geno3141

Kilograms measure mass; liters measure volume.

So, if you want to know how many kilograms are in a liter, you must specify what you are talking about: iron, water, air, etc.

An infinite number of solutions will occur if you have two equations that, when graphed, give the same line.

For instance, when trying to find the solution for these two equations:  2x + 3y  =  6   and  4x + 6y  =  12,

if you graph them, you will get the same line, drawn twice.

So, each solution of the first equation will also work in the second equation. Since the first equation contains an infinite number of points, and each point is a solution, you get an infinite number of solutions. 

(This will also be true for other pictures, not just straight lines.)

2x² - 7x + 6  =  0

This can be factored:

(2x - 3)(x - 2)  =  0

Either  2x - 3  =  0     or     x - 2  = 0,

So, either  x  =  3/2   or   x = 2

If the line  y = x  is reflected through the y-axis it becomes  y = -x.

Adding one more term to an infinite set does not increase the size of the set (infinity has some strange conclusions).

It means to find the lim of the function as you approach 0 from the right side of the number line.

That is, as x gets closer to zero, as you approach from 0.1, then 0.01, then 0.001, then 0.0001, etc.

lim_x→0⁺x = 0  because x becomes 0.1, 0.010.001, 0.0001, ... → 0

An example:  lim_x→0⁺(1/x)  =  

  when x = 0.1 ---> lim becomes 1/0.1 = 10

  when x = 0.01 ---> lim becomes 1/0.01 = 100

  when x = 0.001 ---> lim becomes 1/0.001 = 1000

  so the lim approaches ∞.

However, lim_x→0^-(1/x)  =  

  when x = -0.1 ---> lim becomes 1/-0.1 = -10

  when x = -0.01 ---> lim becomes 1/-0.01 = -100

  when x = -0.001 ---> lim becomes 1/-0.001 = -1000

  so the lim approaches -∞.

Thus the  lim_x→0(1/x)  doesn't exist, because you get a different value when you approach from the right side than you do when you approach from the left side.

(z + 1)(3z - 2)

Using FOIL  (First, Outside, Inside, Last):

=  (z)(3z) + (z)(-2) + (1)(3z) + (1)(-2)

=  3z² - 2z + 3z - 2

=  3z² + z - 2

Divide (12.4 x 10²) by (3.1 x 10^-3):

--->  (12.4 x 10²) ÷ (3.1 x 10^-3)  =  (12.4/3.1) x (10² ÷ 10^-3)

--->  To divide numbers that have the same base, subtract their exponents)

--->  (12.4/3.1) x (10² ÷ 10^-3)  =  (12.4/3.1) x (10^{2 --3})  =  (12.4/3.1) x (10⁵)  =  ...   the answer 

(1/4)x + 3  =  2

Subtract 3 from both sides:

--->   (1/4)x  =  -1

Multiply both sides by 4:

--->   x  =  -4

z/9 - 3  =  15

Add 3 to both sides:

--->   z/9  =  18

Multiply both sices by 9:

--->   z  =  162