The measures of angles a and b are both positive, integer numbers of degrees. the measure of angle a is a multiple of the measure of angle b, and angles a and b are complementary angles. how many measures are possible for angle a?

there are 9 possible measures for A

Step-by-step explanation:

since angles A and B are complementary then,

A + B = 90

we also know that the measure of angle A is a multiple of the measure of angle B, then

A = B*n , with n=1,2,3...

If both are positive, integer numbers of degrees then the possibles solutions are

A = 60º and B = 30º

A = 45º and B = 45º

A = 80º and B = 10º

A = 75º and B = 15º

A = 85º and B = 5º

A = 89º and B = 1º

A = 88º and B = 2º

A = 84º and B = 6º

A = 72º and B = 18º

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.