geno3141

If the function is:  g(x)  =  -2x - 1,

then                    g(-3)  =  -2(-3) - 1  =  5

An equation for the situation where you are paid $500.00 plus 4% commission on total sales will be:

     y  =  500.00 + 0.04x

The other equation will be:  y  =  $400.00 + 0.05x

When graphed, the first equation has a higher y-intersect but a smaller slope.

Their intersection point can be calculated by setting the two equation to each other{

     500 + 0.04x  =  400 + 0.05x

     100 + 0.04x  =  0.05x

                  100  =  0.01x

--->   x  =  $10,000.00

Therefore, on total sales less than $10,000.00 the first situation is better ($500.00 plus 4% commission on total sales); over $10,000.00, the second situation is better; at exactly $10,000.00 they yield the same amount.

You need a number such that  x  and the  integer value(x)  when multiplied will give you 27.

If the answer is a perfect square, then the square root will be your answer.

Since 27 is between the perfect squares 25 and 36, the answer will be between their square roots, 5 and 6.

The integer value of a number between 5 and 6 is 5, so now you are looking for a number x that satisfies the equation:  x · 5  =  27                      (because 5 will be the integer value of x)

Solving this, you get  27/5  =  5.4

a*b = a - b + a - b

12*3 = 12 - 3 + 12 - 3 =  ?

10*5 = 10 - 4 + 10 - 5 = ??

Then subtract ?? from ?

32²  =  1024

But, if you meant √(32), this can be done two ways:

   ---   first, using a calculator:  √(32)  ≈  5.65685, so, rounded to the nearest whole number  ≈  6

   ---  second way, without a calculator:  5² = 25 (too small)   and  6² = 36 (too large), but 32 is closer to 36              than it is to 25, so choose 6 (but this can get tricky) 

As an example:   108     45     480

First, factor each number, using exponents:  

        108  =  2² · 3³          45  =  3² · 5          480  =  2⁵ · 3 · 5

Now, take each factor, with its largest exponent.

   ---   the largest exponent on 2 is 5, so use 2⁵

   ---   the largest exponent on 3 is 3, so use 3³

   ---   the largest exponent on 5 is 1, so use 5

Multiply these together:     2⁵  · 3³ · 5   =   4320

Let  x  equal 1.7333333...

To make it easier, get the non-repeating part to the left side of the decimal by multiplying by 10:     

     10x   =   17.33333...

Since the repeating part has only one digit repeating (just the 3), multiply this last answer by 10 to get:

    100x  =  173.3333....

Place the larger number on top, the smaller number below:

    100x  =   173.3333....

      10x   =   17.33333...

Subtract:

      90x   =   156

Divide by 90:

         x   =   156/90  =  26/15

The tree makes a right triangle.

From the corner angle of 46°, the line to the tree is the adjacent side (2 m), and the tree is the opposite side (x).

Using tangent:  tan(46°)  =  x / 2   --->   x  =  2 · tan(46°)   --->   x  =  2.1 meters

If the price was decreased by 60%, you ended up paying only 40%.

40% of the original price is 18.60

Letting  x  represent the original price:

   0.40 · x  =  18.60

Dividing both sides by 0.40 --->   x  =  46.50

I believe that it will end in three zeros for this reason:

11 = 10 + 1

So:  11^100  =  (10 + 1)^100

Using the Binomial Theorem:

The last term will be:  100C0·(10^0)·(1^100)  =  1

This term will be coancell by the -1 term. So it will end with a zero.

The second last term will be:  100C1·(10^1)·(1^99)  =  (100)(10)(1)  =  1000    (three zeroes)

The third last term will be:  100C2·(10^2)·(1^98)  =  (4950)(100)(1)  =  495.000    (three zeroes)

The fourth last term will be:  100C3·(10^3)·(1^97)  =  (161700)(1000)(1)  =  161700000    (won't change the three zeroes at the end)

The fifth last term will be:  100C4·(10^4)·(1^96)  =  (3921225)(10000)(1)  =  whatever, but won't change the three zeroes at the end.

Similarly for all the other terms; the power of ten won't change the three zeroes at the end.