Find the value of x.

x= 37.5°

Step-by-step explanation:

∠CBD

= 180° -75° (adj. ∠s on a str. line)

= 105°

∠BCD= ∠BDC (base ∠s of isos. △BCD)

∠BCD= x

∠BCD +∠BDC +∠CBD= 180° (∠ sum of △BCD)

x +x +105°= 180°

2x= 180° -105°

2x= 75°

x= 37.5°

Alternative working:

∠BDA= (180° -75°) ÷2 (base ∠s of isos. △ABD)

∠BDA= 52.5°

∠BDA +∠BDC= 90°

52.5° +x= 90°

x= 90° -52.5°

x= 37.5°

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 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.