# Graphing, Inequalities, slopes, Variables, and Elimination

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

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#### 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!

Linear Equations and Inequalities

1) Given one point on the graph (-3, -5) and the slope, m = -2, develop an equation in the slope-intercept format Lecture).

2) Given one point on the graph (- 2/3, 2/5) and the slope, m = - 3, develop an equation in the slope-intercept format(Lecture).

3) Given the following two points, (- 4, - 2) & (-1, - 5),develop an equation in the slope-intercept format(Lecture).

4) Given m = - 2 and the y-intercept = 3, give me an equation in the slope intercept format (Lecture)?

5) Given the following ordered pairs, develop the slopes(Lecture).

a) (3, - 2), (3, -1) b) (- 2, 1), (- 3, 1)

6) Solve the following system of equations: Use the substitution method for a. & the elimination method (addition/subtraction) for b (Lecture).

a) 2x + y = 6 b) 5x - 3y = 24

3x + 4y = 4 3x + 5y = 28

7) Graph the following inequalities in two variables: Do not turn this problem in, work it out at home and then compare it to the solutions you will be sent. Learn how to do this problem, you may see it on the Final (Lecture).

a) 6x - 2y < 12 b) 2x + 3y < 6 c) 2x + 4 < y + 7 d) 2y + 6 > 3x + 7

8) A particular piece of machinery has a yearly depreciation of $2,400. What would be the depreciation for the first year (straight-line method) if the piece of machinery were purchased on July 14th? (Assume that the company depreciates on a calendar year from Jan 1st to Dec 31st.)

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