Atoy company is packaging its toys to be shipped. each small toy is placed inside a cube-shaped box with side lengths of 1/2 in. these smaller boxes are then placed into a larger box with dimensions of 12 in. × 4 1/2 in. × 3 1/2 in.
a. what is the greatest number of small toy boxes that can be packed into the larger box for shipping?
b. use the number of small toy boxes that can be shipped in the larger box to determine the volume of the shipping box.

a) The greatest number of small toy boxes that can be packed is 1512.

b) The volume of the large box is 189 in³.

Step-by-step explanation:

a) We analyze the quantity of smaller boxes that fit in each side:

Width: 12 in ÷ 1/2 in= 24

Length: 4 1/2 in ÷ 1/2 in= 9

Height: 3 1/2 in ÷ 1/2 in= 7

So if we multiply each number we can get the quantity of small boxes:

24×9×7=1512 small boxes

b) The volume of the small box is:

V=(1/2 in)³=1/8 in³

Now, we multiply the volume of the small box by the total quantity of small boxes:

Total volume=1/8 in³×1512=189in³

y=mx+b

step-by-step explanation:

m slope

b y-intercept

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.