course Mth 121
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.*********************************************
Your solution: (type in your solution starting in the next line)
8x = 72; 72/8 = x; x = 9
OK
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution: (type in your solution starting in the next line)
(8 + 3) * 5
(11) * 5
55
Parentheses are done first (Please excuse my dear Aunt Sally)
8 + 3 * 5
8 + 15
23
Multiplication is done first
The answers are different because of the way the question was grouped, the problem was evaluation by the order of operations
OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
(2^4) * 3
(16) * 3
48
2^(4 * 3)
2^(12)
4096
Again, the answers differ because of the order of operations; equations in the parentheses are done first.
OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
3 * 5 - 4 * 3 ^ 2
3 * 5 – 4 * 9
15 – 36
-21
3 * 5 - (4 * 3)^2
3 * 5 – (12)^2
3 * 5 – 144
15 – 144
-129
Parentheses are done first, followed by exponentials, multiplication, and then subtraction
OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
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Your solution:
To obtain the result for y, I simply inserted the coordinates provided for x in the equation given.
x y
-2 -1
-1 1
0 3
1 5
2 7
The graph was linear, starting at (-2, -1) and increasing to (2, 7). The line increased by (1, 2) each time. The graph was linear because it was a straight line that did not curve.
OK
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
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Your solution:
x y
-2 7
-1 4
0 3
1 4
2 7
The equation is quadratic; the shape is a parabola.
OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
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Your solution:
x y
1 5
2 7
3 11
4 19
The line is exponential.
OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
It will be the same as the original number.
OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The answer will depend on the original number. If the denominator is greater than the numerator, the result will be less than the original number; if the denominator is less than the numerator, the result will be greater than the original number; if the denominator and numerator are the same, the result will depend on the original number; if the denominator is 1 and the numerator is any other number, the result will be the original number.
OK
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result will be greater than the original number.
OK
&#Your work looks good. Let me know if you have any questions. &#