Which of the following equations best models the data in the table above?
(a) y = 5· 1.2x - 2
(b) y = 4· 1.2x
(c) y = 5· 1.3x
(d) y = 5· 1.2x - 1
(e) y = 5· 1.3x 1
Answer: The easiest way to solve this problem is to check the results of the 5 answers for x = 0:
(a) y = 5· 1.20 - 2 = 3
(b) y = 4· 1.20 = 4
(c) y = 5· 1.30 = 5
(d) y = 5· 1.20 - 1 = 4
(e) y = 5· 1.30 + 1 = 6
and (c) must be the correct answer. We can verify at this point the results of y = 5· 1.3x for x = -5, x = 3 and x = 7
If a, b and c are the sides of any triangle, which of the following inequalities is not true?
(a) a·b > 0
(b) a + b > c
(c) a + c/2 >b
(d) b + c > a
(e) (a + b)·(b + c) > a·c
Answer: The first answer is true, since the product of 2 positive reals will be positive.
The second and the fourth answers will also be true, since the sum of 2 sides of a triangle is always higher than the third side.
The fifth answers is also true because it is just a multiplication of the second and fourth inequalities of positive terms.
Answer three should be the one that is not true, and we can verify this result with an example: an isosceles triangle with a = 3, c = 3, b= 10 will satisfy the inequality.
Question #3: In the figure below, quadrilateral ABCD has AB parallel with CD. What is the area of triangle ABD?
Answer: The area of triangle ABD is equal to (1/2)AB·DE, where DE is the altitude from D to AB.