A contractor digs a rectangular hole for the basements of a new house that is 10 1/2 feet deep. What is the width of the hole if 6,510 cubic feet of dirt are removed?

w = 2√155 ft ✅

Step-by-step explanation:

Given that:

depth (d) = 10½ ft

Volume (v) = 6,510 ft³

Find the width (w) of the hole!

If the base is a square, then

the width and the length of the base is 'equal', so the

Volume of a cuboid =

V = w²d

width = square root of the division of volume by depth

w = √(V/d)

w = √(6,510/10½)

w = √620

w = √(4×155)

w = 2√155 ft ✅

#StayPositive - kexcvi

from Indonesia

∠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.