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YES!! When the line is VERTICAL it is NOT a function!!

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Do you mean like this???

I would put it together into one square root:

Simplify:

Put all the perfect square factors in the first square root, and leftover factors in the second square root:


Rationalize the denominator of the second fraction by multiplying inside the radical by .


Simplify:




For more help on square roots, please see my own user-friendly explanation by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." You may need to see Basic Algebra in Chapter 5, or click on Intermediate Algebra and choose Chapter 3. Explanation varies in level of difficulty between these two. If you want College Algebra, go to the MATH IN LIVING COLOR pages, and Choose College Algebra, Chapter 1.

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a. Five subtracted from a number. Let x = the number. Now, this is NOT 5-x, It has to be 5 subtracted FROM x, which is x-5.

b. The ratio of a number and six. Ratio means a quotient, so you divide. Let x = the number.

See my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and take the second link on my home page which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, choose Chapter 1, and look for Section 1.09 for an explanation of word problems that is probably a LOT easier to understand than your own traditional textbook.

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Xintercept = (-3,0)
Yintercept = (0,2)

First find the slope. Can you do that? If not, check out my website!! Send me an Email, and I'll tell you where to look!!



Therefore the equation is y=mx+b, where m = slope and b= yintercept.
FINAL ANSWER

For more on this, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Choose Basic Algebra, and look for Chapter 4. The first three sections explain graphing and slope of a line. The slope of a line is in Section 4.02. The equation of a line is in Section 4.06.

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A) Let T= height of Tony in feet.

B) Let S = freeway speed.

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Each pound equals 16 ounces. If the apples are 4 ounces each, then this is 4 apples per pound. Multiply the number of pounds times 4, and you should get 4*46 = 184 apples.

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Let x= width of the rectangular field
x+2 = length of the field.

Area = Width * Length
120 = x(x+2)
120 = x^2 +2x

This is a quadratic equation so set it equal to zero:
0=x^2 + 2x - 120

Let's hope it factors:
0=(x-10)(x+12)
x=10 or x=-12

Reject the x=-12, since you can't have a negative width.
x=10 yds = Width
x+2= 12 yds = Length

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6/16=3/8

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When you solve an inequality by dividing both sides by a POSITIVE number, the inequality sign remains the same. When you divide by a NEGATIVE number, the inequality sign must be reversed. In this case, you divided by a POSITIVE number, so the inequality sign stays the same.




This means go to 9 on the right side of the numberline, and from 9, shade the number line from 9 to the RIGHT, with an arrow pointing to the right towards number larger than 9. Use a SOLID circle on the point at the 9.

The solution will be { x| }.

For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 1. Problems like this one will be found in Section 1.11 Inequalities. Students tell me that my explanations are easier to understand than expensive, traditional textbooks.

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The y-intercept is where the graph crosses the x-axis. It is the point where x=0. If x=0, then y=7. It turns out that the number term in this type of equation is always the y-intercept. Next, find the slope, which, in this type of equation, is always the coefficient of x. The slope is 9/4.

Slope is the . So the RISE =9, and the RUN=4.

Start by plotting the y-intercept by going UP 7 units on the y-axis, and put the FIRST point. Next, start with your pencil ON the y-intercept, and measure from this point UP a distance of 9 units (that would be a total of 16 units!), then go from there OVER 4 units to the RIGHT, and put the SECOND point. Connect the two points with a straight line, and you have the graph, which should look like this:



For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 4. Problems like this one will be found in Section 4.02 Slope Intercept Method. You may find my explanations easier to understand than traditional textbooks.

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Let x = the unknown number (or whatever letter you would like to use!)

You realize (I hope!) that 16% can be written as a decimal, 16%=.16, so take the "product" of these, which is .16x.

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Since the second equation is stated in the form "x= ____", I would recommend the substitution method. Substitute what x= in the second equation, back into the first equation:

x+2y=7 (1)
x=8-2y (2)

(_____) +2y = 7
(8-2y) +2y=7

A funny thing happens here!! All the variables subtract out, and you are left with 8=7. This is NOT POSSIBLE, so there is NO SOLUTION. Actually, the two given straight lines are PARALLEL LINES.

For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 4. Problems like this one will be found in Section 4.07 Systems of Equations. You may find my explanations easier to understand than traditional textbooks.

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To solve for e, you must get the "e" by itself. You have to eliminate the 7. Since the 7 is multiplied times the e, in order to UNDO this, you have to DIVIDE both sides by 7. This would be:





For additional help in an easier to understand format, see my website, by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and look for Chapter 1, Section 1.08 Equation Solving.

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Subtract 3 from each side:


Here is the tricky step! When you muliply or divide both sides of an inequality by a negative number, you must REVERSE the inequality sign!



For a simpler explanataion of this than the one you have in traditional textbooks, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for about the second link on my home page, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on "Basic Algebra", "Chapter 1", and look for "Section 1.11 Inequalities." My own students and students who discover my website tell me that I have a "user-friendly" explanation. I hope you will find it helpful.

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Do you mean the VERTICAL line?? It means "such that".
The set of all values of y, SUCH THAT, y> what value.

Of course the answer, if you add +5 to each side, is y>-10.

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Factor by grouping:




Zeros are at x=-7,x=1, and x=-1, each of multiplicity 1. D is correct!

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First multiply 5 times 16 =80. Secondly, when you multiply with the same base number, you must ADD the exponents!


Next, divide out the 80s, and when you divide, you must SUBTRACT the exponents!


You probably need additional explanation! I have a complete explanation that is designed for folks who have trouble with math. See my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, then click on Chapter 2, and look for Section 2.12 Positive Exponents. At least I think it is Section 2.12.

See if this helps.

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It's what the acorn said after it grew up!!

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In case you didn't get this one, "Gee! I'm a tree!"

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To find the domain, you must make sure the denominator does NOT equal zero. In this case, make sure that 4-9x does NOT equal zero.

To solve this, solve
4-9x=0 and the domain will be all values of x EXCEPT this value!
4=9x
x=4/9

Domain is all values of x EXCEPT 4/9.

For additional explanation, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for MATH IN LIVING COLOR, which is about the third link on my homepage. Choose College Algebra, then Chapter 2, the section called "Functions, Domain, and Range".

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Find the LCD= 6.





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Do you have a particular problem or two to post? We don't have your textbooks!!

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Is the small 2 written as a superscript (an exponent?) or a subscript??? My guess is that these are exponents!

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These points form a vertical line, so the slope is UNDEFINED!

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RISE = 4, RUN = 1

Slope m= =

y=mx+b
y=4x+8

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Multiply both sides of the equation by the LCD which is 10:








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Volume =L*W*H
V=10*10*21=2100 cu cm

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Start by adding +2 to each side:
3= 5/11 x-2
5=5/11 x

Next, you must "undo" the multiplication by the fraction 5/11. The best way to do this is to multiply both sides of the equation by the "reciprocal" of 5/11, which is 11/5.





Did we make it by 12:00 May 12???

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An equation has infinitely many solutions when, in the process of solving for the variable, you come down to a statement (for example, 0=0) that is ALWAYS TRUE. In math, this is called an IDENTITY.

An equation has NO SOLUTIONS when, in the process of solving for the variable, all of the variables subtract out, and you get a statement (for example, 0=3)that is NEVER TRUE. This is called a CONTRADICTION.

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4x^2+y^2+8x-4y-28=0

Sort it out and factor the coefficient of x^2. Leave spaces in order to complete the square in the next steps:



To complete the square, you must take half of the x coefficient (Half of 2 is 1, and square which is 1. On the right side, however, you must add 4*1 which is 4. It should look like this:




Divide both sides by 36 to write this in standard form for an ellipse:




This is an ellipse, with center at (-1,2), with a "radius" of 3 in the x direction, and a "radius" of 6 in the y direction.

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