Qr has the endpoints q(–10, 7) and r(1, –4). gabrielle found the x-coordinate of the point that partitions the directed line segment qr in the ratio 2: 3. her work is shown below. 1. x = (x2 – x1) + x1 2. =(1 – (–10)) + (–10) 3. =(11) – 10 4. = = the x-coordinate of the point p that partitions the directed line segment qr in the ratio 2: 3 is , or –5.6. the y-coordinate of the point p is

The x-coordinate of point P = -5.6

The y-coordinate of point P = 2.6

P(-5.6,2.6)

Step-by-step explanation:

QR has the endpoints Q(–10, 7) and R(1, –4).

Line segment QR divides at point P in ratio 2:3.

Using section formula:

where,

Hence, The x-coordinate of point P = -5.6 and The y-coordinate of point P = 2.6

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents