If the interior angles of a triangle are 15, 15(x+y), and 25y and the relation between x and y is given by 5x-4y+2=0, then what is the measure of the smallest angle of the triangle

The sum of 3 angles inside a triangle is 180 deg, then:

=> 15 + 15(x + y) + 25y = 180

=> 15x + 40y = 165   (1)

And we have:

5x - 4y + 2 = 0

=> 5x - 4y = -2

=> 15x - 12y = -6       (2)

From (1) and (2), we have:

52y = 171

=> y = 171/52

=> 5x - 4 x 171/52 = -2

=> 5x = -2 + 171/13

=>  x = 145/65

=> First angle: 15 deg

=> Second angle: 15*(145/65 + 171/13) = 82.788 deg

=> Third angle = 25 x 171/52 = 82.211

=> Minimum angle: 15 deg

Hope this helps!

:)

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.