR similar. Option A is correct.
Answer: Check out the attached diagram below for the filled out table.
Explanation:
- A) This is correct. You basically stick a minus sign out front to reflect over the x axis (aka the line y = 0).
- B) Replacing x with x+2 will shift the graph 2 units to the left. Adding on 3 at the end will shift it up 3 units.
- C) A vertical stretch, aka vertical dilation, makes the graph taller than it already is. In this case, we want to stretch it to make it twice as tall. That explains the 2 out front. The negative is there to reflect over the x axis.
- D) The -2 is to apply a dilation of 2 and do a reflection. The +6 is so ensure that the vertex arrives at the proper location (0,6) so that we reflect over y = 3.
- E) This is similar to part B. Replacing x with x-3 shifts the graph 3 units to the right. We subtract off 2 at the end to shift the graph down 2 units. The 1/2 out front applies the dilation, which in this case is a vertical compression by a factor of 2.
- F) A vertical compression by a factor of 4 is the same as dilating by a factor of 1/4. So we'll multiply f(x) by 1/4.
- G) Similar to part F, but we'll be using the scale factor 4 this time.
