Answer:
k = 5
Step-by-step explanation:
When a certain number [tex]n[/tex] is multiplied by a scale factor [tex]k[/tex], the final number is given by
[tex]n'=kn[/tex]
and the final number will be:
- Larger than the original number if [tex]|n'|>|n|[/tex]
- Smaller than the original number if [tex]|n'|<|n|[/tex]
In this problem, the number [tex]n[/tex] represents the size of the decoration.
If we apply the 4 scale factors given, we have:
- If [tex]k=5[/tex], then [tex]n'=5n[/tex]: this means that the final decoration is larger than the original decoration --> this is the correct option
- If [tex]k=1[/tex], then [tex]n'=n[/tex]: so the final decoration has same size as the original decoration
- If [tex]k=1/5[/tex], then [tex]n'=\frac{1}{5}n[/tex]: so the final decoration is smaller than the original decoration
- If [tex]k=-1/5[/tex], then [tex]n'=-\frac{1}{5}n[/tex], so the final decoration is smaller and inverted
