How many numbers between 2 and 12 (inclusive) is the following number divisible
by? 378

There are 5 numbers between 2 and 12 (inclusive) by which 378 is divisible.

Step-by-step explanation:

We have to find how many numbers between 2 and 12 (inclusive) is the number 378 divisible  by.

Firstly, 378 is divisible by 2 as the last digit of the given number is even.

378 is divisible 3 because the sum of the digits (3 + 7 + 8 = 18) is divisible by 3.

378 is divisible by 6 because any number which is divisible by 2 and 3, will be divisible by 6 also.

378 is divisible by 7 as = 378.

378 is divisible 9 because the sum of the digits (3 + 7 + 8 = 18) is divisible by 9.

And, the number 378 is not divisible by 4, 5, 8, 10, 11, and 12.

Hence, there are 5 numbers between 2 and 12 (inclusive) by which 378 is divisible.

step-by-step explanation: step 3 should really go to step seven, but anyway never mind.

1 ∠oln ≅ ∠lno

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3