A cereal company is creating new boxes for its product. In order to display the boxes, the stores they sell to require that the boxes
be 10.3 inches high and no longer than 8.2 inches.
The printing department requires exactly 228.12 square inches of space in order to use the planned design that covers the box. If
the company wishes to maximize the length of the box, then what should be the width of the box?
A.
0.8 inches
B.
10.3 inches
C.
1.6 inches
D.
8.2 inches

C.  1.6 inches

Step-by-step explanation:

Width (W)

Surface area = 2wl + 2lh + 2hw

228.12 = 2 x (10.3 x W + 8.2 x W + 10.3 x 8.2)

228.12 = 2 x (18.5W + 84.46)

114.06 = 18.5W + 84.46

W = (114.06 - 84.46) / 18.5

W = 1.6 inches

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~