How many 3 digit codes are possible that do not contain the number 3?

729

Step-by-step explanation:

Including 3, there are 10 digits, from 0 to 9.

If you exclude 3, then there are 9 digits.

Each code will have a first digit, a second digit, and a third digit.

Each of those three digits can be chosen from 9 different digits.

We use the counting principle, and we multiply the number of possible digits for each position in the code.

number of possible first digits * number of possible second digits * number of possible third digits =

= 9 * 9 * 9 = 729

729

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

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