Beatrice is weighing combinations of geometric solids. she found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder and 8 prisms weigh 35 ounces. write and solve a system of equations to determine the weight of each cylinder and prism.

Step-by-step explanation:

Let's call cylinders and prisms.

Now, if 4 cylinders and 5 prisms weigh 32 ounces, that can be expressed as

Also, 1 cylinder and 8 prisms weigh 35 ounces, so

To solve this sytem of equation, we isolate in the second equation

Then, we substitute this into the first equation and solve for

Then, we use this value to find the other one

Therefore, 1 prism weighs 4 ounces and 1 cylinder weighs 3 ounces.

can you add an image ?

step-by-step explanation:

∠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.