Problem 6
Part A
Slope:
m = (y2-y1)/(x2-x1)
m = (9-5)/(4-2)
m = 4/2
m = 2
Use this slope to find the y intercept b
y = mx+b
5 = 2(2)+b
5 = 4+b
b = 1
Therefore the equation is y = 2x+1
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Part B
Slope:
m = (y2-y1)/(x2-x1)
m = (20-10)/(4-2)
m = 10/2
m = 5
Use this slope to find the y intercept b
y = mx+b
10 = 5*2+b
b = 0
Therefore the equation is y = 5x
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Problem 7
A) The coefficients are 7, 25, and -2. These are the values in front of the variables
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B) The variables are m, y, and y^3. Basically any term with a letter in it.
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C) The constant is 44. This is the term without any variables (letters) attached.
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D) There are four terms and the four terms are: 7m, 25y, 44 and -2y^3
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E) 25y and 2y^3 are NOT like terms. We cannot combine unlike terms. It's like trying to add 25a and 2b. We could think of it as having 25 apples and 2 bananas. We can't combine them to get 27a (there aren't 27 apples, only 25). Likewise we can't add them to get 27b (there aren't 27 bananas, only 2). Saying 27ab is also incorrect.
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Problem 8
Plug in n = 1
2^2*(n+3)
2^2*(1+3)
4*(1+3)
4*4
16
So the output is 16
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Plug in n = 3
2^2*(n+3)
2^2*(3+3)
4*(3+3)
4*6
24
So the output is 24
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Plug in n = 4
2^2*(n+3)
2^2*(4+3)
4*(4+3)
4*7
28
So the output is 28
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Plug in n = 6
2^2*(n+3)
2^2*(6+3)
4*(6+3)
4*9
36
So the output is 36
See the image attachment for the completed table.
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Problem 9
Plug in d = 6 and evaluate
C = 40 + 8(d-3)
C = 40 + 8*(d-3)
C = 40 + 8*(6-3) ... Replace d with 6
C = 40 + 8*(3)
C = 40 + 24
C = 64
It will cost 64 dollars.