The volume of the rectangular prism is 60x3 + 145x2 + 70x. factor to find the possible expressions for length, width and height of the prism.

Possible expressions of length, width and height are 5x, (3x + 2) and (4x + 7)

Step-by-step explanation:

Since volume of the prism is represented by

V = Length × width × height

Expression that represents the volume of the rectangular prism has been given as 60x³ + 145x² + 70x

Now we will factorize this expression to convert it into the length, width and height form.

V = 60x³ + 145x² + 70x

  = 5x(12x² + 29x + 14)

  = 5x[ 12x² + 21x + 8x + 14]

  = 5x[3x(4x + 7) + 2(4x + 7)]

  = 5x[ (3x + 2)(4x + 7)]

  = 5x (3x + 2)(4x + 7)

Now we can say that the possible expressions of length, width and height are 5x, (3x + 2) and (4x + 7)

omg what happend to your question? if you could edit this question i can

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.