If you are moving the center of circle 2 to the the center of circle 1, then the translation rule is (x,y) ---> (x+4, y+10). 
Note how x = 1 turns into x = 5. So we add 4
Also, y = -2 turns into y = 8. We add 10
The scale factor to turn the radius r = 4 into r = 8 is 2. Basically we double the radius. We can divide the two radii to see 8/4 = 2
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Summary:
To go from circle 2 to circle 1, we apply these two transformations
translation: (x,y) ---> (x+4, y+10)
dilation: scale factor 2
note: 
if you want to go backwards, go from circle 1 to circle 2, then undo the transformations above
        
             
        
        
        
Water can freeze at 32 degrees f 
        
                    
             
        
        
        
Answer:
2√2
Step-by-step explanation:
<u>By </u><u>using </u><u>trigonometry,</u>
sin 45° = x/4
          x = 4sin 45°
          x = 2√2
<u>By </u><u>using </u><u>Pythagorean</u><u> </u><u>theorem</u><u>,</u>
Since you know that it is an isosceles triangle and it's also a right-angled triangle,
4² = x² + x²
16 = 2x²
x² = 8
x = √8
  = 2√2
 
        
             
        
        
        
To solve this you must use a proportion like so...
 
The total number of students that can be chosen are 4,663. This number will represent the whole of one fraction in the proportion. We want to know what percent probability out of these students are engineer, medical doctor/surgeon. This would be considered the part of this fraction. Sum the number of engineering students (615) with medical doctors/surgeons (723) to find this number
723 + 615 = 1,338 students that want to be an engineer or medical doctor/surgeon
Percent's are always taken out of the 100. This means that the other fraction in the proportion will have 100 as the whole and x (the unknown) as the part.
Here is your proportion:
 
Now you must cross multiply
1,338*100 = 4,663*x
133,800 = 4,663x
To isolate x divide 4,663 to both sides
133,800/4,663 = 4,663x/4,663
28.7 = x
This means that there is a 28.7% of a student with the intent of becoming an engineer or a medical doctor/surgeon to be chosen at random
Hope this helped!
~Just a girl in love with Shawn Mendes
 
        
                    
             
        
        
        
8/20as well,since the number of green beads and yellow beads is the same,so equal probability