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We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.
Since these are different, this is not linear.
We now find the second differences:
5-3=2; 7-5=2; 9-7=2. Then:
Since these are the same, this sequence is quadratic.
We use (1/2a)n², where a is the second difference:
(1/2*2)n²=1n².
We now use the term number of each term for n:
4 is the 1st term; 1*1²=1.
7 is the 2nd term; 1*2²=4.
12 is the 3rd term; 1*3²=9.
19 is the 4th term; 1*4²=16.
28 is the 5th term: 1*5²=25.
Now we find the difference between the actual terms of the sequence and the numbers we just found:
4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.
Since this is constant, the sequence is in the form (1/2a)n²+d;
in our case, 1n²+d, and since d=3, 1n²+3.
The correct answer is n²+3
Answer:
(d) All of the above
Step-by-step explanation:
In order to solve this question we will have to find out which numbers are located in which group (the group of numbers are U, B, B').
So lets start of with finding out what numbers are a part of group U. By looking at that picture we can see that all number on the graph are a part of group U. So.....
U = {0,1,2,3,4,5,6,7,8,9}
Then we can find out what numbers are part of the group B. We just have to include the numbers that are located within the circle and exclude all of the numbers out side of the circle. So........
B = {0,1,4,5,6,7,8}
We find numbers that are parts of group B' by using a similar method that we used to find out what numbers were part of group B (Just this time we include all numbers outside of the circle and exclude all of the numbers inside the circle). So ......
B' = {2,3,9}
Now we see that the right option is option d.
Remember when solving inequalities the sign of your inequality reverses when dividing or multiplying negative values. k/-12<15. k>-180 [-180, positive infinity)
Use completion of sq method
x^2+y^2+14x+10y-7=0
(x+7)^2+(y+5)^2=7+49+25
(x+7)^2+(y+5)^2=81
so centre is(-7,-5) radius is9
