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In the English language we use "pronouns" to take the place of a noun. In the same way, a variable is like a "pro-number", in that we use it to take the place of a number. A real life problem does not come with an equation, does it. For example, suppose you are trying to find the length and width of a particular rectangle that has a certain perimeter and some additional characteristics. You don't know what the width and length of the rectangle are, so you assign variables like x or w or l to these unknown quantities until you can find out what they are. Then you can write an equation in terms of these variables, you can solve the equation and find out what numbers those variables represented. That is the whole process of algebra dating back to the Greeks in days of B.C.

As to your question of how can you get your algebra credit or be proficient in algebra, I tell you, I LOVE that question. You have to get a good teacher, plan to spend a LOT of time doing homework and PRACTICING, like a musician or an athlete must do to become proficient, and get LOTS of HELP from TUTORS, especially the TUTORS on algebra.com!!! I could write a BOOK on this topic!!

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Just to finish up your problem here, remember that the negative of a negative is a positive:

-15/24 - (-22/24)
-15/24 + 22/24
7/24

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Let x = number of students who took the exam.
.7 x = number of students who solved Problem A.
.6 x = number of students who solved Problem B.
9 = number of students who solved both problems correctly.

Since everyone got at least one problem correct, adding the two categories of students (.7x + .6x) together would include ALL the students who took the exam, but the 9 students who got both problems correct will be counted twice. So when writing the equation, you add these two categories and subtract the overlap, in order to get the total number of students who took the exam

This gives the following equation:
.7x + .6x - 9 = x
1.3 x - 9 = x

Subtract x from each side
1.3x - x - 9 = x - x
.3x - 9 = 0
.3x = 9

Divide by .3
x = = = 30

Check:
70% of 30 = 21
60% of 30 = 18
The total of these is 39, which means that 9 got both problems correct.

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Let x = "WHAT" you are trying to find.

22,985 IS WHAT PERCENTAGE OF $34,505


Divide both sides by 34505


(I hope you are allowed to use a calculator on this one!)
Dividing it gives you a decimal, which is approximately .666135
and change to a percent by moving the decimal two places to the right: 66.61% (approximately)

Likewise for the second problem:
11,520 IS WHAT PERCENTAGE OF $34,505

x = = .333864 or 33.39%

Now (NO EXTRA CHARGE!), notice that if you add these two percents together, you get 100%. Also notice that if you add the numbers 22,985 and 11,520 you just happen to get the TOTAL which just happens to be the other number in this problem $34,505.

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-30

See Lesson Plans on "Signed Numbers" by either me or Longjonsilver.

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-21

See Lesson Plans on "Signed Numbers" by either me or Longjonsilver.

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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 -19 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 -19 is + or - . The solution is Here's your graph:

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The problem says "do NOT combine fractions." Just find the LCD.
and

The LCD must have all the factors of all the denominators. Also, you have to know that a^2 is a factor of a^3, so if you have a factor of a^3, that takes care of the a^2 also. See my Lesson Plan called "Least Common Denominators" for more explanation and examples, and also my own website for free sections of explanation under Basic Algebra. Anyway, for this problem, the LCD must have . This might be the final answer for this problem. However, I'll go to the next step just in case!

In the first fraction, your denominator has a 5 factor and an a^2 factor, but it needs another factor of "a" to bring it up to the LCD. So multiply the first fraction, numerator and denominator, by "a":
=

For the second fraction, you have the a^3 factor, but you are missing the factor of 5. So multiply the numerator and denominator of the second fraction by 5:
=

According to the instructions in this problem, you are not supposed to put the fractions together. So that should do it, right?

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and

Notice that the denominator of the first fraction factors so you really have:
and

The objective is to get the denominators to be the same. You are allowed to multiply the numerator and denominator of any given fraction by the same quantity. Can you see that the Least Common Denominator (LCD) is (x-4)(x+4)?

The first denominator HAS the LCD, but the second denominator is missing a factor. The second denominator is missing a factor of (x+4). So you must multiply the numerator and denominator of the second fraction by (x+4):

and or
and

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It's an open interval since the endpoints are NOT included.

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I sure do!! Check for "Basic Algebra Practice Finals" under the "Tests" topic for Lesson Plans. Also, you can check my own website by clicking on my tutor name "rapaljer" at the top of this solution, and go to "Basic Algebra" then look for "Samples from Basic Algebra: One Step at a Time". There are Practice Tests at the end of each chapter. ALL FREE . . .

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This is what I got:








log 5y^3/x^2
log 5y^3 - log x^2
log 5 + log y^3 - log x^2
log 5 + 3 log y - 2 log x

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Equal fractions have equal cross products! By the way, what is a demonitor??

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60 miles per hour = =

Therefore the car will move 88 ft in the 1 second that the driver is recovering from the alcohol!! PLUS other side effects of the alcohol that cause delays in thinking and poor judgment! DON'T DRINK (even a little bit!) and DRIVE!!!

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=

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so

x+y = 98


Multiply both sides of the equation by 9

14y = 882
y= 63





Check: Sum = 63+35 = 98

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Solve for y:
x+y=4
y=4-x
Substitute into the second equation:
x-y=5
x-(4-x) = 5
x-4 +x = 5
2x - 4 = 5
2x = 9
x=9/2 or 4.5

y = 4-x
y = 4 - 4.5
y = -.5 or -1/2

Independent, since there is a unique solution.

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Divide both sides by 9:


Rewrite this as:


The center of the ellipse is at (0,0), and the radius in the x direction is 1, the radius in the y direction is . Therefore the major axis is in the Y-direction, and the foci will be on the y-axis at (0, c) and (0, -c), where

Solve for c:



or

Therefore, I have the foci at ( 0, ) and ( 0,).

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The mistake is that the equation has a DIFFERENCE of squares, which makes this equation a HYPERBOLA that opens right and left. If it is indeed an ELLIPSE, then it must be a SUM of . We would need to know which one is correct to continue.

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2.5x + 48x
x(2.5 + 48)
x(50.5)
50.5x

(50.5)*(435) = $21967.50

Check:
Down Payment = 2.5*435 = $1087.50
Payments = 48* 435 = $20880
Total = $21967.50

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If the equation for a graph is in the form , then it is a quadratic function, and it is a parabola. If a>0, then the parabola opens upward, and if a<0, then it opens downward. The larger the value of a, the steeper (more narrow!) the graph. If the value of a becomes smaller, like a fraction less than 1, then the graph becomes broader.

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cross products

means the same as , where ad and bc are sometimes called "cross products."

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.45 with a line over the top of it actually means the repeating decimal: .4545454545454545. . .

To find the fraction that it represents,
let x = .4545454545 . . .

Multiply both sides of this equation by 10 for each digit that repeats. If a single digit repeats, multiply by 10, if two digits repeat (as in this case), multiply both sides by 100, if three digits repeat, multiply by 1000.

100x = 45.45454545 . . .

Now subtract the x= .45454545 . . . from each side:

100x = 45.45454545 . . .
- x = - .45454545 . . .

The result is
99x = 45
so x =

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I'm going to have to disagree with the previous solution to this one!!

According to order of operations, you must do multiplications and divisions from LEFT TO RIGHT!

Do Parentheses first:
28/ (5-1) x 3

Do multiplications and divisions from LEFT to RIGHT (in this case, the division comes first!):
28/4 x 3
7*3
FINAL ANSWER = 21

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13/17 Rational number, Real number

3.12112111211112 Irrational number (there is a pattern, but it does NOT repeat), Real number

801.35 Rational number, Real number

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2x = -x + 9

Add +x to each side of the equation:
2x + x = -x + x + 9
3x = 9
x = 3

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8y - (2y-3) = 9

It might help to re-write this as
8y -1(2y-3) = 9
8y - 2y + 3 = 9
6y + 3 = 9
6y +3 - 3 = 9 - 3
6y = 6
y = 1

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I think my solution must have been posted at exactly the same time that you re-posted this problem. I think I corrected that error for you. By the way, I also emphasized that the parentheses notation (-5,2) is NOT appropriate for this type of an answer. There are different notations that (-5,2) could refer to, but THIS is NOT one of them.

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Are you serious?? This is just the distributive property!
4(x+1 ) = 4x + 4

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Since y=x
and y = x+2,

substitute the x in the first equation for the y in the second equation:
y = x+2
x = x + 2

Add -x to each side:
x-x = x-x + 2
0 = 2

And when does 0 = 2? Not in this lifetime!!! So there is NO SOLUTION for this problem. There is no solution because the lines are PARALLEL!!

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This is like the last Solution that I posted. But YOU are supposed to tell ME what value of x to substitute. I'll make up a problem for you. Suppose you wanted to find f(-3).

f(x) = 10x + 1
f(-3) = ______
First, this is a special notation that does NOT mean f times x. It is a special notation that is read "f of x", and it means that you are to substitute a value of x into this formula and simplify the result to find the value of the answer. It is MUCH easier than everyone can possibly imagine.

Given
f(x) = 10x + 1
f(-3) means that you sustitute the value of -3 in place of the x value(s).
f(-3) = 10(-3) + 1
f(-3) = -30 +1 = -29


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