Lydia graphed ΔLMN at the coordinates L (0, 0), M (2, 2), and N (2, −1). She thinks ΔLMN is a right triangle. Is Lydia's assertion correct? Yes; the slopes of segment LM and segment LN are opposite reciprocals. No; the slopes of segment LM and segment LN are not opposite reciprocals. Yes; the slopes of segment LM and segment LN are the same. No; the slopes of segment LM and segment LN are not the same.

The correct option is

No; the slopes of segment LM and segment LN are not opposite reciprocals

slope of LM:  = 1

And,  

slope of LN: =

Here two lines should be perpendicular at the time  when the multiplication of their slopes is equalivalent to negative one.  

So,  

= slope of LM × slope of LN

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No; the slopes of segment LM and segment LN are not opposite reciprocals

Step-by-step explanation:

slope of LM: (2 - 0)/(2 - 0)  = 1

slope of LN: (-1 - 0)/(2 - 0) = -1/2

Two lines are perpendicular when the multiplication of their slopes is equal to negative one, that is, they are opposite reciprocals. In this case:

slope of LM*slope of LN = 1*(-1/2) = -1/2

1 1/4 hours

step-by-step explanation:

2/4 + 2/4 + 1/4 = 5/4 or 1 1/4

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form