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parallelogram is all I see since we know nothing about angles
and a rhombus has four equal sides but we only know about two sides.

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Nor do I!
How about the problem?

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An isosceles trapezoid with sides 15,23,4sqrt(2), 4sqrt(2) units
height =4 units
base angles 45 degrees
area (15+23)*4/2=72 square units
upper base is 15 units
lower base is 4+15+4=23 units
perimeter 15+23+8sqrt(2)=38+8sqrt(2)=49.31 units

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(30+x)*t=9
(30-x)*t=1
t=1/54 time
x=24 rate of current
another way of solving
t=9/(30+x)
t=1/(30-x)
9/(30+x)=1/(30-x)
x=24= rate of current
check
9/(30+24)=1/(30-24)
9/54=1/6
1/6=1/6
ok

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1 1/2 hours=1.5 hrs
30 minutes=.5 hrs
1.5/.5=3 times faster

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A/B=(4/5*pi^2*x^8)/(5/4*pi^2*x^8)
Eeverything but (4/5)/(5/4) cancel out
4/5 divided by 5/4=(4/5)*(4/5)=16/25 or .8*.8=.64=64%

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.25*(x+5)=.20x+5
x=75
75 animals yesterday
15 rabbits yesterday
check
(1/4)*(80)=(1/5)*(75)x+5
20=15+5
ok

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4^3=4*4*4=16*4=8*4*2=64=64*1
8!=40320=8*7*6*5*4*3*2=64*630
7*6*5*3=630
8*4*2*1=64
B. 64

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add up all the small trips by distance and time
75+7500+500+5=distance=d= 8080 miles
1.5+15+48+150/60=time=t= 67 hours
d=r*t
rate(speed) =d/t=120 40/67=120.6 mph
c. 120.6 mph

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v=pi*r*h
r=d*.5
r=.5*.5
250=pi*.5*.5*h
250=3.14*.5*.5*h
pi=3.14159
h=318.31 cm
h=318/100=3.18 meters
D.3.18 meters

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Let 1.00*x=total votes
.10x+.35x+.30x+10=1.00x
x=40 votes
vonda.10x=4
emma .35(40)=14
frank .30*40=12
bobby 10
difference 14-4=10

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9*12=108 sq meters
so only 54 sq meters are to be covered
9*6 is neat and clean but the decorator wants the rug to be centralized in the room with even space around it. This would leave exactly one half of the room bare
(9-x)(12-x)=54
108-21x+x^2=54
54-21x+x^2
x=3 and x=18
x=18 gives us negative dimensions
6*9 actually gives us 1.5 meters all around.
but the rug will be turned so that the length of 9 meters will go on the 12 meter length of the room.

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It can't be "solved" because you haven't asked any questions about it.
If there were another equation I could tell you where they meet or that they don't meet
There are many solutions because there are two unknowns.
I can tell you the slope. I can tell you where x=0 and y=0.
I can get another equation parallel or even perpendicular to it.
If you give me a point (ordered pair) I can tell you if it is on this line.
I can make another equation that will have the same solution set.
Graph it by picking any x of your choosing and calculate y.
Usually for a linear equation we pick where x is zero and y is zero

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Do you have a little more info and maybe a question?

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First we have two unknowns and need two equations.
The first thing we learn is the two numbers add up to 46
n+m=46
Now the next part is a bit hard to understand so lets break it down.
(four times one number)4n
It doesn't matter at this point which one- n or m will do.
so I choose n
then it says that 4n is (means =} 4 more (4+ )than twice the other number 2m
4n=4+2m
so now we have our two equations in two unknowns
n+m=46
4n=4+2m
solve the first one for either m or n it doesn't matter
n=46-m
or
m=46-n
just choose one and stick with it all the way
4n=4+2m
every time we see n in the above equation we will put 46-m
4(46-m)=4+2m
now we have one equation with one unknown
so now we just have bring everything together and combine and get the all the m's on one side and all the numbers on the pother
first let's multiply out
4*46-4m=4+2m
add 4 m to both sides
4*46=4+6m
4*45+4*1=4*1+6m
subtract 4*1 from both sides
4*45=6m
(2*2)*(3*15)
2*3*2*15=6m
6*30=6m
divide by 6
30=m
46-m=n
46-30=n
16=n
so far so good
now we go back to the second equation and check our work
4n=4+2m
4*16=4+2(30)
64=64
ok

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Solve: Any system of equations: has solution or (x=5, y=3}

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They are the same line.
The second is the first multiplied by 3

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P=2L+2W=130
W=L-3

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p=2l+2w=44
l=3w

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You are close. I appreciate that you mention what you tried.
What will be the same for both of them?
not the speed not the time but the distance.
d=rt
r1*t1=d1
r2*t2=d2
d1=d2
r1*t1=r2*t2=
t1=t+3
t2=t
6*(t+3)=10t
t=9/2
t=4.5
so instead of dividing them we make them equal.
Using t for the 10 mph means that the time t will be the answer to the question asked about the second cyclist. I also don't like dealing with negatives.
check
6*7.5=10*4.5
45=45
ok
BTW
We could have used t-3
6*(t)=10(t-3)
t=15/2=7.5
but we weren't asked about this guy
so we have to subtract 3
7.5-3=t-3

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p=plastic cups
and c=ceramic
p+c=400
c=400-p
3.50p+4*c=1458
3.50p+4*(400-p)=1458
3.5p+1600-4p=1458
-.5p=-142
p=284
c=116

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It is a horizontal line where x can be and is anything and y is always -7
The slope is zero and the y intercept of course is -7 since y is always -7

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plug them into 5x+3y=-2
and when you get -2=-2 that is the solution
if you get anything but -2=-2 it is not a solution
what would gives us -2
5-3=+2
so the x must be negative and the y positive
There is one solution like that

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let x = other number
(N+x)/2=A
N+x=2A
x=2A-N

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You have three denominators :m^2, n and m
Clearly m is a factor of m^2
so the common denominator will be nm^2
so multiply the fraction with m^2 as the denominator by n/n
the n denominator by m^2/m^2
the m denominator by mn/mn
The parts with no denominator by nm^2/nm^2
nm^4 +n^3 -m^2*n^4 +nm^3- nm^3+ m^2n^2+m^2n^2
now combine terms
nm^4-m^2n^4+n^3+2m^2n^2
All over nm^2

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I=prt
55.73=p*.19*2/3
solve for p

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I am assuming the steps you mention are what you have tried.
The second should be divide both sides by 4 (the coefficient of x^2)
third step should be take 1/2 the coefficient of x and square it and then add it to both sides
Possible intermediate steps:
4 x^2-4 x+3 = 0
Solve the quadratic equation by completing the square:
Divide both sides by 4:
x^2-x+3/4 = 0
Subtract 3/4 from both sides:
x^2-x = -3/4
Add 1/4 to both sides:
x^2-x+1/4 = -1/2
Factor the left hand side:
(x-1/2)^2 = -1/2
Take the square root of both sides:
|x-1/2| = i/sqrt(2)
Eliminate the absolute value:
x-1/2 = -i/sqrt(2) or x-1/2 = i/sqrt(2)
Add 1/2 to both sides:
x = 1/2 (1-i sqrt(2)) or x-1/2 = i/sqrt(2)
Add 1/2 to both sides:
x = 1/2 (1-i sqrt(2)) or x = 1/2 (1+i sqrt(2))

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Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -32 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -32 is + or - . The solution is Here's your graph:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -2 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -2 is + or - . The solution is Here's your graph:

4x^2-4x+3=0

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plug in the values of y's and x's
11-2/(1-(-2))=m
9/3=3=m
11-y=3(1-x)
11-y=3-3x
8-y=-3x
8=y-3x
y-3x=8
y=3x+8

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3x+2y=4
-2x+2y=24
subtract the second from the first
5x=-20
x=-4
3*(-4)+2y=4
-12+2y=4
2y=16
y=8
(-4,8)
check on second equation
-2(-4)+(2*8)=24
8+16=24
24=24 ok
check first equation
3*(-4)+2*8=4
-12+16=4
4=4 ok

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Did this as #252020
But if you are adding the two groups together you get zero
(5+2i)-(4-7i) and (4-7i)-(5+2i)

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(5+2i)+(4-7i)
remove parentheses and perform operations (addition)
Remember, if there is no sign, it is plus.
so +1*+4=+4
+1*-7i=-7i
5+2i+4-7i
9-5i
(4-7i)-(5+2i)
4-7i-5-2i
-1-9i