geno3141

The asymptotes will go through the center of the hyperbola, which is (-2,5).

The square roots of the denominators of the x-term and the y-term give the slope of the lines. Since slope is y-value over x-value, the slopes will be 9/11 and -9/11. 

The equations will be y - 5  =  ± (9/11)(x + 2).

When graphing, you draw the box; the asymptotes are the lines created by the opposite corners of the box.

The "set of all sets" would have to contain itself, along with all the other possible sets. 

For ease of writing, let's pretend that there are only three sets: X, Y, and Z.

Now the set of all sets is this set: {X, Y, Z}. Let's call this set S so that S = {X, Y, Z}.

But, S doesn't contain set S. Now the set of all sets is {S, X, Y, Z}.

Let's call this set T so that T = {S, X, Y, Z}.

But T doesn't contain set T. Etc. Etc. Etc. Do you see the problem? 

By graphing, I get an answer that is approximately 2.8.

I don't have an algebraic way of solving this problem.

The minimum amount of the loan could be $0.00; so, let's find the maximum amount of the loan.

Let  L  be the amount of the loan. We need to borrow L and 2% of L and $600.00; so, we need a total of  L + 0.02L + 600,  or  1.02L + 600.

1.02L + 600  ≤  120 000

          1.02L  ≤  119 400

                L  ≤  119 400 / 1.02

                L  ≤  117 058.82

I believe that you need more information; just knowing that the water content depends upon the width of the leaf is not sufficient; you need to know how (the mathematical amount) it depends.

Do what is inside parentheses first:  16 ÷ 8  =  3=2  and  15 - 2  =  13

(2)2 + [13x32]

4 + 416  =  420

9(4 - 7x) - 3(2 + 5x)

Distribute first:

36 - 63x - 6 - 15 x

Simplify, by combining like terms:

30 - 78x

6(5 - 8v) + 12  =  -54

First:  use the distributive property:

30 - 48v + 12  =  -54

Now, simplify the left side:

-48v + 42  =  -54

Subtract 42 from both sides:

-48v  =  -96

Divide both sides by -48:

v  =  2

(5/2)^x - 1  =  4/25

Add 1 to both sides:

(5/2)^x  =  29/25

To solve an equation with the variable in the exponent, use logs:

log(5/2)^x  =  log(29/25)

An exponent in a log expression comes out as a multiplier:

x · log(5/2)  =  log(29/25)

Divide both sides by log(5/2):

x  =  log(29/25) / log(5/2)

x  =  0.162  (approximately)

How many 1/3^rds are there in 14 1/3?

Divide 14 1/3 by 1/3 to get the answer.

14 1/3  ÷  1/3

Write both as common fractions:

14 1/3  =  (14 x 3 + 1)/3  =  (42 + 1)/3  =  43/3

43/3  ÷  1/3

To divide by a fraction, multiply by its reciprocal:

43/3 x 3/1  =  (43 x 3) / (3 x 1)  =  129 / 3  =  43