Which polynomial represents the difference below? (8x^2 + 9) - (3x^2 + 2x + 5)
2 answers:
Answer: The correct option is (A)
Step-by-step explanation: We are given to select the polynomial that represents the following difference :
To find the required difference, we need to subtract the coefficients of the same powers of the unknown variable x.
From (i), we get
Thus, the required difference is
Option (A) is CORRECT.
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Answer:
- The first graph (see figure attached)
Explanation:
<u>1. Number of pages read by Robert</u>
Set a function for the number of pages read by Robert, taking into account that this is an arithmetic sequence, whose first term is 30, and the common difference is 20:
- R(n) = 30 + 20 (n - 1)
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<u>2. Number of pages read by Tony:</u>
The arithmetic sequence that represents the number of pages read by Tony has first term 40, and common difference 14:
- T(n) = 40 + 15 (n - 1)
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<u>3. Find the numbers of pages read by Tony in terms of the number of pages read by Robert.</u>
To do that, you must clear n from both equations and equal the two expressions obtained:
From R(n) = 30 + 20 (n - 1):
- R(n) = 30 + 20n - 20
- R(n) = 10 + 20n
- n = [R(n) - 10]/20
You can change R(n) to r:
- n = (r - 10) / 20
From T(n) = 40 + 15 (n - 1)
- T(n) = 40 + 15n - 15
- T(n) = 25 + 15n
- n = [T(n) - 25]/15
Change T(n) to t
- n = (t - 25)/15
Equal both expressions:
- (r - 10) / 20 = (t - 25)/15
Solve for t:
- 15(r-10) = 20(t - 25)
- 15r - 150 = 20t - 500
- 15r - 150 + 500 = 20t
- 15r + 350 = 20t
- 3r + 70 = 4t
- 4t = 3r + 70
- t = (3/4)r + 70/4
- t = 0.75r + 17.5
Find some points of the equation t = 0.75r - 17.5 to compare with the points of the graph:
- r = 0 ⇒ t = 17.5, that means that the line intercepts the vertical axis at 17.5. The only graph that matches this is the first graph
Find other point:
- r = 30 ⇒ t = 0.75(30) + 17.5 = 40.Thus, the graph must contain the point (30, 40), which the first graph does.
