<h3>Answers:</h3>
- A) Correct. Linear.
- B) Correct. Linear.
- C) Incorrect. Nonlinear.
- D) Incorrect. Linear.
- E) Correct. Nonlinear.
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Explanation:
A)
The product of a number n and 7 is the same as n*7 or 7*n or 7n
The number next to the variable implies multiplication, so we don't have to write the asterisk or multiplication symbol.
This expression is linear because the exponent is 1. Think of 7n as 7n^1
Or you could graph it out and you would get a straight line.
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B)
n = first number
n+1 = number right after number n
n+2 = number right after n+1
This shows we have 3 consecutive numbers
The sum of this leads to 3n+3 which is linear.
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C)
Tina needs to square 3n to get (3n)^2. So she forgot to square the 3
(3n)^2 is equivalent to 9n^2
Both of which are nonlinear. They graph out a curved parabola which isn't a straight line. The exponent being larger than 1 is another indication of a nonlinear expression.
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D)
The sum of a number and 8 can be represented by n+8 where n is the unknown number. Then sticking "twice" out front means we double all of n+8. So we double it to get 2(n+8) which is equivalent to 2n+16
Tina mistakenly only doubled the n and not the 8
2(n+8) and 2n+16 are both linear. It might help to think of it like y = 2x+16 and to graph that out to get a straight line.
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E) Tina is correct here in dividing n^3 over 2
This is nonlinear since the exponent is larger than 1. It graphs out a curved cubic, rather than a straight line.
