Triangle PQR where P(1,4), Q(-3,-4),R(7,k) is right-angled at Q. find the value of k

k = - 9

Step-by-step explanation:

Since the triangle is right- angled at Q then PQ is perpendicular to RQ

Calculate the slope of PQ using the slope formula

m =

with (x₁, y₁ ) = P(1, 4) and (x₂, y₂ ) = Q(- 3, - 4)

= = = 2

Given a line with slope m then the slope of a line perpendicular to it is

= - = - , thus

= -

Calculate the slope of RQ and equate to -

= = - , that is

= - ( multiply both sides by 10 )

k + 4 = - 5 ( subtract 4 from both sides )

k = - 9

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

answer: 5/2     2 1/2

step-by-step explanation:

5/2              

5 goes into 2 two times so its 2 and 1/2