Graphing, Inequalities, slopes, Variables, and Elimination

#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 the domain of the function g(x)=1/9-2x
All real numbers (there is no value of x that makes this function untrue)

#12find the indicated outputs for f(x)=5xsquare-4x
I'll assume you want f(0), f(1), and f(2), but there was none given
f(0)=0
f(1)=5*1^2 - 4(1)
f(1)=1
f(2)=5*(2^2)-4(2)
=5*4-8
f(2)=32

#13 solve the system of equations ( an ordered pair ) x+8y=8 x=7-8y
No solution (there is no y value that is true for this, indicating parallel lines)
#14solve the compound inequality 7>-4x+6 or 8<_-3x=4
7>-4x+6
1>-4x
-1/4<x
THEN
5<_-3x
-5/3_>x
Therefore
-1/4<x<_-5/3

#15graph using the slope and the y intercept y= 8/7x +7
y-intercept is 7. Slope is 8/7

#16 use distributive property 4(w-4)=8
4w-16=8
4w=24
w=6
#17 solve -4&#8804;3x-x&#8804;-2
-4&#8804;2x&#8804;-2
-2&#8804;x&#8804;-1
#18 graph and identify y intercept y+x=-9

y-intercept=-9

#19 is (-8,3) a solution to 8x-4y=-4
8*(-8)-4(3) = -4
-64-12 = -4
No it is not
#20 use the intercepts to graph the equation x + 5y =10
x-int=10
y-int=2

#21 multiplication principle -3/4x+-9/10
I am not sure what is being asked here, since it does not equal anything

#22 are the lines parallel, perpendicular, or neither 2x+3y=4 3x+2y=2
Change to y=mx+b
y=-2/3x +4/3
y=-3/2x + 1

They are neither, since parallel requires the same slope and perpendicular requires the negative reciprocal. Neither is present.
#23 soybean meal is 12%protein, cornmean is 6% protein. How many of each should be mixed together to get a 240lb mixture that is 9% protein? How many pounds of cornmeal? How many pounds of soybean
9% is the midpoint between 12 and 6, so we can mix them 50:50. 120lb of cornmeal, and 120lb of soybeans

#24 find the slope and the y intercept f(x)=-3x-5
slope= -3
y-int= -5

#25 find the domain and the function p(x)=xsquare-2x+3
Domain: All real numbers
Range: All real numbers
#26 find the slope (8,5) and (9,-2)
m=dy/dx
m=(5-(-2))/(8-9)
m=7/-1
m=-7
#27collect like terms 13x+6y-7x-9y
13x-7x+6y-9y
6x-3y
#28 the width of a rectangle is fixed at 16cm. What lengths will make the perimeter greatger rgan 90cm?
We can set up a function
P=2w+2L
w=16
We want P>90
Therefore, 2w+2L>90
2(16)+2L>90
32+2L>90
2L>58
L>29
So if L is greater than 29, then we are successful
#29 solve using multiplication principle -2x>1/9
(9)*-2x>9*(1/9)
-18x>1
x<-1/18

#30 Amy paid 69.51 for a pair of running shoes during a 30% off sale. What was the regular price?
70% of the price is 69.51
0.70x=69.51
x=99.3
$99.30
#31 solve 5/4x+1/8x=5/8+x
8(5/4x+1/8x)=8(5/8x+x)
10x+x=10x+8x
11x=18x
-7x=0
x=0
#32 Media services charges $40 for a phone and 20/month for its economy plan. The equation c=20t+40 describes the total cost, c, of operating a media service phone for t months. The total cost of 10 months of service is? If a customer had $90 available how many months of service can he receive?
10 months, t=10
c=20(10)+40
200+40
240$

c=90
90=20t+40
50=20t
t=2.5 months

#33 elimination method 3r-5s=-16 5r+3s=30
3(3r-5s=-16)
5(5r+3s=30)
9r-15s=-48
25r+15s=150
34r=102
r=3
3(3)-5s=-16
-5s=-25
s=5
#34 solve 5+5x<35
5x<30
x<6
#35 evaluate z+y/6 for z=46 and y =2
46+2/6
46 1/3
#36 solve 8x-(3x+7)=28
5x-7=28
5x=35
x=7
#37 50% of what number is 15?
0.5x=15
x=30
#38 graph the line containing the given pair of points and find the slope (2,0), (-4,-3)

slope = 1/2
#39 solve the system, graph, and classify as consistent, inconsistent, dependent or independent 8x-4y=-16 4y-8x=16
y=2x+4
and
y=2x+4
These are consistent and dependent

#40 graph the inequality on a plane 4x+5y&#8804;20

#41 on 3 consecutive passes a football team gains 7 yards, loses18yards, and gains 46 yards. What number represents the total net yardage??
7-18+46= 35 gained
#42 h(x)=2.75x+71.48 predcit height of 33cm
2.75(33)+71.48
162.23
#43 find slopx=-7
There is no slope since this line is vertical. It is undefined
#44 multiplcation principle 9x=-72
1/9(9x)=1/9(-72)
x=-8
#45 graph y&#8805;-3 x&#8805;4

#46 solve for indicated letter d=8h, for h
h=d/8
#47 solve then graph 6x&#8805;30
x&#8805;5

#48 eliminatiion method 4x+5y=5 8x+10y=10
(-2)4x+5y=5
8x+10y=10
-8x-10y=-10
0=0
These are the same equation

#49 solve .08x+2&#8804;1.2x-9
2&#8804;0.4x-9
11&#8804;0.4x
27.5&#8804;x
#50

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