Calculus

You want to factor (x4 -91)

First notice that the factors of 91 are 1, 7, 13, and 91.

If we try them all , we see that x4 -91 is a prime polynomial.

Even though the polynomial is prime, that is cannot be factored over the set of rational numbers, it is factorable over the set of irrational numbers.

x4 - 91

= (x2)2 - (√91)2

= (x2 - √91)(x2 + √91)

= [x2 - (√√91)2](x2 + √91)

= (x - √√91)(x + √√91)(x2 + √91)

4x + 6 = -82 - 7X

add 7X to each side

4X + 7X + 6 = -82 -7X + 7X

11X + 6 = -82

subtract 6 from each side

11X + 6 - 6 = -82 - 6

11X = -88

divide both sides by 11

X = -8

check in original equation

4(-8) + 6 = -82 - 7(-8)

-32 + 6 = -82 + 56

-26 = -26

checks

If y = 2t + 5, then 5 = y - 2t

A person who has dyslexia but who is good at math can succeed in the sciences. Science depends much more on math, than it does on writing.

The answer will depend on whether the question refers to

|x| + 1 = 5

or |x + 1| = 5

Probably not, though it is hard to work out the mapping "r equals 1 2"

In more simple terms, 27 is 128.

'X' is the unknown term in a problem. It can be anything depending on the equation or terms involved.

I assume you mean the quadratic formula. Alternative methods include factoring. In this case, it is not easier, since the factors are not obvious. Another alternative method is completing the square, but it isn't really simpler than the quadratic formula, either - at least, not in this case.

If you want to solve it by using the graphing calculator:

7/(x - 5) = x

x2 - 5x = 7

So graph y = x2 - 5x and y = 7, then find the point of interception where its x-coordinate is the solution of the given equation.

0.002

Remember BODMAS/PODMAS (or variants).

3 + 7 * 5 - 1 = 3 + 35 - 1 = 38 - 1 = 37

-26

x-2y=0

x=2y

The solution set is the set of all (x,y) such that x=2y

A U shaped parabola

Suppose to the contrary that square root of two is rational. This means we can write square root 2 = a/b where a/b is a fraction that CANNOT be reduced..that part is important. Now, 4a^2=b^2 from square both sides and multiplying So we know the left side is even since it is a multiple of 4. So the right hand side must be also even since they are equal, but that implies they were not relatively prime to start with which is a contradiciton. we conclude square root of 2 is irrational. I will help to make this a little clearer, just in case some people to not fully understand the proof. We assumed a/b was in reduced form which is equivalent to saying there are NO COMMON Factors. For exampel 1/2 or 1/3 is in reduced form but 2/4 is not because they have a common factor of 2. No if b^2 is even, then b must be even (easy to prove) . This causes a problem because if b is even then a cannot be even or they would not be relatively prime (that means they have no common factors) Here is an example of a rational number so you can see how it works 8 for example 8=a/b 8b=a so 8b is even since it is 2(4b) now that means a is even. b can be odd since even x odd is even, we can write 8=8/1 and this is inreduced form Try it with 2/3...3b=2 etc.. it works! The conclusion is that square root of two is irrational There are many many other ways to prove this, some people understand some proofs more than others. I will put some more here later.

364 ' and 2.07 "

tracking and trapping.

Like all middle school algebra problems, first convert what is given into an equation. In this case, we have:

R = x(a+b)

The question is "what is b =" ?

first we divide both sides of the equation by x to get:

R/x = (a+b)

Then subtract a from both sides:

R/x - a = b.

Thus, b = R/x - a.

7x=20+20x

collect terms containg x on one side and then factorize

-13x=20

0r, x=-20/13

2.14x - 12.18 = -5.76

add 12.18 to both sides:

2.14x = 6.42

divide both sides by 2.14

x= 3

The fraction for 45% is 45/100 or 450/1000 or 4500/10000, and finally 45000/100000. Also, reduced to lowest terms, it is 9/25.

Yes! Any multiple of 11 that is in the form of 11x10^n +209 will have an odd digit sum and will be divisible by 11. 209 is divisible by 11, and 11X10^n is too. Remember that n has to be over 1,000 for it too work.

ex. 11x10^5+209=1100209.

1100209/11=100019

it is an identity.

1) Y=2x-4

2) x-Y=1

Since you already have Y alone in the first equation, plug the first equation into the second equation. This will give you:

2) x-(2x-4)=1

Now solve for X. To do this, first change the signs of (2x-4) since it is being subtracted. This gives you:

2) x-2x+4=1

Subtract 4 from both sides, giving you:

2) x-2x=-3

Combine like terms, giving you:

2) -x=-3

Of course, from this we can see that x=3.

Now plug x=3 into equation 1) Y=2x-4 which gives you:

1) Y=2(3)-4

Solve for Y. Y=2

X=3 Y=2

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