In a given quadrilateral, each side is parallel to its opposite side and the diagonals are not perpendicular. What could it be?
2 answers:
You might be interested in
Answer:
- A (-4, -3)
- C (2, 4)
- E (3, 2)
Step-by-step explanation:
It is convenient to use technology to plot the points and the functions to see what lies where. The first attachment shows such a plot.
_____
Of course, you can do the function evaluations. For example, testing answer B, we find ...
... 3·6 ≤ -2·1 +18 . . . . <em>false</em> for the first equation — not a solution
Checking all the points requires 10 function evaluations. When things get repetitive like that, I like to use a graphing calculator or spreadsheet.
_____
<em>Using a calculator</em>
The second attachment shows a calculator evaluating the viability of each point as a solution. The equations have been rearranged to ...
- -2x -3y +18 ≥ 0
- -x +4y +12 ≥ 0
This makes it easy to look at the evaluation results to see if the solution is viable or not.
The x-values of the points are entered into list L₁ and the y-values into L₂. The result of the first inequality above is in L₃ and the result for the second inequality is in L₄. Any negative value in L₃ or L₄ shows a point that is <u>not</u> part of the solution set. Points B and D fail to match problem requirements.
Points A, C, and E are in the solution set.
Answer:
<em><u></u></em><em><u></u></em>
Step-by-step explanation:
The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
<u>Using trial and error method we will find the first root of the polynomial.</u>
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
<u>Now by long division or by using synthetic division we can find other factors.</u>
<u>Synthetic Division :</u>
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
------ ( 1 )
<u>Next further factorize x² - 11x - 42</u>
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,