Kim wants to use cubes that are all the same size to fill a box that measures 3 1/2 ft x 3 1/4 ft x 2 ft without gaps. He has 1/2 ft cubes, 1/4 ft cubes, and 1 ft cubes. Which cubes should he use? Explain?

he should use 1/2 ft cubes and 1/4 ft cubes.

Step-by-step explanation:

The dimensions of the large box that Kim wants to fill are

3 1/2 ft x 3 1/4 ft x 2 ft

The formula for determining the volume of a cuboid is expressed as

Volume = length × width × height

Volume of the box = 3.5 × 3.25 × 2 = 22.75 ft³

The formula for determining the volume of a cube is expressed as

Volume = s³

1) Volume of the cube whose side length is 0.5 ft is 0.5³ = 0.125ft³

Number of this cubes that he would use to fill the box is

22.75/0.125 = 182 cubes

Since it is a whole number, then it can fill the box without gaps.

2) Volume of the cube whose side length is 0.25 ft is 0.25³ = 0.015625ft³

Number of this cubes that he would use to fill the box is

22.75/0.015625 = 1456 cubes

Since it is a whole number, then it can fill the box without gaps.

3) Volume of the cube whose side length is 1 ft is 1³ = 1ft³

Number of this cubes that he would use to fill the box is

22.75/1 = 22.75 cubes

Since it is not a whole number, then there would be gaps.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.