geno3141

The rule is:        n² + 3

First term:       (1)² + 3

Second term:  (2)² + 3

Third term:      (3)² + 3

I don't know what you mean by "factor out in 3"?

Are you asking:  How do you factor  24x³ + 375 ?

You can use the calculator at this site to find the answer to  2^40

Getting an average of 79 on three tests is the same as getting a 79 on each test.

So after four tests, he will have the same score as    79 + 79 + 79 + x

The average of these four scores can be found by:  (79 + 79 + 79 + x) / 4

Since this average is 82, use the equation:             (79 + 79 + 79 + x) / 4  =  82

Simplify:                                  (237 + x) / 4  =  82

Multiply both sides by 4:                  237 + x  =  328

Subtract 237 from both sides:                    x  =  91

If the original of each length is  x,

then the new length of each is:  3x + 2                  (two more than three times the original)

Perimeter of new triangle:  (3x + 2) + (3x + 2) + (3x + 2)  =  42

--->     9x + 6  =  42

--->     9x  =  36

--->       x  =  4 

If you have two complex numbers written in polar notation, for example:

A = a(cosα + i·sinα)     and     B = b(cosβ + i·sinβ)  

Then A / B  =  (a/b)( cos(α - β) + i·sin(α - β) )

Can you see how to apply this?

A "recursive" definition is one in which the first term (or terms) are given and the rest of the terms are defined in terms of previous terms.

For the Fibonacci sequence, the first two terms are given, both are "1". After that, each new term is the sum of the previous two terms.

Construct rectangles that are 1x1, 1x2, 2x3, 3x5, etc.

The last two questions are "explore" questions; the intent is for you to learn through the process of exploration, not just repeating the answers of others.

Solve    7.00 ÷ 0.84    --    use the calculator at this site ...

(4b^-2) ÷ (4b^-3)        Write with positive exponents:

=  (4/b²)  ÷  (4/b³)       Replace division with multiplying by the reciprocal:

=  (4/b²)  x  (b³/4)        Multiply numerator times numerator and denominator times denominator:

=  (4b³) / (4b²)             Cancel like factors:

=  b

Your question is:  3471 - 2300 =  ?

Can you solve this?