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9514 1404 393

  8.  50 yards

  9.  9%

Step-by-step explanation:

In each case, we fill in the given values in the formula, then divide both sides of the equation by the coefficient of the variable.

The missing formula is ...

  A = LW . . . . where A is area, L is length, W is width

  6000 yd² = (120 yd)W

  W = (6000 yd²)/(120 yd) = 50 yd . . . the width of the field

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The missing formula is ...

  I = Prt . . . . where I is the interest on principal P at rate r for t years

  1800 = 5000(r)(4)

  r = 1800/20000 = 0.09 = 9% . . . interest rate on the investment

∠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.