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I'm not sure what you are asking here. If you are given the equation of a line in STANDARD FORM (Ax+By = C), then in order find the slope, you must solve for y in terms of x. Then the coefficient of x is the slope.

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First of all congratulations on writing the equation box for this particular problem!!


Next, remove parentheses in the denominator. Remember that when you raise a power to a power you multiply exponents!!



Next, you can divide out the in the numerator with in the denominator, leaving in the denominator (subtract exponents!!). You can divide out the in the numerator with the in the denominator, leaving a in the denominator. The 2 stays in the numerator, and the 5 stays in the denominator.

The final result is:

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I think you have an error in the statement of this problem. The symbol * means multiply, and you have to have TWO numbers to have a multiplication!!

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Yes, I agree!!!

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The amount of increase is 22,001.55-22,000 = 1.55

The percent of increase (always make a ratio of the amount of decrease to the original amount) = which is 0.0000775 -- This is VERY close to zero. The nearest whole percent is 0%.

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Because this is in standard form, it's probably easiest to find the two intercepts:

5x +2y = 10
If x = 0, then 2y=10, so y = 5
If y = 0, then 5x = 10, so x = 2.

Graph these two points, and connect the points with a line. It should look like this:


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Let n = the unknown ("What percent" means n!)
"of" usually means "times"
"is" means "="

What percent of 175 is 35


This looks like the multiple choice b. 175n = 35

To eliminate the d. answer, you can divide both sides by 175, which gives you
, which is NOT d!

Final answer = b. 175n = 35

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-(4-5a)-(-2+3a)
-4 + 5a + 2 - 3a
-2 + 2a

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The first step for me is to clear the fraction, by multiplying both sides by the denominator which is 3.




This is an IDENTITY, so the solution is all real values of c.

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To solve by substitution, you have to solve for one of the variables in terms of the other. Probably the first equation is the easiest to solve for y.

4x+y=-19
y = -4x - 19

Substitute this into the second equation for y:
7x-y=8
7x - (______) = 8
7x - (-4x - 19) = 8
7x + 4x + 19 = 8
11x + 19 = 8
11x + 19 - 19 = 8-19
11x = -11
x= -1

Now, substitute this value of x into the y = equation to solve for y:
y = -4x - 19
y = -4(-1) - 19
y = 4 -19
y=-15

Check by substituting into the OTHER equation:
7x - y = 8
7(-1)-(-15) = 8
-7+15 = 8
8=8
It checks!

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This is not clear exactly what you mean. Do you mean:
?

If so, then remember this one? means that

Likewise:
means that

Multiply the parentheses:


Get all the variables on the right side by subtracting 12u from each side:



Add +42 to each side:



Divide both sides by 9


That's a pretty ugly answer, but that's life sometimes!! It's a hard problem to check, and the check on one like this is probably harder than just solving it again. If anyone finds an error, please send me an Email so I can fix it!!

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Change everything to feet. 2 yards = 6 feet, 1 foot = 1 foot, and 4 inches = 4/12 = 1/3 foot. The total is 6+ 1 + 1/3 = 7 1/3 feet or 22/7 feet, or 7.333. . . feet.

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First, hopefully you know what n! means.

For examples:
1! = 1
2! = 2*1 = 2
3!= 3*2*1=6
4!=4*3*2*1 = 24
5! = 5*4*3*2*1 = 120
etc.
n! = the product of the integers beginning with n and counting down to 1.

Now,
Beginning with n=1:
n=1, so
n=2, so
n=3, so
n=4, so
n=5, so

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What did you want to do, find a common denominator and subtract the fractions?


The LCD = 8mc

Multiply the first fraction by and the second fraction by .



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Because this is an addition problem, it calls for a common denominator, which is (x+y)(x-y).

Now, multiply the first fraction by and the second fraction by

It should look like this:
+



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I don't think there is enough information to solve this one.

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I'm not sure what kind of problems you are talking about.

If you have two straight line graphs, then the lines USUALLY intersect in ONE point. That is, USUALLY, except for TWO possibilities. If the lines are parallel, then the lines do NOT intersect, so there will be NO SOLUTION. The other possibility is that the lines could actually be the SAME LINE. In this case, the entire line is the solution, so there are infinitely many solutions.

Two straight lines CANNOT intersect in TWO points. However, if you had a quadratic function (i.e., a parabola), then it could intersect a straight line in TWO points (or in ONE point, or no points which would be no solution).

Is this what you had in mind?

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I would multiply both sides of the equation by the denominator which is 3. That clears the fractions and makes life a little easier!





Now, get all the y terms to the left side by adding -y to each side.



Add +6 to both sides:




Check: Substituet y = 6 back into the original equation:




It checks!!

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Graph the line . Since the equation is in standard form, I would find the two intercepts:

.
Let x = 0, then 2y = 6, so y = 3
Let y = 0, then 4x = 6, so y = 6/4 or 3/2

Graph the points and connect the dots with a line that should look like this:

Now, because the intequality to graph is , since the inequality is a LESS THAN OR EQUAL TO you need to graph a SOLID LINE and SHADE BELOW THE LINE. I can't do this in algebra.com, so you will have to do this. Remember, a SOLID LINE and SHADE BELOW THE LINE.

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I would always use the slope-intercept method. For decades it seems I taught to find the equation of a line using the point-slope formula. I thought this was the #3 formula in all of mathematics, behind the quadratic formula and the Theorem of Pythagoras. Then someone showed me that the slope intercept formula y = mx+b was so much easier! So it probably depends upon who you ask!!

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I recommend that you FOIL it out. Do you know about FOIL?
F= First times First
O= Outer times Outer
I = Inner times Inner
L = Last times Last


F =
O =
I =
L=

Total:

Combine like terms:

Total:

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This one would be

The first step is probably to set this inequality to zero by adding +2 to each side. WARNING: DO NOT MULTIPLY BOTH SIDES OF THE INEQUALITY BY A VARIABLE x!!


As I said, do NOT multiply both sides of the inequality by x, but you CAN find a common denominator of x, and express the left side as a single fraction! That is allowed, and it will help solve the problem.



Now draw the graph. The numerator does not factor, and probably does NOT have any real roots. The denominator will equal zero at x=0, so this is an ASYMPTOTE. With this done, now draw the graph, either with a graphing calculator or with the calculator in algebra.com. For this, you can use the original form of the inequality after you set it equal to zero, :

In this problem since it is a LESS THAN OR EQUAL TO problem, you will be looking for all values ON OR BELOW the x-axis. This will be the values of x to the left of the y-axis. Because the problem says "less than or EQUAL to", you would normally be INCLUDING THE ENDPOINTS. However, you NEVER include DENOMINATOR endpoints, since division by zero is NEVER allowed. So the final answer is x<0. Interval notation is (-inf, 0).

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This is a special problem in that you can just combine like terms in the parentheses:



Remember that


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I'm assuming that you mean .

If so, then I would begin by setting the inequality to zero. DO NOT MULTIPLY BOTH SIDES OF THE INEQUALITY BY (X+2)!!
.

Next, find a common denominator, which is x+2:




Now, you have two choices for method of solving the inequality. You can use some algebra explanations to solve it, or you can use a graphing calculator (or the algebra.com calculator!!). I will choose the latter method. You need to graph . Before drawing the graph, notice that there is one place that the numerator equals zero, and that is at x= -1. There is one value of x that would make the denominator zero, which is NOT allowed, and that would be x= -2. This tells me that there is a ROOT at x = -1 and an ASYMPTOTE at x= -2. Now, draw the graph with this in mind:


Now, since the problem is to solve , which is solving a problem that is "GREATER THAN", you need to find all values of x for which the graph is ABOVE the x-axis. And do NOT include the endpoints.
Notice that the graph is above the x-axis from -infinity to -2, and also from -1 to infinity.
This means that the solution is x<-2 or x>1.
In interval notation this will be:(-inf, -2) U (-1, inf).

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6x-(3-2x)>3x+2

Distribute the -:
6x - 3 + 2x > 3x +2
8x - 3 > 3x +2

Subtract 3x from each side:
8x - 3 -3x > 3x +2 -3x
5x -3 > 2

Add +3 to each side:
5x-3 + 3 > 2+ 3
5x > 5

Divide both sides by 5:
x>1

Graph on a numberline by going 1 unit to the right, and shade everything to the right of 1, with an arrow on the right end of the numberline, since x>1 means x is any number LARGER than 1, and since it goes forever in the right direction. To indicate that the endpoint at x=1 is NOT included, make an open circle at the point x=1. In higher math, we use an open parentheses on the point x=1, opening to the right.

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If you know that the slope is 4 , and it passes through the point (2,4), then your first step is to use y=mx+b to find b which is the y-intercept. Substitute everything you know (m=4, x= 2 and y = 4) into that formula:

y=mx+b
4 = 4*2 + b
4=8 +b
b=-4

So graph the line by starting at the y-intercept going DOWN 4 units on the y-axis. Put a point there. Then with your pencil on that point, rise UP 4, and go RIGHT 1, and put another point. Connect the points, and that should give you a line that goes through the points you mentioned in the problem. The equation of the line is , and the graph should look like this:


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How about this: 5 + 2 * 7 + 11 -13 = 17
I've never heard of Krypto numbers. Can you change the order of the numbers? Do you have to use them all exactly once??

Interesting!

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Add +4 to each side:


Divide by 2:


Locate 8 on the right side of the numberline, and the solution is all values to the right of the 8 and INCLUDING the 8. You can indicate this either by drawing a SOLID circle on 8 and shade to the right of 8 with an arrow on the end of the line to indicate that it continues forever. Also, instead of the solid circle, in higher math, you would place a BRACKET [ on the 8, and opening to the right, and shade to the right.

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w(3w+5)=22

This is going to be quadratic, so multiply out the parentheses, and set it equal to zero:
3w^2 + 5w -22 = 0
(3x ______)(w ______)=0

Factoring this will probably be the hard part of the problem. Here we go:

Two numbers whose product is 22 would probably be 2 * 11. Try the 11 in the first slot and the 2 in the last slot, and the middle term should come out to -6w +11w= 5w:

(3w+11)(w-2) = 0

Two solutions:
3w+11= 0
3w=-11
w=-11/3 Reject! The width cannot be negative!

w-2=0
w=2 cm. This one works!

Now, find the length:
L = 3w+5
L =3*2+5 = 6+5 =11 cm.

Check: Area = LW = 11*2 = 22 cm^2.

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Before you can graph , first graph y = -x-4, which is a straight line with y intercept -4 and slope -1. This means to plot the y-intercept by going DOWN 4 units on the y axis. The the slope of -1 means . With your pencil on the y-intercept at -4, go DOWN 1 and RIGHT 1 unit and put another point. Graph this line as a DOTTED line because the inequality with the symbol "<" means DO NOT INCLUDE THE LINE. Also shade BELOW the line. In algebra.com I can only draw the line for you. You will need to make it a DOTTED LINE, and you will have to shade BELOW the line.

Dont' forget: DOTTED LINE, SHADE BELOW THE LINE!!

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Hi, can you help me solve

3x-2      2
————— - —————
 x+2     x-2

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Because this is a subtraction problem, you must first find a common denominator, and in this case the LCD = (x+2)(x-2)

You'll have to multiply the first fraction by and the second fraction by .

It should look like this:
-

Place this all over the common denominator and multiply out the binomials in the numerators. HOWEVER, be CAREFUL to keep the negative between the numerators.




This can be factored, but it does NOT reduce the fraction, so factoring is optional:


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