a once-popular children's doll is slowly declining in popularity. the quartic function f(x)-0.002x^4 0.025x^3-0.364x^2-7.243x 86.993, where x is the number of years from 1993 to 2003. Estimate the number of dolls of this type that were sold (in thousands) during a given year from 1993 to 2003. Estimate how many dolls were sold in 2001.

10,361 dolls were sold in 2001.

Step-by-step explanation:

Number of dolls sold in x years after 1993:

The number of dolls sold in x years after 1993 is given by:

Estimate how many dolls were sold in 2001.

2001 is 2001 - 1993 = 8 years after 1993, so this is f(8).

10,361 dolls were sold in 2001.

∠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.