A proportional relationship is also a direct variation.
The general equation of direct cvariation is
y = kx,
where k is a number.
In your case, if k = -1, then y = kx becomes y = (-1)x which is the same as
y = -x
Because you're trying to make them congruent, equal the two expressions to each other.
So, for #10 you would equal them so it would look like this.
2x+2=5x-19
Then you would just go ahead and simplify
2x+2=5x-19
-2x -2x
---------------
2= 3x -19
+19 +19
---------------
21=3x
--- ----
3 3
x=7
This means that x should be 7. You can check this just by plugging it in
2x+2
2(7)+2 = 16
5x-19
5(7)-19= 16
Same with #11.
x+8=3x-14
-x -x
--------------
8=2x-14
+14 +14
--------------
22=2x
--- ----
2 2
x=11
Check.
x+8
11+8= 19
3x-14
3(11) - 14 = 19
C: 4 is the right answer
Step-by-step explanation:
Given
a1 = -3
a15 = 53
We know that explicit formula for the arithmetic sequence is:
For the 15th, term it will be
Adding 3 on both sides
Dividing both sides by 14
Hence,
C: 4 is the right answer
Keywords: Arithmetic sequence, Common Difference
Learn more about arithmetic sequence at:
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