geno3141

if you want to know the equation of a line that has a slope of 2 and passes through the point (1,3), use the point-slope form for a straight line:          y - y1  =  m(x - x1)

For this problem:  m  =  2       x1  =  1         y1  = 3

y - 3  =  2(x - 1)

y - 3  =  2x - 2

y  =  2x + 1

The value bd is the length of a diagonal. If you know no more about the rectangle, the only restriction upon x is that the length of the diagonal must be positive.

Therefore, 2x - 3 > 0     --->      2x > 3     --->     x > 1.5

The domain consists of all possible x-values.

In the function:  f(x)  =  x² + 1, every number can be used for x; therefore the domain of x consists of all real numbers.

In the function:  g(x)  =  1/x, every number can be used for x except for zero, because division by zero is undefined; therefore the domain of x consists of all real numbers except zero.

One example:  if you drive thorugh a hilly/mountainous area, roads that have severe slopes (4% or greater) are marked so that you will be more aware of the difficulty of making it up the hills and the difficulty of keeping control of your vehicle going down the hills.

Going down the hills, they may have special areas for trucks that become out of control and need to have an area which will get them to stop.

Another example: slopes are related to the pitches of roofs.

Both of these, and other examples, can be explored on the internet.

If you need a calculator to solve that problem, please use the one at this site.

I'm assuming that the problem is 3^(x + 2) =7

Since 3^(x+ 2)  =  3^x · 3^2

Then, 3^(x + 4)  =  3^x · 3^4  which is (3^x · 3^2) · 3^2,

Thus, 3^(x + 4)  is 9 times bigger than 3^(x+ 2)  and 9 x 7  =  63

Whenever you want to replace the ⊗ operation with its answer.

If you have the symbol x in any expression, you replace the x symbol with its answer. For instance, when the expression is 4 + 6 x 5, you simplify it by replaceing 6 x 5 with 30, giving you 4 + 30, which is 34.

So, if you have the expression 4 + (49 ⊗ 2 ), you calculate 49 ⊗ 7 to be √49 + 2 = 7 + 2 = 9.

Then, you have 4 + 9  =  13.

If the rule is :  √(A) + B   (with only A under the square root sign):

Work from the inside out:    16⊗9  becomes  √(16) + 9  =  4 + 9  =  13

Then, you have  25⊗13  =  √(25) + 13  =  5 + 13  =  18

The steps to find the inverse:                                  f(x)  =  3 - 2x

1) Replace f(x) with y (makes writing easier)     --->     y  =  3 - 2x

2) Exchange the variables x and y                    --->     x  =  3 - 2y

3) Solve the new equation for y:                            x - 3  =  -2y

                                                                   (x - 3)/-2  =  y

                                                                     (3 - x)/2  =  y

4) Replace y with f^-1(x):                                  f^-1(x)  =  (3 = x)/2  

Try this process for the second problem; if you have problems, repost.                             

What am I missing?

If the original jars held 9 ounces each, then you start with 6 ounces of pickles? pickle juice?

You could fill 1 jar if it held 6 ounces; 2 jars if both held 3 ounces, 3 jars if each held 2 ounces, 4 jars if each held 1.5 ounces, etc. ...