geno3141

They are both transcendental numbers (a special type of irrational number).

As irrational numbers, they have an infinte decimal expansion, which never ends and never repeats.

You can set up a proportion:

       scale percentage / actual percentage  =  scale size / actual size

             8 % / 100 %   =  1.2 m / unknown m

               8 / 100  =  1.2 / x

Cross-multiply:  8x  =  100·1.2

                          8x  =  120

                             x  =  15 m

tan(x - 2) = 0.2

Find the invTan of both sides:

  x - 2  =  invTan( 0.2 )

  x - 2  =  0.1974

     x  =  2.1974

5% of $13.53  is  0.05 x  13.53  =  0.68  (rounded)

$13.53 + 0.68  =  $14.21

If it were simple interest, you would use the formula i = P·r·t

where i = interest,  P = principal (amount borrowed), r = rate (as a decimal)

and t = time (years)    --->  i = 120000(.05)(30) = $180,000.00.

However, that is unrealistic.

Paying off a house loan is done monthly, so you need to use a compound interest formula to find the monthly payment.

The monthly payment will be $644.19 (using an online calculator for home loans).

Paying this monthly for 30 years:  

     $644.19 (per month) x 12 (months per year) x 30 (years)  =  $231,908.40

Since $120,000.00 was borrowed,  $231,908.40 - $120,000.00  =  $111,908.40 will be the amount of interest paid.

To find the number that completes the problem, ask yourself:

Is there a number that, when multiplied to -6, will result in -90?     (-90 ÷ ? = -6)

Will this number, when add to -6, result in +9?                                (? + -6 = 9)

If you can find that number, you will have your answer.

3x³ + 3x² + x + 1

Divide into two groups:

[3x³ + 3x²] + [x + 1]             Factor 3x²  out of the first group.

3x²(x + 1) + (x + 1)               Rewrite the second term.

3x²(x + 1) + 1(x + 1)             Factor out the common term of  x + 1.

(x + 1)(3x² + 1)

A good way to try to factor an expression with four terms is to break it in the middle:

    [8g³ + 10g²] - [12g + 15]        (notice that a negative sign was factored out)

     2g²(4g + 5) - 3(4g + 5)           (factor each part; notice that the same factor remains) 

    (2g² - 3)(4g + 5)                       (factor  4g + 5  out of each part)

The first two terms are  5h^3  and  20h^2.

Their greatest common factor is:  5h^2.

The last two terms are:  4h  and  16.

Their greatest common factor is:  4.

4x² - 81y²

This is the difference of two squares:  (2x + 9y)(2x - 9y)