There are 900 toothpicks in a regular-sized box. if a jumbo box is made by tripling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?

When you triple the height of the box, it can hold (900 x 3) = 2,700 pieces.

Then triple its length, and it can hold (2,700 x 3) = 8,100 pieces.

Then triple its width, and it can hold (8,100 x 3) = 24,300 pieces.

When you triple the dimensions of a 3D object, it has 27 times its original volume.  (900 x 27) = 24,300 .

24300 toothpicks

Step-by-step explanation:

The volume of the box can be written as:

V0 = W*L*H

where W is the width, L is the length and H is the height.

We know that in V0 we can put 900 toothpicks.

Now, if we triply each of the dimensions we have that:

V = 3W*3L*3H = (3*3*3)*W*L*H

and we know that W*L*H = V0

V = 27*V0

and if in V0 we can put 900 toothpicks, then in V we can put 27 times that amount, this is:

27*900 = 24300 toothpicks

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation: