Many insects migrate (travel) between their summer and winter homes. The desert locust migrates about 800 miles farther than the Monarch butterfly every spring, and the pink-spotted hawk moth migrates about 200 miles less than four times the distance of the Monarch butterfly every spring. Laid end to end, the distances traveled by a Monarch butterfly, a desert locust, and a pink-spotted hawk moth is about 12600 miles every spring. How far does each species travel?

Distance travelled by Monarch butterfly = 2000 miles

Distance travelled by desert locust  = 2800

Distance travelled by pink-spotted hawk moth= 7800 miles

Step-by-step explanation:

Let the distance travelled by Monarch butterfly  be "X" miles

Distance travelled by desert locust is equal to X + 800 miles

Distance travelled by pink-spotted hawk moth is equal to 4X -200 miles

The total distance travelled by the three is equal to 12600 miles

Distance travelled by Monarch butterfly = 2000 miles

Distance travelled by desert locust  = 2000 + 800 = 2800

Distance travelled by pink-spotted hawk moth = 4 * 2000 -200 = 7800 miles

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.

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