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i is defined as the
So
i^1 = i
i^2 = -1
i^3 = -i
i^4 = (-1)(-1) = 1
And it repeats in a cycle of 4
i^5 = i^4*i = 1+i = i
i^6 = i^4*i^2 = 1*i^2 = 1 *(-1) = -1
i^7 = i^4*i^3 = 1*i^3 = -i
etc etc
how do you use in a radical? If the value under the radical is negative, then look at that as (-1)*aPositive
for instance = plus or minus 3i

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Don't let the algebra fool you. These LCM problems are done the same way you did them in arithmetic.
1)Find the prime factors in each term
2)Find which prime factor is used more times in each term
3)Collect all of most used prime factors
4)Multiply it all out
=
=
So there are three different prime factors, each used once.
Collect them


Now multiply and simplify and you're done

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This URL can factor
http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic

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}



So n = -9 or n=6
Since n=-9 is not possible in n!, then it must be n=6
Which makes sense since n+1=7 and n+2=8 and 7*8 = 56

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I don't know any easy way to work this other than 'trying' all the factors.
Divide thru by 2 and then grind out the various factors of 2475.
Or go here and have them give you the answer --> http://www.wolframalpha.com/input/?i=2q^3+-+8q^2+-+4950+%3D+0

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Let the twins age be given by A. You are told Kevin is 5 years older than the twins, so his age is
You are told the three of their ages total 53





So the twins are sweet sixteen and Kevin is 21.
Check your answer is 16+16+21 = 53?

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use this --. http://www.algebra.com/algebra/homework/quadratic/quadratic.solver

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The biggest value any sin can get is 1. So the amplitude is set by the coefficient 4. look at this graph -->
http://www.wolframalpha.com/input/?i=+y%3D4+sin(3x)

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The size of a radian is determined by the requirement that there are radians in a circle. So each revolution is radians
=


radians per second

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If you 'see' an easy factorization, you can always use that. But for me, once the factors get that large, I prefer the quadratic equation. here is a solver that does it for you --> http://www.algebra.com/algebra/homework/quadratic/quadratic.solver

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 : . Discriminant d=5625 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 30, -45. Here's your graph:

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read this --> http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php

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Look at this tool --> http://www.algebra.com/algebra/homework/Linear-equations/equation-parallel-or-perpendicular.solver

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Look at this solver --> http://www.algebra.com/algebra/homework/Linear-equations/equation-parallel-or-perpendicular.solver

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You know that roots result in zeros.
So a zero at x=-2 means (x+2) is a factor in the formula for the polynomial.
Likewise you are told you have an imaginary root at 7i. You know that imaginary roots come in pairs (7i , -7i)
So two more factors are (x-7i) and (x+7i)
Now you have three terms. The polynomial is the product of those three factors.



All you need to do now is simplify by multiplying it all out. I'll leave that to you, because I know you can do that. Ping me if you need more help

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Use your calculator and find the "tan-1" button. Mine is the yellow above TAN (TI-83)
Depends on the calc you have, but you need to find the 'arctan' or 'tan -1'.
Tangent takes degrees and turns them into a ratio.
ArcTan takes a ratio (fraction) and turns it into degrees.
When you plug in tan-1(5/6), you'll get 39.8 degrees. Now you need to know which quadrant the plot it in to find 180-39.8

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Let the ? be represented by z. Now solve for z
Use distribution on the left side numerator
divide both sides by 9
multiply both sides by z
isolate z
simplify

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thats as simple as it gets.
http://www.wolframalpha.com/input/?i=sqrt(6%2Fx)

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Solve each part separately first
break it up as
and
now solve each part

-->


Now plot them both and find where they are 'both true"
in this case, you would the numbers that satisfy both equations are

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Act like it is a "minus 1" and then distribute that across the values inside he parens
For instance
-(2x+3)
-1(2x+3)
-2x -3
get it?

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The sum of the measures of the interior angles of a polygon with n sides is (n-2)180
You have 32 sides, so

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Let the three numbers be x , x+ 2 and x+4




So the numbers are 10, 12 and 14

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You want to get x "by itself" on one side of the equal sign

Let's go one small step at a time
1) clear the denominator on the left side.
multiply both sides by 7
divide both sides by -2


Check your answer
Does

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Use the area to rid the radius of the wheel




So the radius is 0.7m
Now use the equation for circumference


meters
How many circumferecnes are in 176m?

Allowing for rounding, I would say 40 revolutions.

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Yes. that is the equation of a line and the line is not vertical. So every value of x maps to one and only one value for y. Which is the definition of a function.

You can always use the vertical line rule. Plot the given equation. If any vertical line intersects the plot in more than one point, then the equation is NOT a function.

You can plot things at the website -->
http://www.wolframalpha.com/input/?i=8y%3D7%2B3x

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Use Pythagorean theorem.
The 13 meter ladder will be the hypotenuse, one leg is 6 meters. You are asked to find the other leg
Pythagorean theorem




meters

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Let x be the number. You are told



Check your answer is 3*8 - 12 = 12??

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Several ways to do this. The sinplest is to plug the value given for y in the second equation, into the first equation and then solving for the remaining variable

plug this value for y into the first equation
simplify and collect terms


Now that you have a value for x, plug that in to either original equation and solve for y




You can also plot the two equation and see where they intersect

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Use the same idea for the next one



Same for the next one


3^(1/3)


For the last one

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so either 7x=0 or (x-7)=0
That means x=0 or x = 7