Find the smallest natural number that is a multiple of 45 and where all of its digits are zeros and ones.

1111111110

Step-by-step explanation:

45 is 9, and 5.

9 divisibility rule: Digits have to add up to 9.

We know this has to be 1's and 0's.

So there has to be 9 1's.

111111111.

5 divisibility rule: Last digit has to be 0 or 5.

1111111110 will be our final answer.

Wait- let's check if it's divisible. Using a calculator, this determines it does work.

Enjoy.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is