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Were you given any information in the problem for this one?

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Let x=side of square.
By Theorem of Pythagoras,




As good fortune would have it, also just happens to be the area of the square. Therefore, the area of the square is 32 square centimeters.

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3a+4b-(-6a-3b)
3a+4b+6a+3b
9a+7b

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If they gave you a figure and each side is labeled in terms of x, then remember that PERIMETER means to add up all the sides! So add up the sides and combine like terms. That's it!
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If they gave you a figure and each side is labeled in terms of x, then remember that PERIMETER means to add up all the sides! So add up the sides and combine like terms. That's it!

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You have to give us the problem!! We aren't THAT good!!

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This is a piece of cake, since you are given the y-intercept and the slope of the line! Start by graphing the y-intercept by going DOWN 9 units on the y-axis, and put a point. Now the slope is -6/7, so the RISE is -6, and the RUN is 7. Now, with your pencil on the y-intercept that you just graphed, move DOWN 6 more units, then go to the RIGHT 7 units and put the next point. Connect the dots, and it should look like this:


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What you did is correct. Unfortunately, when you find the x and y intercepts, you get the same point (0,0). You need to get another point or find the slope in order to draw the line. To get another point, choose an appropriate value of x, say x=3. From this you can easily see that y=1. So plot this point, as well as (0,0), and connect the dots.


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If you graph these two points, you will see that they form a HORIZONTAL line. The equation of a HORIZONTAL line is in the form of "y= " a number. In this case, the equation requires that the value of y be 9, so the equation of the line is .

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If the length of a side of a square is 3 units, then the surface area of one "face" is or 9 square units. There are 6 faces on the square, so the total surface area = 9*6 = 54 square units.

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You probably have a whole list of exercises, and in each exercise, TWO points are given. For each exercise, then , you are given only two points. To find the slope, you must find the , which can be found with this famous formula:


According to this formula, to find the RISE, you must subtract the y coordinates, and to find the RUN, you must subtract the x coordinates. Then just take the RISE OVER the RUN. That will be the slope between the two points.

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You probably have a whole list of exercises, and in each exercise, TWO points are given. For each exercise, then , you are given only two points. To find the slope, you must find the , which can be found with this famous formula:


According to this formula, to find the RISE, you must subtract the y coordinates, and to find the RUN, you must subtract the x coordinates. Then just take the RISE OVER the RUN. That will be the slope between the two points.

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2x+3y=6

To find the slope, you must solve for y in terms of x. In this case, get the 2x +6 terms to the right side of the equation:
3y=-2x-6

Next, divide both sides by 3:



The slope is the coefficient of x, which is .

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Polynomial functions with rational coefficients always have irrational and complex zeros in conjugate pairs. That is a fancy way of saying that if you have a zero of ,then you also have a zero at . If you have a zero at , then you also have a zero at .

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As in the pervious graph that I posted, this equation is in SLOPE-INTERCEPT FORM, y=mx+b. In this case , the y-intercept is -1, and the slope m==, which means that the RISE =1, and the RUN =2. Start graphing the y-intercept by going DOWN 1 unit on the y-axis. Put a point there. Now, with your pencil on this point, go UP 1 unit, then go to the RIGHT 2 units, and put another point. Connect the dots. It should look like this:


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In contrast to the last problem that I posted about graphing straight lines, these two lines are given in SLOPE-INTERCEPT FORM (y=mx+b). In these cases, you can immediately identify the slope and the y-intercept of each line. The number term is always the y-intercept, and the coefficient of x is always the slope, which can be written as a fraction that we call the "RISE OVER THE RUN". Then you can graph them as follows:

y=3x-4
The y intercept is -4, and the slope m=3, which means .
Start by graphing the y-intercept by going DOWN 4 units on the y-axis. Then starting with your pencil on this point,GO UP 3 units, then go to the RIGHT 1 unit, and put the next point. Connect these two points with a line, and continue the line in both directions.



y=-3x-4
The y intercept is -4, and the slope m=-3, which means .
Start by graphing the y-intercept by going DOWN 4 units on the y-axis. Then starting with your pencil on this point,GO DOWN 3 units, then go to the RIGHT 1 unit, and put the next point. Connect these two points with a line, and continue the line in both directions.


If you want to see the point of intersection for these equations, then graph the two lines on the same graph, and see where the lines cross. This point is the point of intersection of the two lines.


For additional help on most AMU topic in algebra, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the topic "Math in Living Color", choose a level of math, either Basic, Intermediate, or College Algebra, and look for the topic you need help with. If you can't find what you need, send me an Email, and maybe I can help you find the right page on my website!!!

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Because these equations are given in standard form, it's easiest to graph each of these by the TWO INTERCEPT METHOD.

x-y=-5
If x=0, then -y=-5, so y=5
If y=0, then x=-5

2x-6y=-18
If x=0, then -6y=-18, so y=3
If y=0, then 2x=-18, so x=-9

Graph these points and connect the respective dots! It should look like this:

It looks like the graphs cross at x=-3 and y=2. Therefore the solution set is the point { (-3,2) }

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Again, you have TWO many equal signs (joke!!) in the first equation!!

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I think there is an error in the way you copied the problem. You have two equal signs in the first equation.

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Multiply both sides by the common denominator :







However, there is a restriction that you can't have a log of a negative. This answer for gives the log of a negative number in BOTH logarithmic expressions, so it must be rejected. Therefore there is NO SOLUTION to this problem.

For additional exercises and detailed solution IN COLOR, see my webpage on logarithms by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "Math in Living Color", "College Algebra", "Section 4.04 Solving Exponential and Logarithmic Equations."

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See my website by clicking on my tutor name "rapaljer" anywhere here in algebra.com. Then click on "Basic Algebra", then "Basic Algebra: One Step at a Time," then "Chapter 1" (or whatever chapter you want to see!). Next select any topic. You will find an entire explanation with examples and exercises with answers at the end for most of the topics in Algebra 1. If you go back to my main page and click on "Math in Living Color", you will find many of these problems, the ones that my own students have had questions about, solved "in color". This is all FREE!!

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This just means to write the expression with the highest powers of x first!



The degree is the highest power of x, which in this case is 6.

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Are you trying to rationalize the denominator? What are the instructions on the problem? Maybe this is it:



*


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You solved this correctly, but then in your last step, you blew it away!!

Your correct answer is this:
a=3sqrt10

How did you ever get this???
a=2sqrt5

The correct answer is , which is approximately
A 9.487 feet

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Write down the formula:
m=kn

Plug in what you are given in the problem:
144=k*8

Solve for k (divide both sides by 8!)



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It may help to think of this and rewrite it as


Multiply the numbers that are OUTSIDE the square root and keep them OUTSIDE the square root, and multiply the numbers that are INSIDE the square root and keep them INSIDE the square root:





For more detailed explanation of radicals see my Lesson Plans about Square Roots in algebra.com, or go to my website (click on my tutor name "Rapaljer" anywhere in algebra.com!), and look for "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time," then Chapter 5 Radicals, Section 5.04 Multiplication of Radicals. See also my "Math in Living Color" page, "Basic Algebra," "Chapter 5." I hope you will find this helpful.

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When compounding semiannually, let n= 2 in this formula, P=$7000, t=8, and r=.089


A=$14048.60

When compounding continuously, use this formula, P=$7000, t=8, and r=.0875


A=$14096.27

If I did the calculations right, it looks like the continous compounding at a slightly lower rate came out better!

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In order to "undo" the "e" raised to the power, you must take the ln of each side of the equation. Remember that the :




Finally subtract 4 from each side:

x= -2.208 approximately.

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f(x) = -3x-2 is a straight line with y-intercept at -2 and with slope , which means a rise (down) -3 and run (right) of 1.

Start by graphing the point (0,-2) on the y-axis. From this point go DOWN 3 units, then RIGHT 1 unit, and put a second point. Connect the points, and that's the line.


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Let x = amount of money that Jan has. Now, just translate the sentence into an equation:
Twice the amount of money PLUS $25 more equals $499.
2x+ 25 = 499

Subtract 25 from each side:
2x+25 -25 = 499-25
2x = 474

Divide both sides by 2:

x= $237

You can check this by doubling the amount and adding $25. You should get $499.

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