Answer:
Scale factor = 4
Step-by-step explanation:
Scale factor = 
Since, S is being dilated with a scale factor to form T,
So, the figure S is the preimage and figure T will be the image,
Length of one side of image T = 8
Length of one side of preimage = 2
Therefore, Scale factor = 
= 4
Scale factor by which figure S has been dilated to form figure T is 4.

Step-by-step explanation:
Since we have given that
Time taken by steamboat makes the trip=5 hours
Time taken by yacht makes the trip =2.5 hours
Since we have also given that
the yacht is 20 knots faster than the steamboat,
So let the speed of steamboat be x
Let the speed of yacht be x+20
Now, we have given that both boats will travel the same distance ,
So,

Hence,

Answer:
Step-by-step explanation:
hello :
cot x + 2cot x sin x = 0 0≤ x≤ 180
cotx(1+2sinx) =0 means : cotx=0 or 1+2sinx=0
1) cotx=0 so : cosx=0 and sinx ≠ 0 because cotx = cosx/sinx
when : 0≤ x≤ 180 : x=90°
2) 1+2sinx=0 means : sinx = -1/2
when : 0≤ x≤ 180 : no solutions because : sinx ≥ 0
conclusion : one solution : x=90°
5 books for 12 dollars because you basically getting a book free
The quadratic formula is x= -b +/- √b²-4ac / 2a
In this problem,
a=6
b=4
c=-3
Now, we can plug this into the formula:
x= -4 +/- √4²-(4)(6)(-3) / (2)(6)
x= -4 +/- √16+72 / 12
x= -4 +/- √88 /12
x= -4 +/- 2√22 /12
x= -2 +/- √22 / 6
So,
x= -2 + √22 / 6
x= -2 - √22 / 6