⦁scott works as a delivery person for a shipping company. the graph shows a linear model for his delivery times on different days.

questions are on the next page.
⦁ graph is on the previous page

⦁ identify two points on the line and write the coordinate pairs below.

⦁ use your two points to find the slope, and make sure to show your work.

⦁ use your slope from part b and find the equation of the line in point-slope form. show your work and work through the steps to transform the equation from point-slope form into slope-intercept form.

⦁ based on the equation you found in part c, predict how long it initially took scott to deliver his packages. approximately how much did his delivery time decrease per day?

(3, 21), (6, 12)-3y -21 = -3(x -3)  ⇒  y = -3x +3030 minutes; 3 minutes

Step-by-step explanation:

a) The two marked points have coordinates (days, minutes) = (3, 21) and (6, 12).

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b) The slope is the vertical change (rise) divided by the horizontal change (run). For these two points, that is ...

  rise/run = (12-21)/(6-3) = -9/3 = -3 = slope

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c) The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . for slope m through point (h, k)

Using the first point and the slope we found, this is ...

  y -21 = -3(x -3) . . . . . point-slope form

Add 21 and eliminate parentheses:

  y = -3x +9 +21

  y = -3x +30 . . . . . . . . collect terms; slope-intercept form

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d) The initial time is the time corresponding to day 0, the value of y when x=0. It is 30 minutes.

The slope in part (b) tells us the time decreases by 3 minutes per day.

Ithink its 126 hope its

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12