Answer:
Step-by-step explanation:
Given:
The two functions are:


To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The horizontal stretch is defined as:
...(i)
If
, the function f(x) is horizontally stretched by factor
.
If
, the function f(x) is horizontally compressed by factor
.
We have,


Using these functions, we get
...(ii)
On comparing (i) and (ii), we get

Since
, the function f(x) is horizontally stretched by factor
.
Hence, the correct option is D.
Answer:
Option The area is increased by a factor of 
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to scale factor squared
Let
z-----> the scale factor
x------> the area of the dilated rectangle
y------> the area of the original rectangle

we have
------> is an enlargement
so
substitute



therefore
The area is increased by a factor of 
Answer:
11,880 different ways.
Step-by-step explanation:
We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.
We will use permutations for solve our given problem.
, where,
n = Number of total items,
r = Items being chosen at a time.
For our given scenario
and
.





Therefore, offices can be filled in 11,880 different ways.
Answer:
Ted is 6 years old
Leon is 7 years old
Andrew is 8 years old
Step-by-step explanation:
Ted+Leon=13 ⇒T+L=13 ⇒L=13-T
Leon+Andrew=15 ⇒L+A=15 ⇒A=15-L ⇒A=15-(13-T) because Leon =13-Ted
A=2+T
Ted+Andrew=14
T+A=14 ( substitute Andrew age from A=2+T)
T+2+T=14
2T=12
<h2>T=12/2=6 (Ted is 6 years old)</h2><h2>A=2+T=2+6=8 ( Andrew is 8 years old)</h2><h2>Leon=13-T=13-6=7 ( Leons is seven years old)</h2>
check: Ted+Leon=13 ⇒ 6+7=13
Leon + Andrew=15 ⇒7+8=15
Andrew+Ted=14 ⇒ 6+8=14