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This is a parabola that opens downward, and the vertex (maximum point) will be at . In this case, vertex is at .

If x = 3, then y = -3^2 + 6*3= -9 + 18 = 9.

Maximum value is 9. Check it out with the graph:



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1000




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Slope =
=

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What is the question? Perhaps you should clarify this and repost the question.

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-|-5|-|-3|
- 5 - 3
-8

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Because the complex number system does NOT have an order relationship. Notice that the real numbers can be arranged on a numberline, so they can be placed in ORDER. Therefore, when comparing real numbers, each number on a real numberline must be equal to, greater than, or less than any other number. Since complex numbers cannot be "arranged in order, there are no such comparisions, and the Trichotomy Property does not apply.

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49x^2+9 = 42x

First set the equation equal to zero and place in descending powers of x:
49x^2 - 42x + 9 = 0

Factor it. (NOTE: It just happens to factor!!)
{7x - 3)(7x - 3) = 0
7x = 3
x= 3/7

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I think you may have an error in the equation. Your P(x) equation for profit is a parabola that opens upward, since the coefficient of x^2 is positive. A parabola that opens upward has a MAXIMUM, not a MINIMUM value. Whatever it is, to find the profit if 500 are sold, just substitute the 500 into the value of x in the formula and calculate it.

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From the graph, you can see that this is a straight line in which x and y both extend from negative infinity to positive infinity.

D: (-inf, inf)
R: (-inf, inf)

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From the graph, you can see that x extends from left to right, from negative infinity to positive infinity. Y extends from negative infinity up to a maximum at y = 4.

D: (-inf, inf)
R: (-inf, 4]

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By FOIL :


or

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To find an inverse relation, interchange the x and y:


Caylyne
Dr. Rapalje's grand daughter

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There's not enough information sorry

Caylyne
Dr.Rapalje's grand daughter

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A prime factor is a number that can only be divided by itself and one. These are like 2, 3,5,7,11,13,17,19,23,etc. Of these numbers only 2 and 3 can divide into 24.

caylyne
Dr.Rapalje's grand daughter

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I think it is easiest to convert directly from km to miles. If you use the conversion of 1 km. = 0.62 miles, then 4690 km will be 4690 times what 1 km is. In other words, just multiply 4690 times 0.62, which gives you approximately 2908 miles.

See also my website for an entire page on metric system. The link is
http://www2.scc-fl.edu/rrapalje/Tech-Prep-Math/Metric%20System.htm.
If this does not show up as a link, then click on my user name "rapaljer" anywhere in algebra.com, then look for Geometric Topics, then Metric System.

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Did you take the 6% and divide by 4 giving you 1.5% or .015 per period?

Did you take 5 1/2 years and multiply times 4 giving you 22 periods of compounding?

If you do those two items, the rest should work out. I am getting this:



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xa + 2bx - a - 2b
x(a+2b) -1(a+2b)
(a+2b)(x-1)

Your second problem looks strange. Are you sure you meant x^y ??? If that is what you REALLY mean, then here goes. Factor out a common factor of 7 and x:
14x^y - 35xy - 63x


Somehow, I don't think this is what you really meant, however.

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This is an exponential equation, so you will have to take the log or ln of each side of the equation to convert it from an exponential equation to an ordinary linear equation. First subtract 9 from each side:


Now, take the ln of each side. By the way, taking the log of each side works equally well and gives exactly the same answer!


By the third law of logarithms


Divide each side by ln 1.95:

= 5.142 approximately.
Final answer rounded to nearest tenth = 5.1

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If a right triangle is inscribed in a circle, then the legs of that right triangle will be the base and altitude of the triangle, and the hypotenuse of the right triangle will be the diameter of the circle. To find the area and circumference of the circle, you need to find the diameter (and radius!) of the circle.
If altitude = 4 and area = 28, then





Next, Let d= diameter of the circle, which is also the hypotenuse of the right triangle. According to the Theorem of Pythagoras:





Remember that the radius is HALF of the diameter, so if r= the radius, then
and

Area = square units.

Circumference = units.

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The key is to factor the numerator! This is usually a tough factoring problem, but since the denominator has a factor of (x+6), you might just expect a factor of (x+6) in the numerator also. Otherwise, there won't be anything to do in this problem.

I'd start with , and realize it has to start out
.

Expecting the factor of x+6 to show up here, I would next try:
.

Since the LAST term has to be a -6, this means that the blank space left in the previous step will have to be -1. Do you follow this?
. Now, check the middle term: 12x - 1x = + 11x.




Divide out the x+6 factors, and you have a final answer of .

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First I would add up the numbers given in the ratio:
2+5+7+10+20+50 = 94 shares.

The one who receives the least amount, therefore, received 2 shares out of a total of 94 shares of the total treasure, or th of the treasure.

Let x = total treasure, then


Multiply both sides by 47:
pounds = total weight of gold.

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The "or =" just means to make the graph with a SOLID line, which means that the line itself is included.

In my opinion the easiest way to graph this is to use the intercepts method and graph the line with an "=" sign only. We can handle the ">" sign later:


Let x = 0, then y=4.
Let y = 0, then 4x = 4, so x = 1. Graph these two points, and remember that if you have a POSITIVE Y-coefficient, the ">" or ">+" means to shade ABOVE the line. If you have a "<" or "<=" then it means to shade BELOW the line.

In this case you will have to graph with a SOLID line, and shade ABOVE the line. I don't know how to do this in algebra.com graphing so I'll graph the line, and YOU make it a SOLID LINE and SHADE ABOVE the line:


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Since this is addition of two fractions, you must first find a common denominator. Begin by factoring the second denominator:


The LCD must have all factors of the denominators, and this will be (x-2)*(x-6). The second fraction already has the common denominator, but you will have to multiply the numerator and denominator of the first fraction by the missing factor (x-6).



DON'T CANCEL ANYTHING --THESE ARE TERMS!!!
Multiply the numerators out and add them together, and divide by the LCD:



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Denominators can NEVER be zero, so any value that makes a denominator equal zero is a restriction. In this case, the denominator is 4z-6.

Therefore, the denominator 4z-6 must not be zero.
Therefore, the forbidden value would be
4z-6=0

Add 6 to both sides:
4z=6

Divide both sides by 4:

IS THE FORBIDDEN VALUE!!

Therefore the restriction on z is that Z must NOT equal .

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The critical step here is FACTORING, and I mean FACTOR COMPLETELY!!





Divide out the x-2 factor in the numerator and denominator, and this should be what is left:


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Because this is a fraction subtraction, your first step must be to find a common denominator. To do this, you'll have to factor each denominator, and take ALL the factors of all the denominators for the LCD.


The LCD will have to have within it factors of . To set up each fraction so it has the common denominator, you will have to multiply numerator and denominator of the first fraction by the factors 2(w-2), and the second fraction by the factors 5(w+2). It should look like this:


Now, the LCD becomes the denominator of the entire problem, and you subtract numerators:


In this last step, DON'T be tempted to divide anything out! These are TERMS! NEVER DIVIDE OUT TERMS!! Instead, multiply out the numerators, and combine like terms. This should be the answer you are looking for:



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Set up a ratio of Yes votes compared to Total votes cast. If the ratio of yes votes to no votes was 3 to 2, then there were 3 yes votes cast for every 5 total votes. Set up the following ratio:


Now, since means that ,
means taht

total votes cast.

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Did you forget to give us the problem?? Hey, we are pretty good here at algebra.com, but we aren't THAT good!!

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For the graph of a parabola or a quadratic function, the line of symmetry is exactly halfway between the zeros, which are the x intercepts of the graph, which are the solutions to the corresponding quadratic equation in which y = 0. Is that what you were asking??

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Why would you want to find a common denominator for a MULTIPLICATION problem??? Maybe the problem should be re-stated.

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