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1
The length of a rectangular garden is 3 feet longer than the width, and the area of the garden is 100 square feet. If the width of the garden, in feet, is w, which of the following equations could be used to determine the width of the garden?
Your Answer:
ww-3)-180
Correct Answer:
w(w+3)=180
Justification:
If the length is 3 feet longer than the width, then the length is w+ 3. The area of a rectangle is length times width. Substituting 180 for the area, w3 for the length, and w for the width into A Iw gives us 180 (w+3)w, which is equivalent to (w-3)(w-3)=180
2
If n is an integer, which of the following must be an odd integer?
Your Answer:
Correct Answer:
(2n+1)(2n-1)
(2n+1)(2n-1)
Justification:
Suppose n = 5: then (n+1)(n-1) 6°424, (n+1)(2n-1) is 6954, (2n+1)(n-1) is 11*4=44, and (2n+1)(2n-1) is 11*999. Only (2n+1)(2n-1) is odd. In general, if n is an integer, then both 2n+1 and 2n-1 must be odd.
3
If an animal is a whale, then it is a mammal. Which of the following statements is the converse of the statement above?
Your Answer:
If an animal is a mammal, then it is a while
Correct Answer:
If an animal is a mammal, then it is a whale.
Justification:
The converse of a statement switches the order of the phrases following the if and "then"; the converse of "if p, then q" is "If q, then p." Note: the converse of a true statement is frequently false
4
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