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Graphing, Inequalities, slopes, Variables, and Elimination

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Please see attached. help with homework. equation, graphs.

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https://brainmass.com/math/graphs-and-functions/graphing-inequalities-slopes-variables-elimination-348485

Solution Preview

#1. Multiply 6/7 * -1/5
-6/35

#2. Simplify -5[-25-(29-31)]
-5[-25-(-2)]
-5(-23)
115

#3 solve 0.3x<-24
x<-80
#4 solve y-7>-18
y>-11
#5 find the slope of (-4,0) (0,1)
m=dy/dx
m=(0-1)/(-4-0)
m=1/4
#6 graph x + 5y=10
Change to y=mx+b
5y=-x+10
y=(-1/5)x+2

#7 trains A and B are traveling in the same direction on parallel tracks. Train A is traveling 60 mph and train B is traveling 64mph. Train A passes a station at 3:20pm. If train B passes the same station at 3:50pm at what time will train A catch up to train B?
We need to figure out how much time it will take for those 4mph faster to catch up to a 30 minute head start. I assume we want to know how long it will take for B to catch A, not the other way around.

Train A gets a 30 minute headstart, allowing it to move 30 miles ahead. Train B, in order to fill this gap, is basically moving at 4 mph compared to Train A. So we take 30 miles and divide by 4 mph, getting 7.5 hours. So 7.5 hours after Train B passes the station, it catches train A. 3:50 + 7:30 = 11:20PM

#8 translate to an algebraic expression The product of 45% and some number
0.45*x

#9 is the coordinates a function (-3,7) (2,2) (3,1) (7,5)
Yes
We know this because none of the x values are repeated, and none of the y values are repeated
#10 solve by substitution 8x+9y=-47 x=-5-2y
8(-5-2y)+9y=-47
-40-16y+9y=-47
-40-7y=-47
-7y=-7
y=1
x=-5-2
x=-7
(-7,1)
#11 find ...

Solution Summary

49 problems dealing with elimination, graphing, inequalities, finding slopes, percentages, word problems, and solving for variables. A tour de force of different techniques!

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