Two trains leave the station at the same time, one heading east and the other west. the eastbound train travels
12
miles per hour slower than the westbound train. if the two trains are
850
miles apart after
5
hours, what is the rate of the eastbound train?

80 miles per hour

Step-by-step explanation:

Eastbound

r = r - 12

t = 5 hours

d = d_e

Westbound

r = r

t = 5 hours

d_w = 850 - d

The two distances add up to 850 miles

d_w + d_e = 850 miles

(r * t)_w + ( (r -12)*5 ) = 850 miles

r*5 + (r - 12) * 5 = 850                     Pull out 5 as a common factor

5 * ( r + r - 12)  = 850                       Divide by 5

(r + r - 12) * 5/5 = 850/5                  Do the cancellation

2r - 12 = 170                                     Add 12 to both sides

2r - 12 + 12 = 172 + 12

2r = 184                                           Divide by 2

r = 92

r = the westbound train     =  92 mph

r - 12 = The eastbound train  = 80 mph

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form