You can put this solution on YOUR website!
To calculate percentage:
.
43.2/108 * 100 = 40%
.
Done.

You can put this solution on YOUR website!
c = cookies
p = potato chips
.
4c + 3p = 501 cents
3c + 5p = 527 cents
.
multiply the first equation by 3 and the second equation by 4 and then subtract
.
12c + 9p = 1503
12c + 20p = 2108
------------------
-11p = -605
.
p = 55 cents
.
substitute to find 'c'
.
4c + 3(55) = 501
4c = 501 -165
4c = 336
.
c = 84 cents
.
use the other equation to check these values
.
3(84) + 5(55) = 527
.
Answer: Potato chips cost 55 cents, and cookies cost 84 cents.
.
Done.

You can put this solution on YOUR website!
Given the line has slope -2/3 we can define the equation using slope-intercept form:
.
y = -2/3x + b
.
Use the point to find 'b'.
.
12 = -(2/3)*6 + b
12 = -4 + b
16 = b
.
So the equation is:
.
y = -2/3x + 16
.

You can put this solution on YOUR website!
x + y + z = 237
.
y = 2x -9
.
z = 3x +6
.
substitute
.
x +2x-9 +3x+6 = 237
.
6x -3 = 237
.
6x = 240
.
x = 40
.
substitute
.
y = 2x -9
y = 2*40 -9
y = 71
.
z = 3x +6
z = 3*40 +6
z = 126
.
Check the sum
.
40 + 71 + 126 = 237
.
Answer: The three numbers are 40, 71, and 126.
.
Done.

You can put this solution on YOUR website!
7 1/4 - 2 3/4 = 29/4 - 11/4 = 18/4 = 4 2/4 = 4 1/2

You can put this solution on YOUR website!
(x-4)^2 = 4(y-1)
.
x^2 -8x + 16 = 4y -4
.
4y-4 = x^2 -8x + 16
.
4y = x^2 -8x +20
.
y = (1/4)*x^2 -2x + 5
.

.
You will notice the parabola does not cross or touch the x-axis, so there are no solutions with real numbers. You can confirm this with the quadratic equation.
.

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 -1 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 -1 is + or - . The solution is Here's your graph:

You can put this solution on YOUR website!
3y = 5 -x
3y = -x +5
y = -(1/3)x + 5/3
.
2x = y + 3
2x -3 = y
y = 2x -3
.
In the graph that follows:
The red line is y = -(1/3)x + 5/3
The green line is y = 2x -3
.

,
It appears the point (2,1) satisfies both equations.
.
Check:
y = -(1/3)*2 + 5/3
y = -2/3 + 5/3
y = 3/3 = 1
.
y = 2*2-3
y = 4 -3
y = 1
.
Correct.

You can put this solution on YOUR website!

.

.
cross multiply
.

.

You can put this solution on YOUR website!
That appears to define the point (-3,9). You could graph the point. But if that's all the information you have, there's not much that can be done with.

You can put this solution on YOUR website!
It appears your equation is:

so
x can range from -infinity to +infinity
.
However, if your equation in fact is:

If so, x cannot = 0 cannot because that would be dividing by 0.
So the domain is -infinity to 0, and 0 to +infinity.
.
In the following graph;
the red line is y = (4/3)x+7
the green line is y=4/(3x)+7
.

You can put this solution on YOUR website!
One cylinder will have dimensions as follows:
circumference = 8.5 = pi*d = pi*2*r
r = (8.5)/ (2*pi)
height = 11
area of base of cylinder = pi*r^2 = pi * ( 8.5/(2*pi) )^2
volume = 11 *pi * ( 8.5/(2*pi) )^2 = 198.6875/pi
.
The other cylinder:
circumference = 11
r = 11/ (2*pi)
height = 8.5
area of base = pi * ( 11/(2*pi) )^2
volume = 8.5* pi * ( 11/(2*pi) )^2 = 257.125/pi
.

You can put this solution on YOUR website!
x = 6y
.
x + y = 77
so
x = 77-y
.
x = x
so
.
6y = 77-y
.
7y = 77
.
y = 11
.
x = 6*11
.
x = 66
.
Answer: The two numbers are 11 and 66.

You can put this solution on YOUR website!
(2/3+1/2) / (3/4) = (4/6 + 3/6) / (3/4) = (7/6)/(3/4) = (7/6)*(4/3) = 28/18 = 14/9

You can put this solution on YOUR website!
Work problems like this are solved by using fractions.
.
Jennifer can pick 40 bushels of apples in 12 hours.
We can define "picking 40 bushels of apples" as 1 whole job.
She does 1/12 of the job per hour.
.
Tosakan can do the job in 10 hours.
She does 1/10 of the job per hour.
.
x = number of hours working together to do the job
.
(1/12 + 1/10)*x hours = 1 whole job
.
(1/12 + 1/10)*x = 1
.
22/120*x = 1
.
22x = 120
.
x = 120/22 = 60/11
.
60/11 = 5 5/11 hours
.
5/11 hr * 60 min/hr = 300/11 = 27.27272727272727 or about 27.3 min.
.
Working together they can do the job in 5 5/11 hr or about 5 hr and 27.3 min.
.
Always check your solution to see if it is the answer.
.
How many bushels does Jennifer pick in 60/11 hr?
She picks 40 in 12 hr, so she picks 10/3 bushels per hr.
60/11 hr * 10/3 bushels/hr = 600/33 = 200/11 = 18.18181818181818 bushels
.
How many bushels does Tosakan pick in 60/11 hr?
She picks 40 in 10 hr, so she picks 4 bushels per hr.
60/11 hr * 4 bushels/hr = 240/11 = 21.81818181818182 bushels
.
Answer: They can pick 40 bushels in 5 5/11 hr working together.
.
Done.

You can put this solution on YOUR website!
x + y = 12
so
x = 12-y
.
x*y - x^2 = 10
so
x*y = x^2 +10
y = x + 10/x
.
substitute for x
.
(12-y)*y -(12-y)^2 = 10
.
12y -y^2 - ( (12-y)(12-y) ) = 10
.
12y - y^2 -144 +24y - y^2 = 10
.
-2y^2 +36y -144 = 10
.
-2y^2 +36y -154 = 0
.
y^2 -18y + 77 = 0
.
(y-7)(y-11) = 0
.
So
y = 7 or 11
.
x + y = 12
so
If y =7, x = 5
If y = 11, x = 1
.
Using ordered pair (x,y) notation, the solutions are: (1,11) and (5,7).
.
In the following graph:
red line is y = -x+12
green line is y = x + 10/x
.

You can put this solution on YOUR website!
Define the two consecutive integers as follows:
x
x+1
.
x +x+1 = 175
2x = 174
x = 87
x+1 = 88
87+88 =175
.
Answer: The two numbers are 87 and 88.

You can put this solution on YOUR website!
The sum of 5 numbers divided by 5 = 10, which is the average (i.e., the arithmetic mean).
So, the sum of the 5 numbers is 5*10 = 50.
.
When we add a number, the average is increased to 12.
.
(50+x)/6 = 12
.
50+x = 72
.
x = 22
.
Done.

You can put this solution on YOUR website!
x = 2y
.
Note that that means x > y.
.
The product = 6 times the greater number.
.
x*y = 6x
.
Substitute x = 2y
.
2y*y = 6(2y)
.
2y^2 -12y = 0
.
2y(y-6) = 0
.
y = 0 or 6
.
Zero works quite nicely. Zero times anything is zero. So, x*0 = 6*x is true. In this case, x can be any number from -infinity to +infinity. This means there is no ordered pair. (x,0) for any x. This probably is a spurious solution, which means it is one that is not relevant to the practical problem at hand.
.
But how about y=6?
.
x = 2y
x = 2(6)
x = 12
.
Their product = 12*6 = 72.
6*12 = 72.
Correct.
.
Answer: The two numbers are 6 and 12.
.
Done.

You can put this solution on YOUR website!
The notion of three consecutive numbers that are divisible by 4 has to be interpreted. On the number, there is no instance where three consecutive numbers are divisible by 4. So it must mean that you are find three numbers that are multiples of 4 in sequence, but not really "consecutive" in the common meaning of the word "consecutive." So, we can define the three numbers a:
x = a number that, we hope, is divisible by 4
x + 4 = the next number that would be divisible by 4, given x is divisible by 4
x + 8 = the next number that would be divisible by 4, given x+4 is divisible by 4
.
x +(x+4) + (x+8) = 48
3x +12 = 48
3x = 36
x = 12
so
x+4 = 16
x+8 = 20
.
12+16+20 = 48
.
Answer: The three numbers are 12, 16, and 20.
.
Done.

You can put this solution on YOUR website!
A number plus its additive inverse = 0.
.
What number is 9 less than twice its additive inverse.
.
Define y is the additive inverse of x
so
x + y = 0
so
x = -y
.
The number is 9 less than twice its additive inverse.
x+9 = 2y
.
Substitute x = -y.
.
-y +9 = 2y
9 = 3y
3y = 9
y = 3
.
x + y = 0
x + 3 = 0
x = -3
.
So the number is -3. its additive inverse is 3.
Twice the additive inverse = 2*(3) = 6.
-3 is indeed 9 less than 2*3.
.
Done.

You can put this solution on YOUR website!
y = 5x is already in slope-intercept form: y = mx+b
.
y = 5x is actually y = 5x + 0
.
So, the y=intercept is (0,0).
.
Of course that means the x-interept is (0,0), too.
.

You can put this solution on YOUR website!
P = perimeter
P = 54 in.
P = 2(L+W), where L=Length and W=Width
.
L = W+3
.
substitute
.
2(W+3) + 2W = 54
.
2W +6 +2W = 54
.
4W = 48
.
W = 12
.
L = W+3
L = 12+3
L = 15
.
Check the perimeter to be sure this solution is the answer.
.
2L = 2(15) = 30
2W = 2(12) = 24
30+24 = 54
Correct.
.
Answer: Length = 15 inches; Width = 12 inches.
.
Is this a deck for a doll house? Just wondering...(smile)

You can put this solution on YOUR website!
Three consecutive odd numbers could be defined as x, y, and z.
But then you have 3 unkowns, so you need 3 equations to find a solution.
.
However, you know the numbers are consecutive odd numbers.
So, the first can be defined as 'x'.
That means the next two odd numbers is 'x+2' and 'x+4'.
Now you have only one unknown: 'x'.
.
And you know the sum of the three consecutive odd integers is 129.
.
If you were to have defined x + y + z = 129, then you would be stopped in your tracks.
.
But you've cleverly defined the numbers in terms of one unknown, 'x.'
So,
.
x +(x+2) +(x+4) = 129
.
3x +6 = 129
.
3x = 123
.
x = 41
.
Great! x is an odd integer!
.
x+2 = 43
x+4 = 45
.
Now we have three consecutive odd integers: 41, 43, and 45.
.
But check to ensure they total 129.
41+43+45 = 3*40 + (1+3+5) = 120 + 9 = 129
Correct.
.
Answer: The three consecutive odd integers that sum 129 are: 41, 43, and 45.
.
Done.

You can put this solution on YOUR website!
Ask a question.

You can put this solution on YOUR website!
Problem: The moving sidewalk at Chicago's O'Hare International Airport moves at a speed of 2.0 feet per second. Walking on the moving sidewalk, Nancy Killian walks 120 feet in the same time that it takes her to walk 52 feet without the moving sidewalk. How fast does Nancy walk?
.
Solution: Distance problems always use the fundamental distance equation:
.
d = r*t, where d=distance, r=rate, and t=time.
.
In this case we have two distances and one rate.
.
d = 120
r = w+2, where 'w' is Nancy's walking rate and 2 ft/sec is the speed of the moving sidewalk.
.
d₁ = 52
r₁ = w, where 'w' is Nancy's walking rate without an assist from a moving sidewalk.
.
At this point, we have too many unknowns to solve the equation.
But we have one addition bit of information that is very helpful: it takes the same time.
So, t = t₁ or rather t=t.
That indicates we need to get both distance equations into t=something form to solve the problem.
.
With Moving Sidewalk
.
d = r*t
d = 120
r = w+2
t = 120/(w+2)
.
Without Moving Sidewalk
.
d₁ = 52
r₁ = w
t₁ = 52/w
.
Transitive Property of Equality
.
We know t=t₁, so that means:
.
120/(w+2) = 52/w
.
Cross-multiply.
.
120w = 52(w+2)
.
120w = 52w + 104
.
Subtract 52w from both sides.
.
120w -52w = (52w-52w) + 104 = 104
.
68w = 104
.
Divide both sides by 68.
.
w = 104/68 = 26/17
.
This solution indicates Nancy's walking speed is 26/17 ft/sec or approximately 1.529411764705882 ft/sec.
.
But always check your proposed solution to ensure it is the answer.
.
If w=1.529411764705882, how long does it take her to walk 52 ft?
52/1.529411764705882 = 34.00000000000001 sec.
.
If w+2 = 3.529411764705882, how long does it take her to walk 120 ft?
120/3.529411764705882 = 34.00000000000001 sec.
.
Correct.
.
Answer: Nancy's walking speed is 26/17 ft/sec or approximately 1.529411764705882 ft/sec.

You can put this solution on YOUR website!
x/7 = 9
.
multiply both sides of the equation by 7
.
7*(x/7) = 7*9
.
on the left-hand side, the 7's cancel, leaving you with x
on the right-hand side, 7*9 = 63
.
x = 63

You can put this solution on YOUR website!

You can put this solution on YOUR website!
x/4 = 3/4
.
x = 3

You can put this solution on YOUR website!
You need to specify your problem completely. What you have provided is only an expression, which technically cannot be solved, it can only be simplified. You need an equation to solve.
.
Assuming your equation is:
.

.

.

.

.

.

.
To find the zeroes (roots), set y = 0.
.

.

.

.

.

.
x = -.866 or .866

You can put this solution on YOUR website!
Problem: A light aircraft flies from A to B, 450km away, and returns from B and A in a total time of 5 hours and 30 minutes. Suppose that during the whole journey there is a constant wind blowing from A to B. The speed of the aircraft in still air is 165 km/h. Find the speed of the wind.
.
Solution: The basic approach to solving problems such as these is to begin with the fundamental distance equation and plug in the known values and then solve for the unknowns.
.
d = rt is the basic distance equation.
d = 450 km
.
We are told the wind is blowing from A to B, so on the trip from A to B the airplane's speed is 165 km/h + w, where 'w' is the wind speed in km/h. That means the speed across the ground (the ground speed) is faster than the indicated airspeed. A wind from behind is called a 'tailwind.'
.
Similarly, the ground speed going from B to A will be reduced by the wind. The indicated airspeed will still be 165, but the speed across the ground will be 165 - w. Such a wind is called a 'headwind.'
.
We must assume the distance from A to B equals the distance from B to A. That is a reasonable mathematical assumption, although there are many factors in aviation that could force the path to be quite different going and coming.
.
We assume the plane is flying at an indicated airspeed of 165 km/h in both directions.
.
We are told the roundtrip time is 5 hr 30 min, which = 5.5 hr.
.
A to B trip:
.

.

.
B to A trip:
.

.

.

.

.

so

.

.

.

.

.

.

.

.

.

.

.
Note that sqrt(225) = + or - 15, but a negative wind speed is not applicable.
.
Substitute w = 15
.

.

.

.

.

which is the time flying from A to B with a tailwind.
.

which is the time flying from B to A with a headwind.
.
Check the distances traveled to be sure this is the answer.

.

Correct.
.
Answer: The wind speed is 15 km/h.

You can put this solution on YOUR website!
You can simplify by dividing both sides by 2.
x -2y = 4
.
Subtract x from both sides.
-2y = -x + 4
.
Divide by -2 to get the equation into slope-intercept form.
y = x/2 + 2 = (1/2)x + 2
.
The slope (m) = 1/2.
.
When x = 0, y = 2: (0,2), which is the y-intercept
when x =-4, y = 0: (-4,0), which is the x=intercept
.
With two points you can graph it.
.